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Home , Gliese 710, Local standard of rest, Norma Arm, Perseus Arm

Astronomy 218 Our Place in the Orbiting The Sun’s relative to the , μ” = 5.8 milliarcseconds yr−1 = 2.8 × 10−8 rad yr−1 and its distance from the Galactic center, R0 = 8 kpc, indicate an −1 −1 orbital velocity of �0 = 225 kpc Gyr = 220 km s . The Sun’s orbital period around the Galactic Center is then

= 0.22 Gyr Maintaining this requires that the mass inside of the Sun’s orbit must be 10 = 9.3 × 10 M☉ This 93 billion M☉ for the inner compares to 23 billion L☉, indicating that the galaxy’s M/L > M☉/L☉. Spiral Arms Measurements of the position and motion of gas clouds throughout the Milky Way reveals that the solar environment includes several spiral arms. Scutum-Centaurus Arm Arm Sagittarius Arm Central Bar Orion Spur Arm Outer Arm Galactic Coordinates The Galactic plane defines a galactic coordinate system, in the same way the Equator defines the terrestrial latitude and longitude.

The line from the Sun to * defines the zero of galactic longitude, ℓ, which increases counter-clockwise viewed from the north. The galactic latitude, b, is measured from the plane of the galaxy to the object using the Sun as vertex. Differential Rotation One interpretation of the spiral arms would be the winding up of an initial linear pattern.

However, the differential rotation of the galaxy would have wound up the spiral pattern so tightly that it would effectively disappear, contrary to observations. Thus the spiral arms are not tied to disk material. Density Waves Instead spiral arms are density waves, similar to the over density of cars in a traffic jam. The jam persists even though individual cars move steadily through it. Such density waves persist long after the event that triggered them is forgotten. In the case of , the waves are regions of locally higher density, which accelerate into them and decelerate them as they leave, perpetuating the over density. Spiral Formation Not just the density of stars becomes enhanced as they move through the spiral arms, but clouds of gas and dust are actually compressed. Their increased density triggers star formation. This affects the propagation of spiral arms as the formation of stars leads to supernovae and stellar winds which further compress the gas and dust, leading to waves of ongoing star formation. Spiral Lights It is this ongoing star formation which makes the spiral arms so visible. Newly formed massive stars, and their attendant HII regions and supernova remnants, line the spiral arms, shining bright and dying before leaving the arm. In contrast, older stars move through the arms and have a smoother angular distribution. As one moves to progressively longer wavelengths, the spiral arms become less noticeable. The actual over-density is small, only a few %. Orion Spur The Orion Spur is also referred to as the Orion-Cygnus Arm or the . The Sun sits near the center of the Local Bubble, close to the inner rim of the arm, Facing in the leading direction points in the direction of Deneb and the constellation Cygnus. Facing in the trailing direction points toward Betelgeuse and the constellation Orion. Local Stellar Motions

We can measure the relative motions of nearby �t � stars in two steps. r � The space velocity � can be decomposed into 2 components, relative to the line of sight.

The radial component, �r, along the line of μ d sight, can be measured by doppler shift.

The tangential (or transverse) component, �t, across the line of sight, can be measured by proper motion, μ. To achieve the desired accuracy, these measurements must be −1 corrected for the ’s orbital velocity (�orb ≈ 30 km s ) −1 and the Earth’s rotational velocity (�rot ≈ 0.5 km s ), as well as any binary motions of the distant star. 6.3. STELLAR MOTIONS 137

Figure 6.11: Components of a star’s velocity relative to the Sun.

itself. This can be done by averaging the of the star over an entire orbital period. The radial velocity of forty stellar systems within 5 of the Sun is Localplotted Radialin Figure 6.12. Notice aVelocityfew interesting results: Examination of the radial velocities of 200 ] s the 40 stars closest / 100 m k [

to the Sun, d < 5 r v 0 pc, results in this figure. −100 The number of 1 2 3 4 5 d [pc] redshifted stars approximately equals theFigure number6.12: Radial ofv eloblueshiftedcity of stars within stars.5 pc of the Sun.

Kapteyn’s star, at a •distanceThe radial vofelo cities3.9 shopcw, isappro a ximatelynoticeableequal n umoutlier,bers of blueshifts with a velocity of 250(v rkm< 0) sand−1 redshiftsaway (fromvr > 0). the Sun. • There is one notable outlier on the plot: Kapteyn’s star, alias CD- Ignoring Kapteyn’s star,45◦1841, thealias root-mean-squareGliese 191, which is mo velocityving away from the Sun with dispersion is ~ 35 km s−1 in radial velocity. Proper Motion Measuring the motion of a star across the line of sight is much more time-consuming than measuring the radial velocity via the Doppler Shift. Time must pass for the star to move perceptively on the sky.

In the small angle limit, the proper motion μ = �t/d. If μ is measured in rad yr−1 and d in parsecs,

μ is more naturally measured in arcseconds yr−1, with 1 radian −1 = 206,265 arcseconds. Comparison of �t to �r favors km s with 1 pc yr−1 = 976,582 km s−1. Simplifying

140 CHAPTER 6. OUR GALAXY

For Barnard’s Star, as an example,

10.358 −1 −1 vt = 4.74 km s = 89.8 km s . (6.24) ! 0.547 " The tangential velocity of stellar systems within 5 parsecs of the Sun is shown Local Tangentialin Figure 6.14. The high proper motion Velocityof Barnard’s Star is due both to the

Examination of the 150

tangential velocities ] s / of the 40 stars m 100 k [

t closest to the Sun v 50 results in this figure. 0 The red line marks 1 2 3 4 5 μ = 5 arcsec yr−1. d [pc] Figure 6.14: Tangential velocity of stars within 5 pc of the Sun. Stars above Again Kapteyn’s starthe dotted showsline hait’sve µuniqueness"" > 5 arcsec yr−1. with a large ʋt −1 producing a large factproperthat it motion,is very close toμ us= and8.7to arcsecthe fact that yrits tangential velocity is higher than the average for nearby stars. Barnard’s star, despiteIf the itsav eragesmallertangen tialtangentialvelocity vt do velocity,esn’t vary with hasdistance the from the Sun, then on average, nearby stars will−1 have a higher proper motion than highest proper motion,more distan μ t=stars. 10.4One arcsecway to searc yrh for. nearby stars, if you don’t have the time or patience to measure parallaxes for every star in the sky, is to start −1 61 Cygni, μ = 5.2 barcsecy looking atyrstars, withhashigh theprop highester motion. properThe history motionbooks state that in the 1838, Friedrich Wilhelm Bessel measured the parallax of 61 Cygni. of any star visible Whatto thethey nakedsometimes eye.don’t tell you is why Bessel chose that star to observe: it is, after all, a humble fifth magnitude star. Bessel, in fact, chose 61 Cygni because it has the highest proper motion of any star visible to the naked eye, µ"" = 5.2 arcsec yr−1.12 Of course, any star, no matter its distance, will have 12The unusual nature of Kapteyn’s Star was first recognized in the year 1897, when this otherwise boring M dwarf was found to have a proper motion of nearly 9 arcseconds per year. At the time, this was the largest proper motion known, defeated only when E. E. Barnard measured the proper motion of Barnard’s Star in 1916. 6.4. LOCAL STANDARD OF REST 141

zero proper motion if it’s moving straight toward us or straight away from us. An example of a nearby star with small proper motion is Gliese 710, which −1 "" −1 has vr = −13.9 km s and µ = 0.014 arcsec yr . At the moment, Gliese 710 is over 19 parsecs away from us, and has mV = 9.7. In 1.4 Myr, however, is will be only 0.34 parsecs away (about a fourth the present distance to ) and have mV = 0.9. Putting it all together, the total speed relative to the Sun, 2 2 1/2 v = (vr + vt ) , (6.25) is called the “space motion” or “space velocity”. A plot of the space motion Local forSpacenearby stars (Figure 6.15)Velocityreveals that Kapteyn’s Star again stands out

Combining the 300 radial and tangential ] s velocities for the 40 / 200 m k [ closest stars reveals that 39/40 belong to v 100 a group with a mean 0 relative velocity � ~ 1 2 3 4 5 50 km s−1. d [pc]

These velocities willFigure rearrange6.15: Space theirvelocity proximityof stars within 5topc theof the SunSun. onThe outliera at −1 timescale of t ~ 5 pcd ≈/ 503.9 p cpc, v ≈Myr300 km−1s ~is 0.1Kapteyn’s Myrstar.. For example, Gliese 710, currentlylik e19the propcv erbialaway,sore willthumb. passIts space withinmotion ⅓of v pc≈ 300 inkm 1.4s−1 is twice that of Barnard’s Star, the next speediest star in the solar neighborhood. The Myr, brightening fromaverage mspacev = motion9.7 toof stars0.9.within 5 parsecs of the Sun is v ∼ 50 km s−1 ∼ 50 pc Myr−1. This indicates that the list of stars within 5 parsecs of us will Kapteyn’s star, withb etwicethoroughly therevised velocityon timescales of anyt ∼ 5 potherc/50 pc Myrnearby−1 ∼ 0.1 Myr. star, is in a class by itself, the nearest halo star. 6.4 The Local Standard of Rest

If the disk of our galaxy were perfectly orderly, with all the stars on exactly circular in the same plane, it would be simple to compute the expected Local Standard of Rest The aspherical and time varying distribution of mass within the Galaxy prevents stars from moving in closed elliptical orbits. Instead, stars follow complex rosette patterns. These patterns make actual stellar orbits a poor basis for a coordinate system.

We create an idealized reference frame, the Local Standard of Rest, which moves in a circular orbit at ʋ0 −1 = 220 km s from the Sun’s location at R0 = 8 kpc. Coordinates relative to the LSR are (R,θ,z), with the Sun at (R0, 0, 0 kpc). Velocities are (Π,Θ,Z), with �LSR = (0, �0, 0). Sun’s Peculiar Motion The LSR is moving steadily in the direction of Cygnus. But, the LSR is not the orbit of the Sun. Using a statistical analysis of the radial velocities of neighboring stars, we can determine the Sun’s motion. Relative to the LSR, the Sun has a (�⊙, �⊙, �⊙)

−1 = (Π−Π⊙,Θ−Θ⊙,Z−Z⊙) = (−10.4, 14.8, 7.3) km s Thus the Sun is moving inward (toward the Galactic Center) at 10 km s−1, forward (faster than the LSR in the azimuthal direction) at 15 km s−1 and northward (toward the north Galactic pole) at 7 km s−1. This places the Sun’s apex or direction of motion toward the constellation and its antapex, opposite direction from the apex, toward the constellation Columba. Galactic Rotation Curve Combining tangent point method observations toward the Galactic center with stellar observations in the outer Galaxy reveals the rotation curve of the Galaxy. The expectation was M(2R0) ~ 3 M(R0) that beyond a radius that contained the M ∝ R mass of the galaxy, the velocity should diminish with radius following Kepler’s law. Instead mass continues to increase with radius, well into the region where the light is exponentially declining. Something dim but massive lurks in the Galaxy. Dark Matter The visible structure of the Galactic Disk extends ~15 kpc from the center. 15 kpc Beyond this radius, atomic gas (molecular gas is found for R≤10 kpc) and halo stars map the “missing” mass, 8 kpc whose density is ∝ R−2. But the mass is present, it is the light that is missing. What could the “dark matter” be? Many suggestions have been raised; red dwarves, white dwarves, brown dwarves, stellar-mass black holes, elementary particles, …. Not Red Dwarfs One possibility is that dim red dwarfs are even more numerous that suspected. Many searches, most recently by Hubble, have looked for such red dwarfs, but turned up too few to account for dark matter. Our best accounting of the full stellar population yields M/L ~ 10 while the rotation curve indicates M/L ~ 50. Not Machos Our study of stars suggests several other candidates for dim but massive objects, black holes, neutron stars, white dwarves and brown dwarves. This very dimness makes them difficult to observe directly. However, gravitational lensing can allow us to directly observe their mass by bending more light into the line of sight. Observations have found numerous MACHOS (Massive Compact Halo Objects), mostly low-mass white dwarves, but only ~20% of the missing mass. Not Neutrinos The is in fact flooded with neutrinos, relics of the Big Bang and the lives and deaths of stars. Neutrinos interact extremely rarely, and we’ve learned from neutrino oscillations that they have mass, both promising characteristics for the dark matter. Neutrino oscillation measurements reveal mass differences 2 2 2 2 Δm12 = 0.00008 eV and Δm23 = 0.003 eV , but not the masses. A number of other experiments place limits on the mass of the neutrino < 1 eV. At this mass, neutrinos are not the dark matter. Particle physics predicts a myriad of similar, as yet undetected, Weakly Interacting, Massive Particles(WIMPs) with masses > 100 mp ~ 100 GeV that could be the dark matter. Next Time Rotation Curves and Missing Mass