Our Place in the Milky

Astronomy 218 Our Place in the Milky Way Orbiting Sun The Sun’s proper motion relative to the Galactic center, 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 orbit requires that the mass inside of the Sun’s orbit must be 10 = 9.3 × 10 M☉ This 93 billion M☉ for the inner galaxy 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 Norma Arm Sagittarius Arm Central Bar Orion Spur Perseus 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 Sagittarius A* 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 galaxies, the waves are regions of locally higher density, which accelerate stars into them and decelerate them as they leave, perpetuating the over density. Spiral Star 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 Orion Arm. 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 Earth’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 radial velocity of the star over an entire orbital period. The radial velocity of forty stellar systems within 5 parsecs 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 year 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 Proxima Centauri) 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.

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