rotasi galaksi 2011
DESCRIPTION
kuliah fisika galaksi tema rotasi galaksiTRANSCRIPT
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Kuliah Fisika Galaksi
5 Mei 2010
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Populasi Bintang di Galaksi Bima Sakti
Schematic (edge-on) view of the major components Source: Roland Buser http://www.astro.unibas.ch/forschung/rb/structure.shtml) The disk and halo structure perpendicular to the Galactic plane near the solar neighborhood*
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Gerak Bintang di Galaksi
Bintang2 di Galaksi merupakan anggota dari komponen galaksi yang berbeda2, perbedaannya tidak hanya dlm distribusi ruang saja, tetapi juga kinematikanya.Gerak yang mendominasi bintang2 dan gas di piringan galaksi adalah rotasi terhadap pusat galaksi dg orbit berbentuk lingkaran.Bintang2 di piringan tebal (thick disk) berotasi lebih lambat daripada yang berada di piringan tipis (thin disk). Gerak acak (random motion) bintang tersebut lebih besar.Rotasi bintang2 di halo tidak seperti yang ada di piringan, gerak acak mereka lebih besar dan orbitnya berbentuk elips.*
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Pertanyaan :
Bagaimana kita tahu tentang gerak bintang di galaksi ?Bagaimana menentukan kecepatan rotasi di piringan ?Bagaimana kita dapat menentukan massa Galaksi ?*
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Kerangka Acuan
Untuk mempelajari dinamika galaksi, kerangka acuan dasar pada galaksi sangat diperlukan. Kecepatan bintang pada kerangka acuan ini sering diberikan dalam koordinat silinder (P,Q,Z) atau (VR, Vf, VZ)P : sepanjang arah radial pd bidang galaksi, positif ke arah luar (anti-center), l=180, b=0
W: arah tangential pd bidang galaksi,positif ke arah rotasi galaksi, l=90, b=0
Z: arah tegaklurus bidang galaksi, positif ke arah utara, b=90
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Local Standard of Rest (LSR)
Kita definisikan sebuah kerangka acuan pd bidang galaksi yg bergerak dalam orbit lingkaran mengelilingi pusat galaksi sebagai standar diam lokal (LSR)LSR adalah kerangka acuan lokal yg terletak di daerah sekitar matahari yg bergerak dlm orbit lingkaranSebuah bintang yg bergerak dlm orbit lingkaran pd bidang galaksi akan tetap pada geraknya karena :Galaksi berbentuk simetri sumbu, F=F(R,Z)Simetri thd bidang galaksiDalam keadaan steady state*
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Local Standard of Rest (LSR)
Daerah sekitar matahari (Solar Neighborhood, SN) didefinisikan sebagai ruang bola yg berukuran kecil (thd galaksi) yg berpusat di matahari dan terdiri dari sample suatu tipe bintangDisk : SN adalah sebuah bola dg radius 50-100 pc (1% dari piringan galaksi)Halo : radius ~ 1 kpc (1% dari halo)Kecepatan matahariterhadap LSR
(u,v,w) ~ (-10,5,7) km/s
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31.pdfWednesday Extragalactic astronomy tools
Multi-wavelength astronomy Starcounts Extinction Globular Clusters
Milky way components: Disk: exponential profile, thin/thick disk Stellar Halo, Pop I/II stars, Globular Clusters Age-Metallicity Relation ISM - HII (Hot Ionized), HI (atomic), H2 (molecular) Bulge Dark Matter Halo Satellite galaxies
Kinematics of the Galaxy I - Rotation
CurvesJL 1.3,1.6; Carroll & Ostlie pp 898-907, 915-933
Today Disk, Halo Motions Galactic Coordinates Measuring Distance: parallax pulsating stars Rotation Curves Local Standard of Rest Rotation speed from halo star motions Tangent-Point Method and Rotation Curves Weighing in New results?
Chung et al:http://www.astro.columbia.edu/~archung/research/CRdisk/crdisk.html
Other Galaxies Motions
Radial velocities can be measured with spectra
Can get rotation curves, (radial) velocity dispersions
http://www.astro.columbia.edu/~archung/research/CRdisk/crdisk.htmlhttp://www.astro.columbia.edu/~archung/research/CRdisk/crdisk.htmlWhere are we and how fast
are we moving? Within our own galaxy, more
difficult! Even though we know were
edge on, even local position and rotation speed are uncertain
The Open University
30 kpc
6 kpc
1
50 kpc
dark-matter haloand stellar halo
bulge
(a)
(b)
stellar disc
bulge
stellardisc
locationof Sun
locationof Sun
1 kpc
gaseousdisc
dark-matter haloand stellar halo
JL Fig 1.5
Even now, numbers
jumping around Recent (announced Tues at
AAS meeting) found evidence of ~15% higher rotation rate than generally understood
Using parallax of very bright microwave objects (masers)
Rotation curves of other spirals
Rotation curves of spiral galaxies quite generally have flat rotation curves
Non-visible matter contributing to mass of galaxies, not to light
Dark Matter
Sofue et al (1997)http://www.ioa.s.u-tokyo.ac.jp/~sofue/rotation/fig1/all-new.gif
http://www.ioa.s.u-tokyo.ac.jp/~sofue/rotation/fig1/all-new.gifhttp://www.ioa.s.u-tokyo.ac.jp/~sofue/rotation/fig1/all-new.gifhttp://www.ioa.s.u-tokyo.ac.jp/~sofue/rotation/fig1/all-new.gifhttp://www.ioa.s.u-tokyo.ac.jp/~sofue/rotation/fig1/all-new.gifM
v
r
r
vr
8
Circular velocity around
a mass Assuming symmetry, constant
circular orbit around a (spherical) mass distribution only depends on total mass enclosed:
v2r(R) =GM(< R)
r
`Solid Body
vr = const = vr/r r1
Flat Rotation curve
Keplerian
vr r1/2
r3/2
Examples of
differential rotation
= constvr = r r
Motion w/rt Galactic Centre
Sgr A* shows very regular proper motion, even though surrounded by thousands of starsMotions entirely consistent with being due only to solar motion
Reid & Brunthaler (2004)http://www.journals.uchicago.edu/doi/abs/10.1086/424960
v! = (0.4 0.9)km s1
http://www.journals.uchicago.edu/doi/abs/10.1086/424960http://www.journals.uchicago.edu/doi/abs/10.1086/424960Motion w/rt Galactic Centre
But dont know distance from galactic centre; cant automatically turn this into a rotational velocity
Reid & Brunthaler (2004)http://www.journals.uchicago.edu/doi/abs/10.1086/424960
http://www.journals.uchicago.edu/doi/abs/10.1086/424960http://www.journals.uchicago.edu/doi/abs/10.1086/424960RA & Dec for Solar System
ESO: http://www.eso.org/public/outreach/eduoff/vt-2004/Background/Infol2/EIS-D3.html
http://www.eso.org/public/outreach/eduoff/vt-2004/Background/Infol2/EIS-D3.htmlhttp://www.eso.org/public/outreach/eduoff/vt-2004/Background/Infol2/EIS-D3.htmlGalactic Coordinates
CO Fig 24.17
Galactic Coordinates
CO Fig 24.19
VU
Galactic Orbits
Stars in disk typically have aligned circular orbits
In halo, orbits fill halo
PopI vs PopIIJoshua Barnes,
http://www.ifa.hawaii.edu/~barnes/ast110_01/
http://www.ifa.hawaii.edu/~barnes/ast110_01/tmwaog/orbits.gifhttp://www.ifa.hawaii.edu/~barnes/ast110_01/tmwaog/orbits.gifParallax
1 AUp
D/tan(p) ~ D/p
Definition: 1pc = (1 AU)/(1 (in radians))
But measuring them is hard
First parallax measurement: Bessel (1939)
61 Cygni
Measured parallax of 0.31360.015 (d = 3.04-3.35 pc)
Current distance: 3.496 0.007 pc
Hipparcos mission
For stars larger than few parsec away, limits on seeing prevent good measurements
118,000 stars with high-precision distances, proper motions
Still limited by baseline - ~1 AU Hipparcos: 1989-1993
http://www.rssd.esa.int/index.php?project=HIPPARCOS
http://www.rssd.esa.int/index.php?project=HIPPARCOShttp://www.rssd.esa.int/index.php?project=HIPPARCOSPhotometric Distances
Once know stars distances in local neighborhood, know real luminosity (L) and absolute magnitude M
From observed m, can get distance modulus and distance
But extinction! m is less than it would be with just distance effect.
d = (10pc)10(mM)/5
But extinction can be characterized
Depends on wavelength
So by finding out how much the difference is in different wavelengths, can estimate the magnitude of effect
So can still get a distance
Alves, Lada & Lada (2001)
Visible
Near IR
d = (10pc)10(mMA)/5
But extinction can be characterized
Sketch of how extinction behaves
Less effective at low frequencies
Some similarities to scattering of light in atmosphere
(eg, why is sky blue?)http://www.jb.man.ac.uk/distance/life/sample/stars/index.html
Jodrell Bank Observatory
http://www.jb.man.ac.uk/distance/life/sample/stars/index.htmlhttp://www.jb.man.ac.uk/distance/life/sample/stars/index.htmlSpectroscopic Binaries
R. Poggehttp://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/specbin.html
Like with planets; can get M sin(i), but dont know i
(c) AESOhttp://esomac.as.utexas.edu:81/database/slides/TB/F00001.html
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/specbin.htmlhttp://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/specbin.htmlhttp://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/specbin.htmlhttp://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/specbin.htmlVisual Eclipsing Spectroscopic Binaries Know everything,
because i ~ 90 degrees
Know total mass, mass ratio (why?)
Can get separation
If can see separation, know distance
P 3 =42
G(m1 + m2)a3
D = a()1
D
a
Pulsating Stars
Photometric distance where the intrinsic luminosity is given to you indirectly
Luminosity drives radial pulsations
Galactic Dynamics
CO Fig 24.19
Starting point; average conditions in Suns neighborhood
Sun might be drifting w/rt local motions
Local Standard of Rest (LSR): perfectly circular, non-vertical orbit at Suns position.
LSR
Should be easy to find Suns motion w/rt LSR
Average motions should be LSR (?)
Just find Suns relative velocity to average motions in the neighborhood.
Velocity w/rt neighborhood =
LSRBut this doesnt work
Average motions dont cancel out
Stars passing through from inner orbits moving faster
But then correlation between radial velocity and angular offset...
CO Fig 24.30
LSR still works for u (radial), w (vertical) velocities
for v, must make correction
Has to be statistical; dont know where star is in its ellipsoidal phase
But whats C ? - can measure
CO Fig 24.30
< v >= C < u2 >"= 0
Why ~?
Stars born on nearly circular orbit
Interactions with (stars, gas, spiral arms) `scatter slightly
Kinetic energy tends to be roughly conserved
Why ~?
Off by a factor of 2, but right idea;More details in section on spiral arms
KE =12M!
(u2 + (v + vc)2 + w2
)
u2 + (v + vc)2 + w2 0(v + vc)2 2u2
(v2c + 2vcv + v
2) 2u2
2vcv + v2 2u2
v u2
vc
LSR
Once this is done, can measure Suns velocity w/rt LSR
(u,v,w) ~ (-10,5,7) km/s Moving inwards, upwards, and slightly faster
in direction of rotation than LSR
LSR Yes, but we still dont know the LSRs motion. Can infer orbital velocity
from halo stars
In LSR, huge distribution of old stars (Pop II) in velocity space around LSR
Goes much larger to -ve velocities
Centred around -220 km/s
220 km/s must be local disk velocity
Gives us a distance to the galactic centre!
Standard values; 220 km/s, 8.5 kpc.
Joshua Barnes,http://www.ifa.hawaii.edu/~barnes/ast110_01/
CO, Fig 24.21
http://www.ifa.hawaii.edu/~barnes/ast110_01/tmwaog/orbits.gifhttp://www.ifa.hawaii.edu/~barnes/ast110_01/tmwaog/orbits.gifLess Local Now have LSR down
But want to understand the whole galaxy!
First understand the larger neighborhood -- how does the SR vary with radius?
Assume everything on circular orbits (on average)
R0
R
v(R0) = 220 km/s
l
v(R) = ?
D
`Solid Body
vr = const = vr/r r1
Flat Rotation curve
Keplerian
vr r1/2
r3/2
= constvr = r r
But for anyreasonablerotation curve,angularvelocity
goes up as radius gets
smaller
CO Fig 24.23Vr, Vt as a function of l
The different amplitudesand offsets here are going to
tell us about our local rotation curve.
Less Local
R0
R
v(R0) = 220 km/s
l
v(R) = ?
D
vr = v(R) cos v(R0) sin lvt = v(R) sin v(R0) cos l
Radial velocity difference is greatest for objects moving along line of sight -- youre catching it at the tangent point of their orbits.
Objects Motion
Suns Motion
Tangent Point Method
CO Fig 24.24
But can only use local stars
R0
R
v(R0) = 220 km/s
l
v(R) = ?
D
Measuring Rotation Curve
of disk means looking in disk
Extinction
Can correct for it over short distances, but cant see anything beyond those
But dust largely transparent to lines from atomic gas (eg, 21 cm)
Tangent Point Method
Careful measurements of molecular line emission in plane gives max velocity for each angle
For each angle, know R;
Know rotation curve! 12CO lines from molecular gas cloudsEnglmaier & Gerhard (1999) MNRAS 304:512
sin l = R/R0
Weighing our Galaxy
From rotation curve at LSR, can find mass interior
88 Billion Solar Masses
Rotation Period ~230 Myr
From largely-flat rotation curve can figure out density profile beyond LSR.
vr(R) =
GM(< R)
r(220 km s1
)2 = GM(< R)8.5 kpc
M(< R) =8.5 kpc
(220 km s1
)2
G= 8.8 1010M"
Rotation curve outside of the Solar Circle
Cant use tangent point method for larger R
for
Need to keep original form that involves D and use objects can measure D to directly
vr = ( 0)R0 sin l
0 > R > R0
Harvard/CfA scientists examined masers (microwave lasers) which occur in star forming regions
Bright (all radiation is in one line), not extinguished by dust
Can get velocites; distances by parallax (but how?)
New Results
Monday
More on Rotation curves: Accurately characterizing the rotation curve locally -- Oort
Constants
CO 909-914
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Rotasi Galaksi
Piringan galaksi tidak berotasi seperti benda tegarBintang yg lebih dekat ke pusat galaksi berotasi dg lebih cepatw(R) tidak konstanDikenal dg rotasi diferensialKecepatan rotasi :Exponential disk (full line)Spherical (dashed)Point mass (dotted)Untuk distribusi massa spherical*
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Rotasi diferensial bintang di galaksi
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Kecepatan bintang relatif thd LSR
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Vektor kecepatan radial
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Chart10102030405060708090100110120130140150160170180190200210220230240250260270280290300310320330340350360Bujur galaksi l [deg]Vr [km/s]efek rotasi diferensial thd kec. radial05.472322293210.28460175513.856406460615.756924048215.756924048213.856406460610.2846017555.47232229320-5.4723222932-10.284601755-13.8564064606-15.7569240482-15.7569240482-13.8564064606-10.284601755-5.4723222932-05.472322293210.28460175513.856406460615.756924048215.756924048213.856406460610.2846017555.47232229320-5.4723222932-10.284601755-13.8564064606-15.7569240482-15.7569240482-13.8564064606-10.284601755-5.4723222932-0Sheet100105.47232229322010.2846017553013.85640646064015.75692404825015.75692404826013.85640646067010.284601755805.4723222932900100-5.4723222932110-10.284601755120-13.8564064606130-15.7569240482140-15.7569240482150-13.8564064606160-10.284601755170-5.4723222932180-01905.472322293220010.28460175521013.856406460622015.756924048223015.756924048224013.856406460625010.2846017552605.47232229322700280-5.4723222932290-10.284601755300-13.8564064606310-15.7569240482320-15.7569240482330-13.8564064606340-10.284601755350-5.4723222932360-0Sheet10000000000000000000000000000000000000l [deg]Vr [km/s]efek rotasi diferensial thd kec. radial0000000000000000000000000000000000000Sheet2Sheet3 -
Vektor kecepatan tangential
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Chart10102030405060708090100110120130140150160170180190200210220230240250260270280290300310320330340350360Bujur galaksi l [deg]Vtan [km/s]efek rotasi diferensial thd kec. tangential76.03508193263.2567110899-1-6.2216291573-11.7783708427-17-21.2567110899-24.0350819326-25-24.0350819326-21.2567110899-17-11.7783708427-6.2216291573-13.25671108996.035081932676.03508193263.2567110899-1-6.2216291573-11.7783708427-17-21.2567110899-24.0350819326-25-24.0350819326-21.2567110899-17-11.7783708427-6.2216291573-13.25671108996.03508193267Sheet1007105.47232229326.03508193262010.2846017553.25671108993013.8564064606-14015.7569240482-6.22162915735015.7569240482-11.77837084276013.8564064606-177010.284601755-21.2567110899805.4723222932-24.0350819326900-25100-5.4723222932-24.0350819326110-10.284601755-21.2567110899120-13.8564064606-17130-15.7569240482-11.7783708427140-15.7569240482-6.2216291573150-13.8564064606-1160-10.2846017553.2567110899170-5.47232229326.0350819326180-071905.47232229326.035081932620010.2846017553.256711089921013.8564064606-122015.7569240482-6.221629157323015.7569240482-11.778370842724013.8564064606-1725010.284601755-21.25671108992605.4723222932-24.03508193262700-25280-5.4723222932-24.0350819326290-10.284601755-21.2567110899300-13.8564064606-17310-15.7569240482-11.7783708427320-15.7569240482-6.2216291573330-13.8564064606-1340-10.2846017553.2567110899350-5.47232229326.0350819326360-07Sheet10000000000000000000000000000000000000l [deg]Vr [km/s]efek rotasi diferensial thd kec. radial0000000000000000000000000000000000000Sheet20000000000000000000000000000000000000l [deg]Vtan [km/s]efek rotasi diferensial thd kec. tangential0000000000000000000000000000000000000Sheet3 -
GC
Sun
Star
Ro
R
r
*
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*
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*
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Konstanta Oort
Data kecepatan radial bintang-bintang kelas spektrum A
untuk menghitung konstanta Oort A
(setelah dikoreksi oleh jarak-rata-rata)
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Konstanta Oort
Distribusi bintang cepheid dan
data gerak dirinya, untuk
Menghitung konstanta Oort A dan B
Distribusi ruang
Gerak diri
*
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Kecepatan rotasi di sekitar Matahari
wo=Vc/Ro=A-B
Rotasi diferensial di sekitar Matahari
A+B=dVc/dR|Ro
Solar Motion :
dengan arah Apex :
*
-
*
-
*
49.pdfWednesday Extragalactic astronomy tools
Multi-wavelength astronomy Starcounts Extinction Globular Clusters
Milky way components: Disk: exponential profile, thin/thick disk Stellar Halo, Pop I/II stars, Globular Clusters Age-Metallicity Relation ISM - HII (Hot Ionized), HI (atomic), H2 (molecular) Bulge Dark Matter Halo Satellite galaxies
Kinematics of the Galaxy I - Rotation
CurvesJL 1.3,1.6; Carroll & Ostlie pp 898-907, 915-933
Today Disk, Halo Motions Galactic Coordinates Measuring Distance: parallax pulsating stars Rotation Curves Local Standard of Rest Rotation speed from halo star motions Tangent-Point Method and Rotation Curves Weighing in New results?
Chung et al:http://www.astro.columbia.edu/~archung/research/CRdisk/crdisk.html
Other Galaxies Motions
Radial velocities can be measured with spectra
Can get rotation curves, (radial) velocity dispersions
http://www.astro.columbia.edu/~archung/research/CRdisk/crdisk.htmlhttp://www.astro.columbia.edu/~archung/research/CRdisk/crdisk.htmlWhere are we and how fast
are we moving? Within our own galaxy, more
difficult! Even though we know were
edge on, even local position and rotation speed are uncertain
The Open University
30 kpc
6 kpc
1
50 kpc
dark-matter haloand stellar halo
bulge
(a)
(b)
stellar disc
bulge
stellardisc
locationof Sun
locationof Sun
1 kpc
gaseousdisc
dark-matter haloand stellar halo
JL Fig 1.5
Even now, numbers
jumping around Recent (announced Tues at
AAS meeting) found evidence of ~15% higher rotation rate than generally understood
Using parallax of very bright microwave objects (masers)
Rotation curves of other spirals
Rotation curves of spiral galaxies quite generally have flat rotation curves
Non-visible matter contributing to mass of galaxies, not to light
Dark Matter
Sofue et al (1997)http://www.ioa.s.u-tokyo.ac.jp/~sofue/rotation/fig1/all-new.gif
http://www.ioa.s.u-tokyo.ac.jp/~sofue/rotation/fig1/all-new.gifhttp://www.ioa.s.u-tokyo.ac.jp/~sofue/rotation/fig1/all-new.gifhttp://www.ioa.s.u-tokyo.ac.jp/~sofue/rotation/fig1/all-new.gifhttp://www.ioa.s.u-tokyo.ac.jp/~sofue/rotation/fig1/all-new.gifM
v
r
r
vr
8
Circular velocity around
a mass Assuming symmetry, constant
circular orbit around a (spherical) mass distribution only depends on total mass enclosed:
v2r(R) =GM(< R)
r
`Solid Body
vr = const = vr/r r1
Flat Rotation curve
Keplerian
vr r1/2
r3/2
Examples of
differential rotation
= constvr = r r
Motion w/rt Galactic Centre
Sgr A* shows very regular proper motion, even though surrounded by thousands of starsMotions entirely consistent with being due only to solar motion
Reid & Brunthaler (2004)http://www.journals.uchicago.edu/doi/abs/10.1086/424960
v! = (0.4 0.9)km s1
http://www.journals.uchicago.edu/doi/abs/10.1086/424960http://www.journals.uchicago.edu/doi/abs/10.1086/424960Motion w/rt Galactic Centre
But dont know distance from galactic centre; cant automatically turn this into a rotational velocity
Reid & Brunthaler (2004)http://www.journals.uchicago.edu/doi/abs/10.1086/424960
http://www.journals.uchicago.edu/doi/abs/10.1086/424960http://www.journals.uchicago.edu/doi/abs/10.1086/424960RA & Dec for Solar System
ESO: http://www.eso.org/public/outreach/eduoff/vt-2004/Background/Infol2/EIS-D3.html
http://www.eso.org/public/outreach/eduoff/vt-2004/Background/Infol2/EIS-D3.htmlhttp://www.eso.org/public/outreach/eduoff/vt-2004/Background/Infol2/EIS-D3.htmlGalactic Coordinates
CO Fig 24.17
Galactic Coordinates
CO Fig 24.19
VU
Galactic Orbits
Stars in disk typically have aligned circular orbits
In halo, orbits fill halo
PopI vs PopIIJoshua Barnes,
http://www.ifa.hawaii.edu/~barnes/ast110_01/
http://www.ifa.hawaii.edu/~barnes/ast110_01/tmwaog/orbits.gifhttp://www.ifa.hawaii.edu/~barnes/ast110_01/tmwaog/orbits.gifParallax
1 AUp
D/tan(p) ~ D/p
Definition: 1pc = (1 AU)/(1 (in radians))
But measuring them is hard
First parallax measurement: Bessel (1939)
61 Cygni
Measured parallax of 0.31360.015 (d = 3.04-3.35 pc)
Current distance: 3.496 0.007 pc
Hipparcos mission
For stars larger than few parsec away, limits on seeing prevent good measurements
118,000 stars with high-precision distances, proper motions
Still limited by baseline - ~1 AU Hipparcos: 1989-1993
http://www.rssd.esa.int/index.php?project=HIPPARCOS
http://www.rssd.esa.int/index.php?project=HIPPARCOShttp://www.rssd.esa.int/index.php?project=HIPPARCOSPhotometric Distances
Once know stars distances in local neighborhood, know real luminosity (L) and absolute magnitude M
From observed m, can get distance modulus and distance
But extinction! m is less than it would be with just distance effect.
d = (10pc)10(mM)/5
But extinction can be characterized
Depends on wavelength
So by finding out how much the difference is in different wavelengths, can estimate the magnitude of effect
So can still get a distance
Alves, Lada & Lada (2001)
Visible
Near IR
d = (10pc)10(mMA)/5
But extinction can be characterized
Sketch of how extinction behaves
Less effective at low frequencies
Some similarities to scattering of light in atmosphere
(eg, why is sky blue?)http://www.jb.man.ac.uk/distance/life/sample/stars/index.html
Jodrell Bank Observatory
http://www.jb.man.ac.uk/distance/life/sample/stars/index.htmlhttp://www.jb.man.ac.uk/distance/life/sample/stars/index.htmlSpectroscopic Binaries
R. Poggehttp://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/specbin.html
Like with planets; can get M sin(i), but dont know i
(c) AESOhttp://esomac.as.utexas.edu:81/database/slides/TB/F00001.html
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/specbin.htmlhttp://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/specbin.htmlhttp://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/specbin.htmlhttp://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Movies/specbin.htmlVisual Eclipsing Spectroscopic Binaries Know everything,
because i ~ 90 degrees
Know total mass, mass ratio (why?)
Can get separation
If can see separation, know distance
P 3 =42
G(m1 + m2)a3
D = a()1
D
a
Pulsating Stars
Photometric distance where the intrinsic luminosity is given to you indirectly
Luminosity drives radial pulsations
Galactic Dynamics
CO Fig 24.19
Starting point; average conditions in Suns neighborhood
Sun might be drifting w/rt local motions
Local Standard of Rest (LSR): perfectly circular, non-vertical orbit at Suns position.
LSR
Should be easy to find Suns motion w/rt LSR
Average motions should be LSR (?)
Just find Suns relative velocity to average motions in the neighborhood.
Velocity w/rt neighborhood =
LSRBut this doesnt work
Average motions dont cancel out
Stars passing through from inner orbits moving faster
But then correlation between radial velocity and angular offset...
CO Fig 24.30
LSR still works for u (radial), w (vertical) velocities
for v, must make correction
Has to be statistical; dont know where star is in its ellipsoidal phase
But whats C ? - can measure
CO Fig 24.30
< v >= C < u2 >"= 0
Why ~?
Stars born on nearly circular orbit
Interactions with (stars, gas, spiral arms) `scatter slightly
Kinetic energy tends to be roughly conserved
Why ~?
Off by a factor of 2, but right idea;More details in section on spiral arms
KE =12M!
(u2 + (v + vc)2 + w2
)
u2 + (v + vc)2 + w2 0(v + vc)2 2u2
(v2c + 2vcv + v
2) 2u2
2vcv + v2 2u2
v u2
vc
LSR
Once this is done, can measure Suns velocity w/rt LSR
(u,v,w) ~ (-10,5,7) km/s Moving inwards, upwards, and slightly faster
in direction of rotation than LSR
LSR Yes, but we still dont know the LSRs motion. Can infer orbital velocity
from halo stars
In LSR, huge distribution of old stars (Pop II) in velocity space around LSR
Goes much larger to -ve velocities
Centred around -220 km/s
220 km/s must be local disk velocity
Gives us a distance to the galactic centre!
Standard values; 220 km/s, 8.5 kpc.
Joshua Barnes,http://www.ifa.hawaii.edu/~barnes/ast110_01/
CO, Fig 24.21
http://www.ifa.hawaii.edu/~barnes/ast110_01/tmwaog/orbits.gifhttp://www.ifa.hawaii.edu/~barnes/ast110_01/tmwaog/orbits.gifLess Local Now have LSR down
But want to understand the whole galaxy!
First understand the larger neighborhood -- how does the SR vary with radius?
Assume everything on circular orbits (on average)
R0
R
v(R0) = 220 km/s
l
v(R) = ?
D
`Solid Body
vr = const = vr/r r1
Flat Rotation curve
Keplerian
vr r1/2
r3/2
= constvr = r r
But for anyreasonablerotation curve,angularvelocity
goes up as radius gets
smaller
CO Fig 24.23Vr, Vt as a function of l
The different amplitudesand offsets here are going to
tell us about our local rotation curve.
Less Local
R0
R
v(R0) = 220 km/s
l
v(R) = ?
D
vr = v(R) cos v(R0) sin lvt = v(R) sin v(R0) cos l
Radial velocity difference is greatest for objects moving along line of sight -- youre catching it at the tangent point of their orbits.
Objects Motion
Suns Motion
Tangent Point Method
CO Fig 24.24
But can only use local stars
R0
R
v(R0) = 220 km/s
l
v(R) = ?
D
Measuring Rotation Curve
of disk means looking in disk
Extinction
Can correct for it over short distances, but cant see anything beyond those
But dust largely transparent to lines from atomic gas (eg, 21 cm)
Tangent Point Method
Careful measurements of molecular line emission in plane gives max velocity for each angle
For each angle, know R;
Know rotation curve! 12CO lines from molecular gas cloudsEnglmaier & Gerhard (1999) MNRAS 304:512
sin l = R/R0
Weighing our Galaxy
From rotation curve at LSR, can find mass interior
88 Billion Solar Masses
Rotation Period ~230 Myr
From largely-flat rotation curve can figure out density profile beyond LSR.
vr(R) =
GM(< R)
r(220 km s1
)2 = GM(< R)8.5 kpc
M(< R) =8.5 kpc
(220 km s1
)2
G= 8.8 1010M"
Rotation curve outside of the Solar Circle
Cant use tangent point method for larger R
for
Need to keep original form that involves D and use objects can measure D to directly
vr = ( 0)R0 sin l
0 > R > R0
Harvard/CfA scientists examined masers (microwave lasers) which occur in star forming regions
Bright (all radiation is in one line), not extinguished by dust
Can get velocites; distances by parallax (but how?)
New Results
Monday
More on Rotation curves: Accurately characterizing the rotation curve locally -- Oort
Constants
CO 909-914
-
CO
HI
*
-
To map out vr throughout Galaxy, divide the Galaxy into quadrants based on value of galactic longitude.
Quad I (ll>90) - all los pass through orbits outside of the Suns. No maximum vr but increases with d.
Quad III (270>l>180) - similar to Quad II but opposite signs.
Quad IV (l>270) - similar to Quad I except reverse signs.
*
-
*
-
Orbital Radius
*
-
Vc2 = Vc,b2 + Vc,d2 + Vc,g2 + Vc,h2
*
-
*
-
Bagaimana menghitung massa Galaksi ?
Dari kurva rotasi kita dapat menghitung massa Galaksi MGal= 8,8 x 1010 MOPeriode rotasi = 230 x 106 tahun*
R
)
R
(
GM
V
c
=
2
o
90
=
l
o
0
=
l
o
90
=
l
efek rotasi diferensial thd kec. radial
090180270360
Bujur galaksi l [deg]
Vr [km/s]
efek rotasi diferensial thd kec.
tangential
090180270360
Bujur galaksi l [deg]
Vtan [km/s]
l
cos
R
r
cos
R
l
sin
R
sin
R
l
cos
V
cos
V
V
l
sin
V
sin
V
V
t
r
0
0
0
0
=
+
a
=
a
-
a
=
-
a
=
(
)
(
)
r
l
cos
R
V
l
sin
R
V
t
r
w
-
w
-
w
=
w
-
w
=
0
0
0
0
l
a
=
R
V
w
R
V
w
=