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Lecture 18, Structure of Spiral Galaxies

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GALAXIES 626 Upcoming Schedule: Today: Structure of Disk Galaxies Thursday:Structure of Ellipticals Tuesday 10th: dark matter (Emily©s paper due) Thursday 12th :stability of disks/spiral arms Tuesday 17th: Emily©s presentation (intergalactic metals) GALAXIES 626 Lecture 17: The structure of spiral galaxies NGC 2997 - a typical spiral galaxy NGC 4622 yet another spiral note how different the spiral structure can be from galaxy to galaxy Elementary properties of spiral galaxies Milky Way is a ªtypicalº spiral radius of disk = 15 Kpc thickness of disk = 300 pc Regions of a Spiral Galaxy · Disk · younger generation of stars · contains gas and dust · location of the open clusters · Where spiral arms are located · Bulge · mixture of both young and old stars · Halo · older generation of stars · contains little gas and dust · location of the globular clusters Spiral Galaxies The disk is the defining stellar component of spiral galaxies. It is the end product of the dissipation of most of the baryons, and contains almost all of the baryonic angular momentum Understanding its formation is one of the most important goals of galaxy formation theory. Out of the galaxy formation process come galactic disks with a high level of regularity in their structure and scaling laws Galaxy formation models need to understand the reasons for this regularity Spiral galaxy components 1. Stars · 200 billion stars · Age: from >10 billion years to just formed · Many stars are located in star clusters 2. Interstellar Medium · Gas between stars · Nebulae, molecular clouds, and diffuse hot and cool gas in between 3. Galactic Center ± supermassive Black Hole 4. Dark Matter · The total mass of the far exceeds the mass with stars and interstellar medium put together · Hidden, invisible or missing component The matter in the spiral galaxies emits different kinds of radiation..... Stars: Halo vs. Disk · Stars in the disk are relatively young. · fraction of heavy elements same as or greater than the Sun · plenty of high- and low-mass stars, blue and red · Stars in the halo are old. · fraction of heavy elements much less than the Sun · mostly low-mass, red stars · Stars in the halo must have formed early in the Milky Way Galaxy's history. · they formed at a time when few heavy elements existed · there is little interstellar gas in the halo · star formation stopped long ago in the halo when all the gas flattened into the disk The interstellar gas Disk structure Empirically, the surface brightness declines with distance from the center of the galaxy in a characteristic way for spiral galaxies. For spiral galaxies, need first to correct for: • Inclination of the disk • Dust obscuration • Average over spiral arms to obtain a mean profile Corrected disk surface brightness drops off as: -R/h I R=I 0 e R where I(0) is the central surface brightness of the disk, and hR is a characteristic scale length. In practice, surface brightness at the center of many spiral galaxies is dominated by stars in the bulge. Central surface brightness of disk must be estimated by extrapolating inward from larger radii. s s e e n c t a h f g r i r u s b radius Typical values for the scale length are: 1 kpc h 10 kpc R In many, but not all, spiral galaxies the exponential part of the disk seems to end at some radius Rmax, which is typically 3 - 5 hR. Beyond Rmax the surface brightness of the stars decreases more rapidly - edge of the optically visible galaxy. The central surface brightness of many spirals is ~ constant, irrespective of the absolute magnitude of the galaxy! I 0 »21.65 mag arcsec-2 B Presumably this arises from physics of galaxy and / or star formation… Rotation of spirals Mostly don't rotate rigidly - wide variety of rotation curves depending on their light distribution. The one on the left is typical for lower luminosity disks, while the one on the right is more typical of the brighter disks like the Milky Way What keeps the disk in equilibrium ? Most of the kinetic energy is in the rotation in the radial direction, gravity provides the radial acceleration needed for the ~ circular motion of the stars and gas in the vertical direction, gravity is balanced by the vertical pressure gradient associated with the random vertical motions of the disk stars. Motion under gravity Motions of the stars and gas in the disk of a spiral galaxy are approximately circular (vR and vz << vφ). Define the circular velocity at radius r in the galaxy as V(r). Acceleration of the star moving in a circular orbit must be provided by a net inward gravitational force: V 2 r =- F r r r To calculate Fr(r), must in principle sum up gravitational force from bulge, disk and halo. For spherically symmetric mass distributions: • Gravitational force at radius r due to matter interior to that radius is the same as if all the mass were at the center. • Gravitational force due to matter outside is zero. Thus, if the mass enclosed within radius r is M(r), gravitational force is: GM r F =- r r2 (minus sign reflecting that force is directed inward) Bulge and halo components of the Galaxy are at least approximately spherically symmetric - assume for now that those dominate the potential. Self-gravity due to the disk itself is not spherically symmetric… Note: no simple form for the force from disks with realistic surface density profiles… Rotation curves of simple systems 1. Point mass M: GM V r = r Applications: • Close to the central black hole (r < 0.1 pc) • `Sufficiently far out’ that r encloses all the Galaxy’s mass 2. Uniform sphere: If the density ρ is constant, then: 4 M r = pr3 ρ 3 4 pGρ V r = r 3 Rotation curve rises linearly with radius, period of the orbit 2πr / V(r) is a constant independent of radius. Roughly appropriate for central regions of spiral galaxies. 3. Power law density profile: If the density falls off as a power law: −α r ρr =ρ 0 r 0 …with α < 3 a constant, then: 4 pGρ r α 0 0 α V r = r1− /2 3−α For many galaxies, circular speed curves are approximately flat (V(r) = constant). Suggests that mass density in these galaxies may be proportional to r-2. 4. Simple model for a galaxy with a core: Spherical density distribution: V 2 H 4 pGρr = r2 a2 H • Density tends to constant at small r • Density tends to r-2 at large r Corresponding circular velocity curve is: a H r V r =V 1− arctan H r a H Resulting rotation curve Navarro, Frenk and White profile Numerical simulations of the formation of dark matter halos by Navarro, Frenk and White (1997) suggest that the dark matter has a single `universal’ profile irrespective of mass: d ρr c = ρ 2 crit r /r 1r /r s s ρ δ …where crit, c and rs are all constants which can be calculated if we know the redshift at which a halo forms. Slope of NFW profile is -1 in center, -3 at large radius. Circular velocity rotation curves for NFW profile Measuring galaxy rotation curves Consider a galaxy in pure circular rotation, with rotation velocity V(R). Axis of rotation of the galaxy makes an angle i to our line of sight. If we measure the apparent velocity in the disk at an angle φ, measured in the disk, then line of sight (radial) velocity is: V R ,i V V R sin i cos f r = sys where Vsys is the systemic velocity of the galaxy. If we measure Vr across the galaxy, and can infer the inclination i, then obtain the full rotation curve V(R). Even if the galaxy is not resolved, measuring the amount of emission as a function of the line of sight velocity gives a measure of the peak rotation speed in the galaxy Vmax: W »2V sin i max Can use the Doppler shift of any convenient spectral line to measure the line of sight velocity: λ V obs r =1 λ c emit Optical: for nearby galaxies use Hα spectral line to measure rotation curves. Distant galaxies use spectral line of oxygen. Measures rotation of the stars. Radio: traditional measure of rotation curves. Use 21cm line of hydrogen. Measures rotation of the neutral hydrogen gas disk. Major advantage: detectable gas disk extends further out than detectable stellar disk. Examples of spiral galaxy rotation curves Typically flat or even rising out to many scale lengths of the exponential disk. If all the mass in these galaxies was provided by stars and -1/2 gas, expect that V(R) would drop as R at R > few x hR. Existence of flat (or even rising) rotation curves at these radii imply additional unseen mass - dark matter. Rotation curve measurements on their own only indicate that the dark matter must be: • Dynamically dominant at large radii (required proportion of dark matter ~50% in Sa / Sb galaxies, 80-90% in Sd galaxies). • Have a more extended distribution than either the stars or the gas. Note: no evidence for dark matter on the scale of the Solar System, or in the nearby Galactic disk. The evidence for dark matter is clear for galaxies with 21 cm HI rotation curves that extend far out, to R >> 3 h. maximum disk decomposition for NGC 3198: M/LB = 3.8 for disk observed Why are spiral disks so uniform? Why do the observed galaxies occupy such a a small fraction of possible structural configurations: size, surface brightness, shapes, etc.
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