This week at Astro 3303

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1 This week at Astro 3303 Pick up PE#7 HW#2 is being returned; we ll discuss it Please pass in HW#3 HW#4 is posted Usual collaboration rules apply Today: Interpreting CMDs; review of HW#2 CMDs Stellar populations in the Milky Way Star formation rate, initial mass function Determining the mass of the Milky Way Reading: For next week, Chap 3 of textbook Thurs: Galactic Center: star formation and the SMBH Optional: Remote Observing with Arecibo Sunday March 9pm

2 HW#2: set 1 The HYG stellar database: Hipparcos Yale Gliese V1.1 (there is a larger one!)

3 The HYG stellar database The Hipparcos catalog is the largest collection of high-accuracy stellar positional data, particularly parallaxes, which makes it useful as a starting point for stellar distance data. The Yale Bright Star Catalog contains basic data on essentially all naked-eye stars, including much information (such as the traditional Bayer Greek letters and Flamsteed numbers) missing from many other catalogs The Gliese catalog is the most comprehensive catalog of nearby stars (those within 75 light years of the Sun). It contains many fainter stars not found in Hipparcos. This database contains ALL stars that are either brighter than a certain magnitude cutoff (magnitude +7.5 to +9.0) or within 50 parsecs (about 160 light years) from the Sun.

4 HW#2: Set 2

5 HW#2: Set 3

6 HW#2: Set 3 PE#7: What might explain the differences?

7 HW#2: set 1 The HYG stellar database: Hipparcos Yale Gliese V1.1 (there is a larger one!) Let s take a different look

8 HYG V1.1 catalog

9 HYG V1.1 catalog

10 HYG V1.1 catalog The Malmquist bias (p118 in text): in a flux-limited sample, luminous objects (stars, galaxies) will always be overrepresented because they are visible at larger distances.

11 HW#2: Set 4: ZAMS

12 HW#2 The plot is basically the same with some offset in the color index because of the SED of stars varies. Setting the axes to be the same as before, you can see how the stretch-out in the (V-I) color occurs.

13 Cluster 1: So, we know from Problem 3 that m - M = 5 log D -5+ A. Set A=0. Then, we know how to convert m to M => M = m log (46.3) => M = m In TOPCAT, it is easy to apply this conversion. Click on Views/Column info. Add a column by clicking on the "+". Name=AbsVmag, expression= appvmag Now if you go to graphics and plot, the new column is there, and you can make the plot again replacing AppVmag with AbsVmag.

14 Cluster 1: The Hyades Clearly, this cluster is young - much of the MS is populated. The Hyades Nearest OC to Sun 47 pc (153 lyr) Age = 625 Myr Turnoff around (V-I) = 0.0 which is around A2; using the table in PE#4 gives age ~ 1 Gyr

15 Lewis AJ 131, 2538 Palomar 11 R.A. = 19h45m14.4 Dec = -08d00m26 Age /- 0.5 Gyr Distance = /- 0.4 kpc The Palomar clusters

Palomar 11 There must be a limiting magnitude of ~24. Estimating the distance requires measuring the shift of the main sequence relative to the ZAMS.

16 Palomar 11 There must be a limiting magnitude of ~24. Estimating the distance requires measuring the shift of the main sequence relative to the ZAMS. A crude value of the shift (from overlaying the plots) is about 15 mags. From before, m - M = 5 log D -5+ A. If we ignore A again (which may not be right!), we get 5 log D = m - M + 5 ~ 20 => log D = 20/5 = 4.0, so D = 10**4 pc = 10 kpc.

17 Palomar 11 A rough guess would be a turn-off somewhere around (V-I)= The tabulated values in the ZAMS file shows that (V-I) ~ 0.75 corresponds to a KO star. A KO star has a mass ~0.78 solar masses. Equation B6 in the Appendix gives τ(ms) ~ 8 x 10**9 [(M/Msun)**-2.5] years, or for M=0.78 msun, τ(ms) = 14.9 Gyr (older than the age of the universe). This contrasts with the value given in Lewis et al. of 10.4 Gyr. But, clearly, the cluster is old. We need a more precise definition of the T-O point!

18 Lewis AJ 131, 2538 Palomar 11 R.A. = 19h45m14.4 Dec = -08d00m26 Galactic latitude = -8d E(B-V) = 0.40 A_V = 1.05 mag!!! Age /- 0.5 Gyr Distance = /- 0.4 kpc Actually, extinction is important to correct for! (Our assumption was pretty bad )

Palomar 11 Distance: 14.3 kpc V TO ~ 20.88 ± 0.06 (V-I) TO ~ 1.

19 Palomar 11 Distance: 14.3 kpc V TO ~ ± 0.06 (V-I) TO ~ 1.03 ± 0.01 Age = 10.4 ± 0.5 Gyr Lewis et al. 2006, AJ 131, 2538

20 Sextans A Dwarf Irregular D=1.44 Mpc

21 CMDs of galaxies Only works for very nearby galaxies, for which individual stars can be resolved. Cannot assume all stars formed at the same time or under same conditions Must interpret in terms of star formation history (SFH)

22 CMD of Sextans A Also Dolphin et al. 2003, AJ 126, 187 Actively forming stars for last 2.5 Gyr; increased rate < 100 Myr ago. Some old stars (but images not deep enough to track details) SF found in 3 zones (high N HI ); youngest is single region < 20 Myr old

23 CMD of Sextans A Also Dolphin et al. 2003, AJ 126, 187

24 Spectral evolution

What determines the CMD/spectrum? The star formation rate SFR and how it may vary with time, SFR(t) Is SFR constant? Decreasing over time? A starburst? Episodic bursts?

25 What determines the CMD/spectrum? The star formation rate SFR and how it may vary with time, SFR(t) Is SFR constant? Decreasing over time? A starburst? Episodic bursts? The initial mass function IMF, which stipulates the number of stars per mass interval per unit volume that are created. (M) = dn dm = Const M -(1+x) In the solar neighborhood, we have the Salpeter IMF, x = 1.35 (Salpeter 1955) Other models (Miller; Miller & Scalo) allow multiple slopes over different mass ranges Need to specify the upper and lower mass cutoffs Is the IMF everywhere/time the same? Ed Salpeter ( )

26 Initial Mass Function (IMF) Higher mass *s are less abundance than lower mass *s; => logarithmic decrease in the number of higher mass *s # *s per unit M dn dn per unit V (M) = M dm = M d ln(m) x d ln(m) = dm M = M * /M x = 1 M dlog d log(m) = => Salpeter (1955) IMF Salpeter IMF derived for solar neighborhood & current epoch Other parameterizations have been proposed Scalo (1986) allowed for changes in slope x with M (M) M for M > 10 M M for 1 < M < 10 M M for 0.2 <M < 1 M Sometimes written as (M) M -(1+x) Major questions today: Is the IMF the same everywhere in the MW? Has the IMF evolved over time?

27 (Initial) Mass Function (M) = c M -(1+x) (Beware of different definitions!)

28 Kroupa (Science 2002) IMF # of *s w/ masses in (M, M+dM) formed at a given time in a given volume (M) = dn/dm = 1/M (M) M x with x = for 1.0 M < for 0.5 M < for 0.08 M < for 0.01 M < 0.08

Star formation rate (SFR) Suppose start with initial mass of gas M g,0 SFR => R(t, ) = rate at which the mass of gas is converted into stars per unit time Constraint: R(t, ) dt = M g,0 0

29 Star formation rate (SFR) Suppose start with initial mass of gas M g,0 SFR => R(t, ) = rate at which the mass of gas is converted into stars per unit time Constraint: R(t, ) dt = M g,0 0 Star formation models: Constant SFR until some time t =, then halt M R(t, ) = g,0 0 < t R(t, ) = 0 t If is short: burst Exponential R(t, ) = M g,0 exp (-t/ ) MW ~ 3 M ʘ /yr M82 ~ 10X R(MW)

30 Models vs. Data: Ellipticals Best-fitting age model and composite elliptical spectrum Fairly good fit over entire spectral range Note UV-rising branch, highlighting importance of accurate AGB modeling ELLIPTICALS: The oldest objects formed stars within 1-2 Gyr of the BB and have had little SF since. RED AND DEAD Instantaneous burst models => more on this later BC93 Fig. 5

orbits <=> the system has some prograde rotation.

31 Connection between kinematics & geometry spherical system (Pop II objects) thick disk (1) Thick disk of high-metallicity globular clusters (left-hand panel) is made of objects on low-inclination, nearly-circular orbits <=> the system has some prograde rotation. (2) Spherical system (right panel) has completely disorganized motions, no rotation on average; some clusters have prograge, some retrograde motion, Orbits are highly inclined.

32 Stellar populations in the MW

33 The mass of the Milky Way How do we determine the mass of the Milky Way from gravitational considerations? 1. Escape velocity of high velocity stars 2. Force law to the galactic plane 3. Rotation curve in the plane 4. Velocities of distant globular clusters and satellite galaxies Kinematic studies of the solar neighborhood by convention adopt coordinate system centered on the Sun x direction points toward the GC y direction points in the direction of Galactic rotation z direction points toward the NGP u = v x v = v y w = v z See: Table in PE#5 for values

34 Motion of stars near the Sun

35 High velocity stars High velocity stars are ones moving with high velocities with respect to the LSR. Defined historically as V LSR > 65 km/s. If a star had V > V esc, it would escape the MW. To escape (barely), the sum KE + PE = 0 -G M MW m ½ m * * v 2 * + = 0 R * Assume R=R * v * 2 v esc < ~ < 2GM MW R ~ 2GM MW R Hence, an estimate of the mass comes from observing the maximum velocity of HV stars. The RAVE Survey Smith MNRAS 379, 755. Our results provide a 90 per cent confidence interval of 498 < v esc < 608 km s 1, with a median likelihood of v esc = 544 km s 1. For R=15 kpc, V esc ~ 550 km/s By 2012: 500,000 stars M MW ~ 5.3 x M ʘ

36 Force Law in the Plane A star near the plane actually has some small component of velocity perpendicular to the plane ~ Z. (In the plane Z << Θ) Define the force exerted by the Galaxy in the z-direction to be K z, which is measured in a positive sense for positive values of z. The potential energy of an object a distance z from the Galactic plane is therefore given by: Φ z z K 0 dz' where (z) and K z are defined per unit stellar mass. If an object leaves the the Galactic plane perpendicularly with a velocity Z 0 and reaches a height z above the plane with a velocity Z, then: from the relation for conservation of energy. z' Z Φ z Z 2 0

37 Force Law in the Plane The surface density of material in the disk causes the z-motion of the stars to be constrained. Observe the motion of stars in the solar neighborhood. A ring of material of radius x and thickness dz exerts a gravitational pull upon a star at a distance z above the galactic plane (z=0). By symmetry, the only component of force that counts will be downward along the z axis => F z. The force variation with z depends on the surface density in the disk F z z = 4πGρ Fr r F r In the solar neighborhood, we find that stars with certain spectral types (ages) are characterized by different mean v z and found over different mean z-heights.

38 Finding K z from observations This method dates back to the 1960s but is also being updated by the surveys like RAVE. Gravitational force per unit mass in the z-direction z 2 d ln 0 K z Z0 dz Z 0 (km/s) z max (pc) Grav. Force in z- direction This provided the first evidence for dark matter, as about ½ of the local mass could not be accounted for.

39 Galaxy Rotation Curves V(R) => Assume circular orbits in disk plane Solid Body V(R) R Keplerian Decline V(R) R -1/2

40 Galaxy Rotation Curves

41 Rotation Curve Grav accel Orbital accel G M(R) R 2 = V 2 (R) R A flat rotation curve implies that the mass increases with radius. M(<R) = R V 2 (R) G We will return to this evidence for dark matter later For 8 kpc and 220 km/s, M(<R) ~ 8.9 x M ʘ

42 Distant Satellites The Milky Way has a number of small companions (globular clusters and dwarf satellites) that seem to orbit bound to its gravitational potential. Assume that the virial theorem holds (2 K.E. + P.E. = 0). As a first approximation, assume that all the globular clusters have the same mass, so K. E. gc s = 1 2 m < v2 > The K.E. of the entire system of N clusters is K. E. gc s = 1 2 mn < v2 > = 1 2 M < v2 > Assume the orbits are all isotropic (no flattening, no preferred direction), then the virial theorem holds as M < v 2 > GM2 R = 0 < v 2 > = GM R M = R < v2 > G

43 Distant Satellites In reality, rather than a single R and <v 2 >, we measure R i is the galactocentric distance V r,i is the radial velocity of the cluster or dwarf galaxie M est 4 GN N i=1 v ri 2 r i For N>>1, M est M true e.g., Watkins, Evans and An 2010, MNRAS 406, 264 Let s take a look!

44 Watkins, Evans & An (2010) MNRAS 406, 264 Radial velocities and distances of MW satellites

45 Watkins, Evans & An (2010) An interesting question: How do you make measurements of such exquisite precision???

46 Watkins, Evans & An (2010) Best fit for MW => M(R<300kpc) = 1.4 ± 0.3 x M ʘ

47 The Galactic Center is heavily extincted in the optical. The Galactic Center At 2.2 m: direct stellar emission from cooler stars (types K & M) that coexist in clusters with the hotter ones that heat the HII regions. Time-lapse imaging + spectroscopy allows reconstruction of orbital motions At 10 m: emission from dust which is heated by higher energy (optical) photons emitted by stars and then reemits in the IR. At 100 m, emission due to cooler dust, more extended, heated by energetic photons from hot stars over 10 s of parsecs distant. 1 = 0.04 pc assuming a distance of 8 kpc to the Galactic Center.

HII regions: the Stromgren Sphere In equilibrium in an HII region, there is a balance between ionizations and recombinations: free electrons and protons collide to form neutral HI; however the UV

48 HII regions: the Stromgren Sphere In equilibrium in an HII region, there is a balance between ionizations and recombinations: free electrons and protons collide to form neutral HI; however the UV photons from the *s are continuously breaking up these atoms. If N UV is the number of UV photons per second from a star capable of ionizing hydrogen, the ionization rate is then: R i = N UV The higher the density of photons and electrons, the greater the rate of recombination: R r = n e n p V => V is volume, and depends on Temp. For the volume, we can substitute a sphere of radius r s : R r = n p2 (4 r s3 /3) the Stromgren radius: -> N UV = n p2 (4 r s3 /3) or r s = (3/4 ) 1/3 (N UV ) 1/3 n p -2/3 The size of an HII region depends upon the rate at which a star gives off ionizing photons and the density of the gas.

49 The Galactic Center: Composite 1 = 2.4 pc Image~60 pc Combination of X- ray (blue), 25 (green) and 20 cm (red) observations Both thermal and non-thermal (synchrotron) components seen

Review of stellar evolution and color-magnitude diagrams

Review of stellar evolution and color-magnitude diagrams The evolution of stars can be used to study the properties of galaxies Very characteristic features pinpoint at the age (chemistry) of the stars