Spiral Structure in Galaxies

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1 Department of Physics Seminar - 4 th year Spiral Structure in Galaxies Author: Maruška Žerjal Adviser: prof. dr. Tomaž Zwitter Ljubljana, April 2010 Abstract The most numerous among bright galaxies and the largest in the universe are spirals and represent some of the most beautiful and spectacular phenomena due to the presence of their remarkable spiral arms, which denote young stars and starforming regions. We investigate the phenomenon of well-defined spiral arms through the basics of galactic dynamics and stellar orbits. Instead of the material arms the Lin-Shu density wave theory is introduced as a well accepted theory, which deals with a small-amplitude orbital perturbations and closed orbits in a noninertial frame of reference. We explain the corotation and ultraharmonic resonances of epicycles and mapping of our spiral Milky Way Galaxy.

2 Table of contents 1 An introduction 2 2 Galactic Dynamics 4 3 The Lin-Shu Density Wave Theory Small-Amplitude Orbital Perturbations Closed Orbits in Noninertial Frames The Stability of the Spiral Structure Corotation and Ultraharmonic Resonances Spiral Arms 11 5 Mapping the Milky Way Galaxy A Large-Scale Structure of the Milky Way Galaxy Conclusion 14 1 An introduction Galaxies exhibit a rich variety of shapes from essentially spherical to flattened disk systems. In 1926 Edwin Hubble proposed a morphological classification scheme, based on the appearance of a galaxy at optical wavelengths and known as the Hubble sequence or Hubble s tuning fork, which divides galaxies into ellipticals and spirals. A transitional class between ellipticals and spirals is known as lenticulars. Unclassified galaxies are known as irregulars. While ellipticals are the most numerous among all galaxies, the most numerous among bright galaxies [1] and the largest in the universe [2] are spirals and represent some of the most beautiful and spectacular phenomena due to the presence of their remarkable spiral arms. In consideration of presence or lack of bars and how tightly wound they are, spiral galaxies are further divided into normal spirals and barred spirals (Fig. 1). The latter represent approximately 60 % of all spiral galaxies [2]. These flattened disk galaxies comprise several distinct components (Fig. 2). Multicomponent disk planes of spiral galaxies, involving thin, thick and gas disk, extends across kpc 1 in diameter. Vertical scale heights of thin disk measure only a few percents of its radii, thick disks are somewhat thicker. Thin disks are made of relatively young stars, gas and dust. The latter is responsible for the dark lanes across the disk due to the absorption in visible wavelenghts. In the center of the disk lies a central bulge, containing mostly old stars. Flattened disk is surrounded by a spherical stellar halo of radii more than 100 kpc and made up from old stars and globular clusters. It is enveloped by a dark matter halo, which extends over 230 kpc in our Galaxy. Masses of spiral galaxies range from M 2 [2] and are composed of about stars. Most apparent feature of the disk are well-defined spiral arms, which denote young stars and star-forming regions. They could be one of the main clues of their evolution, via the angular momentum transfer. In between the spiral arms intermediate-age stars are to be found. 1 Parsec, 1 pc = 3.26 light years 2 M = kg, one Solar mass 2

3 Figure 1 Hubble s tuning fork divides galaxies into ellipticals and spirals [3]. A transitional class between ellipticals and spirals is known as lenticulars. In consideration of presence or lack of bars and how tightly wound they are, spiral galaxies are further divided into normal spirals and barred spirals. Figure 2 Side-on view of spiral galaxy [4] (figure is not to scale). Multi-component disk plane extends across kpc in diameter. Vertical scale heights of the disk measure only a few percents of its radii. The thin component of the disk is made of relatively young stars, gas and dust. The latter is responsible for the dark lanes across the disk due to the absorption in visible wavelenghts. In the center of the disk lies a central bulge, containing mostly old stars. Flattened disk is surrounded by a spherical halo of radii more than 100 kpc and made up from old stars and globular clusters. Radius of dark-matter halo extends over 230 kpc in our Galaxy. 3

4 Figure 3 Rotation curve for a flattened-disk spiral galaxy [1]. A dashed line is a prediction for a rotational velocity that obeys the Keplerian dynamics in a case that the visible mass of the galaxy is the total galactic mass and extends to the point A. The measured rotational curve is rather flat (solid line) and reveals unseen dark matter present well beyond the visible radius of the galaxy. 2 Galactic Dynamics A circular Keplerian orbit at a distance r from the center of the galaxy with radius R will have rotation velocity GM(r) v =. (1) r M(r) is the galactic mass from the center to the radius r. On Fig. 3, the visible mass of the galaxy extends to the point A. If visible mass M(R) was total galactic mass, then v should decrease as 1/r (Eq. 1) for r > R. Measurements show that for radius r > R, rotation velocity v is approximately constant as far as 2 3R. Rotation curve reveals unseen dark matter present well beyond the visible radius of the galaxy and which causes the flat curve. Rotational velocities vary with the morphology of galaxy. More tightly spiral arms are wound and more prominent the bulge is, higher is galaxies rotational velocity. Mean velocity ranges from 300 km s 1 for type Sa galaxies to 175 km s 1 for Sc galaxies [2]. Maximum rotational velocities for irregular galaxies are significantly smaller, typically from km s 1. It seems that a minimum rotation speed of roughly km s 1 may be required for the development of a well-organized spiral pattern [2]. 3 The Lin-Shu Density Wave Theory Suggestion that spiral arms are material (composed of a fixed set of stars, gas and dust) and rotate with the galaxy itself, ends up with the so-called winding problem (Fig. 4). Since the disk undergoes a differential rotation, stars on more distant orbits have smaller velocities and start to lag behind those on nearer orbits. After only a few periods (for example, period of the Sun is about yr [2]), arms would become wound too tightly 4

5 Figure 4 The winding problem for material arms, composed of a fixed set of stars, gas and dust [2]. Since the disk undergoes a differential rotation, stars on more distant orbits start to lag behind those on nearer orbits and spiral arms become wound too tightly. to be observed. In the 1960 s, C. C. Lin and Frank Shu proposed that spiral arms are rather generated by long-lived quasistatic density waves, regions in the disk with enhanced density by % that travel through the galaxy triggering star formation. Stars, gas and dust travel on their orbits through the waves. The term quasistatic refers to the fact that when viewing in a noninertial frame of reference, rotating with a globular pattern speed Ω gp, spiral waves exhibit a stationary pattern. However, most of the stars do not rotate with the global pattern angular speed Ω gp. Stars near the center have higher velocities and shorter angular frequencies than Ω gp, but stars on the outher edge of the galaxy have angular frequencies that are larger than Ω gp due to their smaller velocities. Inner stars would overtake the spiral arm while the outher stars would be overtaken by a spiral pattern. Critical radius R c, where the stars and density waves would have the same angular velocity, is called the corotation radius. In noninertial frame of reference, the stars with r < R c will appear to pass through the arms in one direction, the stars with r > R c will appear to move in the opposite sense (see Fig. 5). The hypothesis of quasistationary spiral structure refers only to the large-scale regular structure that is frequently observed in galaxies [5]. Density waves leave the equatorial symmetry unchanged, but on the other hand they are associated with density enhancements and rarefactions that usual break the axisymmetry of the basic state [5]. When the gas and dust clouds on r < R c overtake the spiral arms, the enhancement of the density occurs, resulting in cloud collapse, when the Jeans criterion 3 is satisfied. Due to a finite time of star formation (10 5 yr for a 15 M star [2]), the starburst will appear downstream the arm in the edge of the wave. Since the massive O and B stars 4 have relatively short lifetime in comparison with their existence within the density wave, they die out before leaving the arm. Only longeval red and less luminous stars remain and are passed by the wave. They are found in between the spiral arms. However, there exist local maxima of old red dwarf stars due to the minima of a gravitational potential dwell of the spiral arm with enhanced density. 3 The Jeans criterion tells the minimum cloud mass M c, required for its collapse: M c > ( ) 3/2 ( ) 5kBT 1/2, 3 Gµm H 4πρ 0 where kb is Boltzmann constant, T gas temperature, G gravitational constant, µ a mean particle mass, m H mass of a hydrogenium atom and ρ 0 is a cloud density [2]. 4 O and B stars are young, hot, very massive and luminous. Their lifetime is relatively short, 10 7 yr. 5

6 Figure 5 (a) Trailing spiral arms in an inertial frame of reference (S) [2]. A velocity of a quasistatic density wave is equal to a global angular pattern speed Ω gp. Star A rotates with a speed Ω A > Ω gp, star B with Ω B < Ω gp and star C corotates with a density wave (Ω C = Ω gp ). (b) In noninertial frame of reference (S ), star A seems to take over the density wave, star B lags behind the wave and star C corotates with the wave itself. 3.1 Small-Amplitude Orbital Perturbations In order to reveal the resulting spiral shape from the orbits of the stars, let us determine the axial symmetric gravitational potential and orbital motion of the stars. We take into account that for the statistical majority of galaxies, the underlying potential that is associated with the grand-design spiral structure is stationary in a suitable rotating frame. We consider only a stellar component of the galaxy (N = stars) - the number is large enough for the smoothness of the local potential instead of its natural graininess. Another presumption says that the stellar component can be considered collisionless. We neglect also the potential of the spiral waves. In the cylindrical coordinates (r, ϕ, z) we introduce an effective gravitational potential as Φ eff (r,z) = Φ(r,z) + J2 z 2r2. (2) J z = r 2 Φ is a constant for the star s motion and denotes the z component of the orbital angular momentum per unit mass of the star. Φ(r,z) is defined as Φ(r,z) = U/m, where m d2 r = U(r,z), (3) dt2 m is a mass of the star and U(r,z) is the gravitational potential of the disk. The minimum of the Φ eff occurs, when z = 0 and the orbit of the star is perfectly circular. The perturbation analysis of the first order gives us the following effective potential: Φ eff (r,z) Φ 0 eff κ2 ρ ν2 z 2. (4) 6

7 Φ 0 eff denotes the minimum of unperturbed potential at Φ0 eff (R m, 0), ρ = R m r, R m is the radius at Φ 0 eff. We defined the constants and get the equations of harmonic motion: with the solution κ 2 2 Φ eff r 2 m, ν 2 2 Φ eff z 2 m. (5) ρ κ 2 ρ, z ν 2 z (6) ρ(t) = A R sin κt, z(t) = A z sin (νt + ζ). (7) We proclaim κ to be the epicycle frequency and ν for the oscillation frequency. ζ is a general phase shift between ρ(t) and z(t). A R and A z are amplitudes of the oscillation. The star oscilates around the equilibrium position (R m, 0), which is stable point and rotates on a circular orbit with the angular frequency Ω. Now we search for the difference χ(t) between the azimuthal position of the star and the equilibrium point. We know that φ = v φ r(t) = J z r(t) 2 (8) and r(t) = R m +ρ(t) = R m (1+ρ(t)/R m ). For ρ(t) R m, we use the binomial expansion and it follows that φ J ( z 1 2 ρ(t) ). (9) Rm 2 R m After integration we get φ(t) = φ 0 + J z t + 2J z A Rm 2 κrm 3 R cos κt = φ 0 + Ωt + 2Ω A R cos κt, (10) κr m where Ω J z /R 2 m was introduced. The last term in Eq. 10 acts as the oscillation of the star about the equilibrium point in the φ direction. By defining the difference in azimuthal position between the star and the equilibrium point by the perturbation theory of the first order it follows that χ(t) (φ(t) (φ 0 + Ωt))R m, (11) χ(t) = 2Ω κ A R cos κt. (12) Equations (7) and (12) represent the oscillation of the star around its equilibrium point, which moves in circle around the center of the galaxy with angular speed Ω [2]. In an inertial frame of reference, star s orbit is not closed, but reminds of the rosette pattern (Fig. 6), which is to be explained with help of epicycles. The center of the epicycle corresponds to the equilibrium position. An axial ratio of an oval shaped epicycle η is given by the ratios of the amplitudes of the oscillations in χ(t) and ρ(t), η = χ max ρ max = 2Ω κ. (13) The center of the (χ, ρ) epicycle rotates around the galactic center with the angular velocity of the equilibrium point, Ω (Fig. 6). 7

8 Figure 6 A nonclosed rosette pattern is formed (solid line) by a star s orbital motion when viewing in an inertial frame of reference [2]. The motion reveals the epicyclic behaviour when only the first-order approximation is contributed. The center of the epicycle (dashed line) rotates around the center of the galaxy with Ω. 3.2 Closed Orbits in Noninertial Frames The number of oscillations per orbit is equal to N = 1/2η or N = κ Ω. (14) If N is an integer, the orbit is closed. Most stellar orbits in an inertial frame are not closed and the rosette pattern results, while in a noninertial frame of reference, rotating with the local angular pattern speed Ω lp = Ω, relative to the inertial frame, the orbit is closed and appears at the R m (Fig. 6). In a noninertial frame of reference, a closed orbit would complete n orbits and m epicycle oscillations (m and n are integers). It s valid to choose m(ω Ω lp ) = nκ or Ω lp (r) = Ω(r) n κ(r). (15) m At radius r, only a small number of values m and n would give a substantial enhancements in mass density [2], which means that only selected modes ((n,m) = (1, 2)) are most common to be observed. When looking in a noninertial frame, that is rotating with the global angular pattern velocity Ω gp and when Ω lp Ω lp (r), we can set Ω gp = Ω lp. From the Earth, such closed orbital trajectories (for (n,m) = (1, 2), for example) could be nested with their major axis aligned (Fig. 7a). In case we orient such oval-shaped orbit in a way its major axis is rotated slightly relative to the one immediately interior to it, we get a trailing two-armed grand-design spiral wave pattern (Fig. 7b). Rotation in the opposite sense would give leading arms (Fig. 7c). For example, M51 is a grand-design trailing-armed spiral with (n,m) = (1, 2) (Fig. 8) and M101 is a four-armed galaxy with trailing arms and with (n,m) = (1, 4). 8

9 Figure 7 Nested orbits (a) [6] in a galaxy with Ω gp = Ω κ/2 (i.e. ((n, m) = (1, 3))) in a frame of reference rotating with Ω gp. When rotating the axes of ellipses, there comes to trailing arms (b) or leading arms (c), if rotating in the opposite side. Figure 8 The grand-design Whirlpool Galaxy M51 [7] in interaction with an irregular galaxy NGC This is a trailing spiral pattern with (n, m) = (1, 2) modes and corresponds to regions of active star formation [2]. Dust and gas clouds are spread on the inner edges of the arms as well as in the surroundings of the galaxies. Due to the relatively large size of the galaxies, compared to the average distance between them, the encounters with other galaxies are very likely to occur at least a few times over their immense lifetimes [8] and play an important role in the evolution of the galaxies. 9

10 Figure 9 The Bahcall-Soneira model of our Galaxy [2] for Ω lp = Ω n mκ for various n, m. Curve for Ω κ/2 is nearly flat over a large range of Galactic disk and consequently systems with m = 2 are most frequently found. 3.3 The Stability of the Spiral Structure The stability of the (n,m) = (1, 2) structure depends mostly on whether Ω lp (r) = Ω(r) κ(r) 2 is actually independent of r or not, that is, whether there is an appropriate Ω gp or not. The most frequent systems are two-armed with m = 2, probably due to the fact that their rotation velocity is flat over a wide range of radii, just like the Ω lp (r) = Ω(r) κ(r) 2 (Fig. 9). Observations show that in the statistical majority of galaxies, the dynamics of the disk is dominated by one mode ((n,m) = (1, 2) is most frequent) or by a very small number of modes [5]. We also know that the presence of gas is essential for spiral structure, by means of self-regulation, due to the fact that collapsing gas clouds result in a new-born stars which illuminates the spiral arms. 3.4 Corotation and Ultraharmonic Resonances Now we neglect our previous assumption of insignificance of the potential of the arms. It follows that when the star encounters a density wave with its maximum value of the difference between the equilibrium and azimuthal position χ max, a resonance develops and epicycle oscillation amplitudes A R and A z are considerably increased. If a star is at its maximum χ max each time it enters the density wave, the perturbation of the density enhancement and gravitational potential will always be in the same sense. Perturbations will therefore cumulate. Because Ω is actually not exactly the same over the entire disk, i.e. Ω = Ω(r), there exist only certain radii where Ω lp = Ω gp. From the Earth, such orbits are closed and a resonant amplitude amplifications are possible. When Ω gp = Ω lp = Ω κ/2 (n/m = 1/2), 10 (16)

11 Figure 10 Positions of the resonance radii. Their existence depends on the shape of the galactic rotation curve and on the global angular pattern velocity Ω gp [2]. Normally there may exist one or two inner Lindblad radii (ILR), but none can be found if Ω gp is sufficiently large. In case that Ω gp = Ω, a corotation resonance (CR) exists and stars velocity is equal to the velocity of the spiral wave. If Ω gp = Ω + κ/2, it may come to an outer Lindblad resonance (OLR). an inner Lindblad 5 resonance occurs and is possible at several radii (zero, one or two inner Lindblad radii - Fig. 10b) in dependence of the rotation curve of the galaxy. In case that stellar velocity is equal to the velocity of the spiral wave (Ω gp = Ω), a corotation resonance exists. If Ω gp = Ω + κ/2, it may come to an outer Lindblad resonance (Fig. 10). It is possible for ultraharmonic resonance to develop when Ω gp = Ω κ/4. In resonance, it is more likely for gas clouds to collide and for the dissipation of the energy, which results in damping in spiral waves, unless there is another mechanism sustaining the waves. 4 Spiral Arms Among others, the most prominent variation of spiral structure is in number and shape of its arms. The most majestic spiral galaxies are so-called grand-design spirals, showing only two very symmetric arms. About 10 % of spirals are considered grand-design spirals, 60 % are multiple-armed galaxies and the remaining 30 % present flocculent galaxies, which do not possess well-defined spiral arms that are traceable over a significant angular distance [2]. At visible wavelengths, these galaxies are dominated by their spiral pattern due to the presence of very luminous O and B main-sequence stars and HII regions are located within the arms. In comparison with the rotational period of the galaxy ( yr), lifetime of those stars is very short (10 7 yr), ending with conclusion that spiral pattern corresponds to regions of active star formation [2]. Dust and gas clouds are spread on the inner edges of the arms. An intuitive guess suggests that spiral arms are trailing (Fig. 5), which means that the tips of arms point to the opposite side of rotation of the galaxy. In one case, (galaxy NGC 4622), the Dopper effect seen in the ground-based spectrum [9] showed that at least one of the spiral arms must be leading. An important role in galactic evolution also plays the galactic bar. 5 Bertil Lindblad, Swedish astronomer,

12 5 Mapping the Milky Way Galaxy Surprisingly, among the relatively well-grounded findings about the other galaxies, the large-scale structure of our Milky Way Galaxy still remains somehow misterious due to the fact that we are positioned inside the galaxy itself. Uncertainty in most of the light at optical wavelengths arises from the obscurity of the extensive dust clouds along the Galactic disk [10]. However, there have been successful surveys carried out, one of them are recent GLIMPSE surveys, that have archived over 100 million stars which play an important role in tracing a large-scale Galactic structure [11]. About 90 % of catalogued stars are mostly red-clump giants, which have relatively small range in intrinsic luminosities and therefore act as a standard candles, used in a distance determination. Mapping of the Milky Way basically includes measuring stellar distances, their radial velocities, revealed by the Doppler effect in their spectra and investigation of the density, which is performed by combining the star count per surface area and their distances. Figure 11 Indication of the Milky Way s Figure 12 Number of stellar sources per bar [11] - there is a hump at 12 mag in the deg 2 in dependence of a Galactic longitude [11]. north that is absent in the south and is a signature of the northern arm of the central galactic the central bulge. A Scutum-Centaurus arm can The large excess at the Galactic center is due to bar. be seen, while the Sagittarius arm is not visible. Figure 11 shows the power-law exponent of stars per magnitude per square degree versus magnitude at 4.5 µm and as a function of a Galactic longitude l 6 (plotted for three lines of sight). We note the appearance of a bump at 12 mag and l = 15.5 and its absence at l = The hump is interpreted as a strong evidence for a northern arm of a central bar as a major feature of our Galaxy, with radius 4.4 ± 0.5 kpc and rotated for about 44 ± 10 to the Sun-Galactic bulge line [11]. When looking along the Galactic midplane toward the Scutum-Centaurus arm tangency (see Fig. 13) at 306 < l < 313, there is an enhancement of stars due to the increased line if sight path length through the arm and the increased number of stars in the arm [11]. However, at the opposite side at 54 < l < 51, there is no increase in the star count, although there is the Sagittarius arm expected to be found (see Fig. 12). 6 Galactic coordinate system is aligned with its disk. l is a Galactic plane longitude, defined from a our Sun s position, b is Galactic latitude, see Fig. 13 [2]. 12

13 Figure 13 Observations in radio, infrared, and visible wavelengths show that our Milky Way Galaxy is a grand-design two-armed barred spiral with the Scutum-Centaurus and Perseus arms and several secondary arms (Sagittarius, Norma, the outer arm, and the 3 kpc expanding arm) [11]. 5.1 A Large-Scale Structure of the Milky Way Galaxy To begin with, let us thread on some of the most fundamental physical parameters of our Galaxy. The Milky Way Galaxy is composed of stars. Stellar mass of the thin disk in our Galaxy is about M [2]. Multi-component disk plane of our spiral Milky Way Galaxy, involving thin, thick and gas disk, extends across 50 kpc in diameter. Our distance to the Galactic center is believed to be kpc [11], but there are some suggestions for the value of 7.62 ± 0.32 kpc [11], which has yet to be confirmed by an independent analysis. Vertical scale height of thin disk is 350 pc (1.4 % of its radii), thick disk is more extensive (1 kpc or 4 % of disk s radii). Flattened disk is surrounded by a spherical halo of radii more than 100 kpc and made up from old stars and globular clusters. Radius of dark-matter halo extends over 230 kpc. Among other various possibilities, spiral structure is best defined by detection of the H II regions and ionizing radiation, which indicates young, hot and luminous OB-type stars that are situated in high mass star forming regions (spiral arms) in the Galactic plane. The red light spiral characteristics of older, low-mass stars are less pronounced. New results using VLBA (Very Long Baseline Array) show that estimates of the fundamental parameters of the Milky Way, R 0 and Θ 0 indicate a rotation speed of Θ 0 = 254 km s 1, that is 15 % faster than previous results [10]. 13

14 Our Galaxy probably belongs to type SBbc galaxies [2]. Among its morphological features are the Central Galactic bar and the Long bar. The first one is much more vertically extended than the thin stellar disk [11], the second one is thinner and nonaxisymmetric. There are Near and Far 3-kpc Arms, associated with gas flow roughly parallel to the bar. The Milky Way Galaxy has four principal spiral arms, which are named after the constellation in which they are observed: Norma, Sagittarius, Perseus and Scutum-Centaurus spiral arms. 6 Conclusion We showed that the theory of a material arms, made of stars, gas and dust, ends up with the winding problem and can not explain the occurence of the examined pattern. The Lin-Shu density wave theory was introduced and helps to explain the structure of a well-defined spiral patterns in a flat-disk galaxies very well. We made a small-amplitude orbital perturbations. In the first order, orbital motions of the stars are described by the epicycles. There exist several radii, where the resonance occurs in dependence of the mode and the spiral waves could be damped unless there is another mechanism sustaining the waves. The theory explains the shape of about 70% of all galaxies. Although the existence of difficulties with revealing the spiral pattern of our Galaxy, its shape is relatively well-known. Its is classified as the SBbc galaxy - spiral, barred and with a relatively weak wounded spiral arms. Hovewer, the misteries still remain in our galactic shape and dynamics as well as in the other spiral galaxies. References [1] J. V. Narlikar, 2002, An introduction to cosmology, Third Edition, Cambridge University Press [2] B. W. Caroll and D. A. Ostlie, 2007, An Introduction to Modern Astrophysics, Second edition, Addison Wesley [3] Galaxy classification - Ellipticals, Lenticulars, Spirals, Irregulars, Problems with visual classification, Morphology density relation, Fig. 1., b/a, [ ] [4] Windows to the Universe, [ ] [5] G. Bertin, 2000, Dynamics of Galaxies, Cambridge University Press [6] J. Binney and S. Tremaine, 1987, Galactic Dynamics, Princeton University Press, Third printing, with corrections, 1994 [7] R. Gendler, 2006, M51 (NGC 5194 and 5195) - Colliding Galaxies in Canes Venatici, [ ] [8] R. Gendler, 2006, M51 (NGC 5194 and NGC 5195) (The Whirlpool Galaxy), [ ] [9] R. Nemiroff & J. Bonnell, 2002, The Spiral Arms of NGC 4622, Astronomy Picture of the Day (2002 January 25), [ ] 14

15 [10] M. J. Reid et al., 2009, Structure and Dynamics of the Milky Way: an Astro2010 Science White Paper, arxiv: v2 [astro-ph.ga] [11] E. Churchwell et al. 2009, The Spitzer/GLIMPSE Surveys: A New View of the Milky Way, Publications of the Astronomical Society of the Pacific, 121:

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