The activity of Stars in the skies

every one of the stars move. The motion is very slow, so that is challenging to detect. Best modern data comes again native Hipparcos dimensions The fastest relocating star on the sky is Barnard"s star (RA269.4, Dec4.5)
as soon as you look in ~ a star in the sky you can definea direction and a plane. A line joining her eyes and also the star specifies a direction i beg your pardon we contact the line-of-sight. The plane perpendicular come the line-of-sight is calledthe plane the the sky.The star will be moving in a direction which is no (in general) one of two people the line-of-sight or the plane of the sky. The velocity vector for one example star is shownon the chart below. The vector V is the direction that the star is moving.

You are watching: The rotation curve for our galaxy shows stars beyond the sun moving slower than expected.

Chapter 17 ns 436. Box 17-1.
any kind of vector have the right to be damaged down into component directions. The ingredient of the motion in the heat of sight ismarked Vr on the diagram. The ingredient of the motion in the airplane of the skyis marked Vt. The component of the velocity in the heat of vision canbe measure by the Doppler transition of the light: Vr = c x delta(wavelength)/wavelength The ingredient of the velocity in the aircraft of the sky means that the place in the skies of the star changes. This movement is called appropriate motion. Generally term proper velicty describes angular velocity &mu across the sky. The ideal motion the stars reasons the constellationsto change their shape. Measure suitable motion by measure up the angularchange in position of the star end some duration of time. If you recognize the street to the star, you have the right to calculatethe street that the star moved and also its tangential velocity Vt = d &mu

motion of Stars in the Milky Way

In the 1920"s, 2 astronomers, jan Oort and Bertil Linbladmeasured the velocities of stars close to the Sun. In our solar system, the finest explanation because that the motionof the planets is the all the planets and also the planet allorbit the Sun. Oort and also Linblad came to comparable conclusions: theyfound that the ideal explanation for the activity of thestars is that the stars and our sun all orbit aroundthe galactic centre. The discovered that the galactic center is at the very least a thousands parsec far from the Sun. The allude that the stars seem to be orbiting aboutis the same point which Shapley uncovered to it is in the centre ofthe galaxy. Today"s welcomed value for the distance between the center of the galaxy and the sun is 8 kpc, back therecould be about 10% error in this measurement.
The movement of the stars approximately the galactic centreis no rigid rotation (like a CD). Actually, linear velocity V,not angular velocity &omega the stars, appears to be the sameV = &omega R = const &rArr &omega = const/R The activity of the stars is differential rotation: the starscloser to the centre have actually a much shorter orbital period thanthe stars additional out.

Circular motion of the Sun

through a little bit that trigonometry, it"s feasible tocalculate the activity of the Sun around the galactic centreby observing various other stars" motion relative to us. The velocity the a star moving in a one aroundthe galactic center is V = 2 &pi R/P R = distance from the galactic centre to the star p = orbital duration of the star. For the sun: V = 220 km/s If R = 8.0 kpc, we can calculate the Sun"s orbit period. Ns = 2 &pi R/V = 2 &pi 8.0 x 3.086 x 1016 km/(220 km/s) = 7.1 x 1015 s = 2.2 x 108 years. The sun takes 220 million year to do one complete orbit. The sun is 4.5 billion year old. The variety of orbits make by the Sun since it to be born is: number of orbits = 4.5 x 109 / 2.4 x 108 = 19 orbits.

Peculiar motion of the Sun

The movement of the sun is around a circle roughly the galactic centre. Over there is a little deviation native this movement which iscalled strange velocity. The Sun"s strange velocity is 20 km/s in ~ an edge of about 45 levels from the galactic centre in the direction of theconstellation Hercules.

The activity of other Stars

The activity of stars in the variety of 1 kpc to16 kpc indigenous the galactic centre has actually been measured. The stars move around on one orbits around thegalactic centre follow me with small peculiar velocities. For most of the stars, the velocities range between200 km/s come 250 km/s. The plot of velocity versus distance from the centreof the galaxy is dubbed a rotation curve. The most necessary feature that the rotation curveis that the velocity the stars far away indigenous the galactic centrestays in ~ a large value near 220 km/s. This is no what was expected, due to the fact that there is virtually nostars at 16kpc, where we still check out 220 km/s rotational velocity.According to Kepler"s Laws, the velocity on one orbit that includes all gravitation mass is
i.e have to drop together square root of radius,
if angular velocity have to drop as
once we look at a galaxy we see most of its light comingfrom the main region. If many of the mass of the galaxy is focused in thecentre, then we would intend that stars additional from the centrewould move at a slower velocity 보다 stars closer to the centre. Because that example, in the solar system, most of the massive of thesolar device is focused in the Sun. The velocities that planets to reduce outwards.

Rotation curve of various other Spiral Galaxies

In spiral galaxies thevelocities the stars far from the centre room much faster than expected. Generally circular motion is governed by a balance betweengravity (pulling the star in the direction of the galactic centre) andan reliable centrifugal pressure (pulling the star outwards). The much faster a star moves the stronger the centrifugal force. If us count up all the stars and estimate the massive of thegalaxy, the force of gravity is not big enough come balancethe centrifugal force connected with these fast stars. Us would expect these stars to it is in ripped the end of the galaxy. Yet the stars are in secure circular orbits! This suggests that there is an ext mass in the galaxy thanwhat we deserve to see. We call this mass dark matter due to the fact that we can"t watch it.

Dark Matter

We deserve to estimate the mass of the Milky method by using Kepler"s regulations of motion. Kepler"s legislations are precious anytime two substantial objects relocate arounda usual centre that mass. In a mechanism like a galaxy, the Sun only feels the gravitationalattraction from the parts of the galaxy which space closer to the centre 보다 the sun is. The gravitational attraction in between the Sun and the restof the galaxy is as though the inner component of the galaxy werecompressed come a suggest at the center of the galaxy. Kepler"s law offers us the sum of the massive of the galaxyand the Sun when we recognize the orbital duration and distance Mgalaxy + MSun = (4 &pi2/G)R3/P2 Butthe massive of a star is tiny compared to the massive of thegalaxy, so we have the right to drop the massive of the Sun. Kepler"s legislation for activity in the galaxy:
putting in the numbers for the Sun"s motion, wefind that the mass within of the Sun"s orbit isMgalaxy = 1011 MSun as soon as we look in ~ a star at twin the distance from thegalactic centre, we find that the mass consisted of withinits orbit is double the mass in ~ the Sun"s orbit. However, as soon as we look at this region, it looks like ithas much much less mass than this. Judging from the big circular velocity that stars farfrom the galactic centre, we deserve to only see about 10% the theMilky Way"s mass!

The Dark Halo

It appears from the activity of stars that many of theMilky Way"s massive is invisible. This dark issue seems come be spread in a spherearound the disk of the galaxy. This ball is referred to as the dark halo
. The only visible objects in the dark halo area few globular clusters and also a few stray stars. Neither the globular clusters no one the stars haveenough mass come account for the halo"s mass.

Possible Candidates because that Dark Matter

Dust and also cold hydrogen clouds: We understand that dust blocks out lightand the cold hydrogen doesn"t provide off much visible light. However, dust will certainly emit infrared light, so our infrared telescopes show where the dust is and also there isn"t enough. hydrogen clouds emit 21 cm wavelength radio tide which we would detect if they were there. No evidence for significant amounts that dust or H in the halo. MACHOs: massive Compact gloriole Objects = dim objects choose Jupiter-like planets, white dwarfs, spirit stars and black holes. A variety of these have actually been uncovered when they pass in former of background stars and "lense" castle gravitationally. (See lectures on black color holes.) these MACHOs can account for around 10% of the dark matter in the halo. WIMPs: Weakly interacting Massive particles = corpuscle which don"t interact well v others an example of a Weakly communicating Particle is the neutrino. A neutrino have the right to pass v a thousand light-years the lead prior to interacting through a lead atom. hundreds of billions of neutrinos pass v every square customs of your body every second, every coming from the sun without friend noticing. since the neutrino interacts an extremely weakly, it is very challenging to detect. If over there is some various other particle similar to the neutrino, yet with a greater mass, it would certainly be a WIMP. The WIMPy theory is the the dark aur is filled through WIMPs of some unspecified type. nobody has ever before detected any kind of of these exotic particles (except because that the neutrino).

Spiral Structure

Observations of various other Spiral Galaxies show: Stars are found with equal thickness everywhere in the disk. Young form O and also B stars, however, room only found in thespiral shame arms. type O stars are around 10,000 times more luminous 보다 the Sun, for this reason the light from these stars dominates the photo ofa spiral galaxy, making that look prefer a spiral. The concentration of dark dust lanes and also cool molecularclouds (the birthplace the stars) is biggest in the spiral arms. Hydrogen regions which light red after gift ionized byyoung O and also B stars room mainly uncovered in the spiral arms.
Conclusions: Spiral arms room the of star formation. After gift born in a spiral arm, a star moves out of the arm. Old stars (like the Sun) need not it is in in one arm and won"t commonly be found inside of their birth arm. Form O and B stars have an extremely short life-spans, onlyabout 1 - 5 million years, for this reason they don"t have actually timeto move out of their birth arm.

Mapping the Spiral framework of the Milky Way

since spiral arms are the location of star-birth, wecan map the place of the eight by mapping the locationof O-B stars and ionized hydrogen regions. This functions for small distances (out to about 3 kpc)since the light from these objects is greatly visible lightwhich is obscured by dust. For larger distance mapping of arms, we must look forradio tide emitted by gas in the eight which room not hidden by dust. Neutral Hydrogen and also Carbon Monoxide emit radio waves. H and CO is focused in the spiral arms, so if we can findthe distance out come H and CO clouds we can map the framework ofthe spiral arms.
Figure 18-21

Neutral Hydrogen Maps

Neutral Hydrogen at remainder emits a photon v 21 centimeter wavelengthwhen the electron spin flips. If the Hydrogen cloud is relocating within ours line-of-sight, theemission line will certainly be either redshifted or blueshifted. We deserve to determine the radial velocity (line-of-sight velocity) that H clouds. Due to the fact that we already know the rotation curve for our galaxy, whichtells united state how fast objects orbit the galactic centre, we deserve to usetrigonometry to reconstruct the places of the spiral arms. Reconstructions give a picture comparable to the diagram below.
Figure 23-13

Actually, one requirements to combine different observation to be more certain

Schematic chart of Spiral structure in the Milky Way

most stars room within a one of radius 15 kpc native the centre. Many Hydrogen is discovered within a one of radius 25 kpc indigenous the centre.

What is the beginning of spiral arms in spiral galaxies ?

first of all: Spiral eight cannot be made from the same product throughout thegalaxy history.
factor -- winding difficulty
Galaxy choose Milky method made ~200 changes through that lifetime.

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material spirals arms would certainly be really tightly wound

Density-Wave concept of Spiral Arms

A spiral eight is simply a region where thedensity that gas is small bit higher than average. This spiral eight is referred to as a thickness waveand travels gradually in a circular motion aroundthe galactic centre. Interstellar dust and gas relocate in circlesat a much bigger speed and collide through the density wave. Once the gas start the density wave region,it is compressed and stars start to form. The freshly born stars continue to move at quick speeds and also eventually leave the spiralarm. O and also B form stars don"t live because that long,so they never ever move far from their birth arm. Reduced mass stars live longer and also haveplenty of time to move to regions betweenthe arms. Thickness wave move slower than stars, so stars, dust and HIcatches increase from behind, but new stars are born in ~ the front of the wave.

The Self-Propagating Star-Formation version

M81 Grand design galaxy
M101 "Pinwheel" flocullent galaxy
cool design-like spirals
are an outcome of the thickness waves. Much less regular, flocculent spirals may need a different mechanism. me propagating star formation design works as complies with Star formation begins in some dense molecular cloud in the disk thatdoes not yet have actually spirals Radiation and also stellar winds from first born stars compress matter around. Star formation is triggered in recently compressed regions. Massive stars explode together supernovae, compressing gas and trigerring starformation in larger region This cloud that newly developed stars is sheared by differential rotationlooking like quick spiral eight Bright O and B stars are short lived, so during their lifetime the spiraldoes not wind much, and as birght stars die, disappear from view. Somewhere else brand-new star formation starts ...Next lecture: Galaxy Collisions, Evolution and Redshifts