ASTRONOMY 460: PROJECT INTRO - GALACTIC ROTATION CURVE Snežana Stanimirović, October 6, 2014 1. Introduction This project has two goals: we want to measure the Milky Way (or Galactic) rotation curve by obtaining fully sampled observations at b = 0 deg, and we want to measure the l V r diagram for the same longitude range (future observations will extend this to cover the whole longitude range visible from Madison). Having the information on how fast stars and clouds of gas orbit around the Galactic Center in the disk of the Milky Way, we can do several important things. The most important one is of course related to understanding of dark matter. As Astronomy 330 and 320 cover details of various derivations (but do not go into details of how you do this practically), we will focus on the practical aspects (and doing the measurements). Details can be found in An introduction to modern astrophysics, Carroll & Ostlie Chapter 24, and Galaxies in the Universe, Sparke & Gallagher, Chapter 2.3. New features this year relative to previous years: (1) we want to sample well our observations by observing every 3 degrees in longitude (Nyquist sampling); (2) we want to try a new method for baseline calibration - this should make our data reduction and velocity measurements more robust; (3) we will be working with a larger number of spectra so data processing scripts should be well organized and streamlined to essentially handle different data files easily. 2. Basic Equation and Applications Under a simple assumption that stars and neutral hydrogen (HI) clouds in the disk of the Milky Way (MW) move along circular orbits around the Galactic Center (GC), we can easily express the radial velocity component of star/cloud orbital motion (V r ): ( V V r = R sinl R V ) (1) R where l is the Galactic longitude of the observed star/cloud, V and V are the orbital velocities of the star/cloud and the Sun, respectively, and R and R are the distances from GC to the star/cloud and the Sun, respectively.
2 This main equation is extremely useful and can be used in many ways. If we know the Galactic rotation curve, V(R), we can use this equation to estimate the radial velocity we expect to measure in different regions of the MW. If we plot V r as a function of Galactic longitude l we get something called the l V r diagram (Fig. 24.10 in Carroll & Ostlie). Everything co-rotating with the MW disk will have a special, well-defined appearance in this digram so it is very easy to see objects that have velocities inconsistent with the Galactic rotation model (e.g. high velocity clouds that are likely being accreted from the satellite galaxies, nearby galaxies, etc.). Please see class slides for examples. If we know the Galactic rotation curve, V(R), and we measure V r, we can estimate the Galactocentric distance R to the particular star/cloud; this is directly related to the distance between the Sun and the star/cloud, so essentially we can get an estimate of the object s distance this way. Of course this distance estimate depends on our initial assumption of simple circular motions etc., but for many stars/clouds is the only distance estimate we can ever make so it is very important. Such distances are called kinematic distances as they depend on the assumed rotation curve. If we know the Galactic rotation curve, V(R), we can estimate the total mass of the MW M R inclosed within a particular Galactocentric radius R: where G is the gravitational constant. M R = V 2 R G (2) The shape of the rotation curve is telling us about the distribution of mass in the MW. TheMWrotationcurvestaysflattoaboutR = 10kpc, withsomeindicationthatitincreases beyond this radius. According to Newtonian mechanics, if most of the mass is distributed within particular radius (as we observe that stellar disk goes up to a certain radius), than beyond this radius we would expect orbital velocity R 1/2. As observational data do not support this in the case of the MW and most other spiral galaxies, this suggests the existence of dark matter that extends beyond visible galaxy disks. Clearly, V(R) has many important implications, so how do we measure it? 3. Measuring V(R) Looking at equation (1), if we have objects of known distance and therefore R in the disk of the MW, we can measure their radial velocity and invert equation (1) to estimate the orbital velocity V. However, in reality this is not easy to do. Observing stars right in
3 the MW disk is very hard because of interstellar extinction - dust grains absorb light at optical wavelengths underestimating greatly stellar flux. Observations of HI clouds at radio wavelengths are much better as radio does not suffer from extinction (the extinction law for dust reddening, first worked out at the Washburn Observatory in 1958, says that extinction is inversely proportional to the wavelength), but estimating distances to HI clouds is very very difficult. In addition, the best and most direct way to measure distance to astronomical objects is through trigonometric parallax, but this method works only for reasonably close objects so is very limited. However,thereisasetofpointsintheMWdiskforwhichwecaneasilyestimatedistance based on simple purely geometrical considerations. These points are called tangent points, and the whole method for measuring the Galactic rotation curve is called the Tangentpoint Method. Tangent points are located in the inner Galaxy and are the closest to GC for any longitude direction. Tangent points are located in the Galactic plane on the circle passing through GC and the Sun and having a diameter of R. For each tangent point, the geometry is very simple resulting in: R = R sinl (3) V = V r +V sinl (4) By knowing the Galactic longitude of the observed position, measuring the radial velocity along the line of sight, and taking accepted values for R and V, we can estimate V(R). Tangent points exist only for 0 < l < 90 deg and 270 < l < 360 deg. However, the expected V r for 75 < l < 90 deg and 270 < l < 295 deg is very small and close to 0 km/s so it is best to avoid those longitudes. In addition, close to the Galactic center (l within 20 deg from the GC direction) the orbital motions can be highly non-circular as the density is very high and other dynamical features like the stellar bar exist. So, for us the best range is: 20 < l < 75 deg. 4. Project Observations Tosamplewelltherotationcurve, wewanttoobservelongituderange: 20to80deg(270-360 deg can also be used but we can not observe these positions from the north hemisphere), with a step of 3 degrees. There are 20 positions, and 8 of us including me. Each of you will observe three Galactic positions (I will help if additional verifications are needed). We will process and analyze individually data files, following the same data reduction strategy, and then combine all results to produce the final plot of the rotation curve.
4 PLAN: Clayton (l = 20,23,26 deg), Erich (l = 29,32,35 deg), David (l = 38,41,44 deg), Julia (l = 47,50,53 deg), Leah (l = 56,59,62 deg), Jenni (l = 65,68,71 deg), Sohee (l = 74,77,80 deg). Based on my Az/El vs LST plots, looks like the best window for our observations is around LST = 15-22 hrs, which corresponds to late afternoons CST = 16-22 hrs. YOUR OBSERVING SCRIPT: You should have a single observing script for your 3 rotation positions but save observations for each position in a separate data file. So, you should open 1st data file, set central frequency to 1420.405 and use observing mode 4, go to a selected Galactic position, fire a noise diode, then integrate for 300 sec, and close the observing file. Then in the same script and in exactly the same way execute additional positions. FILE NAMING Example command file: snez rotation.cmd; example data file: snez l50 6sep14.rad (it s nice to know when were observations obtained in case we have to repeat them). Please keep your files/scripts in your class directory and I will copy them from there to OBSERVER. 4.1. Observing sessions We will have two observing sessions - Oct 13 and 20 from roughly 4:30-6pm. This is a good time window for all of our positions. Please have your scripts ready! 5. Data processing To look at our data files, process them into something meaningful, and do calculations of V r and V(R), we will use a commercial package called IDL. We will learn and practice basics of IDL, and will then together learn how to read SRT data files within IDL. But here is a summary of the data processing steps we will need to do with our data: 1. Read a data file in IDL and place data in a 2-dimensional array representing a stack of spectra (each row of the array will be a single HI spectrum). 2. To convert from artificial telescope units to brightness temperature, and for baseline
5 calibration we will use our noise diode observations. Will talk about this in class. 3. Average all HI spectra to produce a single HI spectrum. Your y-axis is now Brightness Temperature in units of Kelvin. Your x-axis is Frequency. Use the Doppler equation to convert from Frequency to Topocentric Radial Velocity. Topocentric means the spectrum is measured relative to our telescope. To convert from Topocentric to LSR Velocity add a velocity factor I will provide. 4. Fit a polynomial function to the portion of the spectrum unaffected by HI emission to remove the contribution form electronics noise and blank sky. Make a nice plot of the resultant HI spectrum. 5. Measure the radial velocity corresponding to the tangent point along that longitude direction. Also, estimate the uncertainty for your measurement. See Section 6 on how we are going to do this. 6. From your spectrum, calculate R and V r. 7. Using other class measurements of R and V r, make a plot of the Galactic rotation curve. Plot uncertainties. 8. Attheendwewillmap/gridallspectraintoadatacubetoexaminethel V r structure. 6. Measuring V r from your spectrum Based on equation (1), radial velocity corresponding to the tangent point along particular line of sight (or Galactic longitude l) is the highest radial velocity in the HI spectrum. There are many approaches in the literature regarding how exactly to measure this. For example, as peaks in the HI spectrum correspond to individual clouds, one approach is to take the radial velocity of the latest (in terms of velocity) peak. As many small clouds can blend to make a broader feature, another approach is to take a particular intensity threshold and measure the largest velocity in the spectrum above that threshold. Yet, third approach would be to model the whole HI spectrum as a composition of several Gaussian functions and then select the highest velocity component. All these methods can work and have been used in the past. We will essentially apply two different methods to estimate both the radial velocity and the uncertainty on our measurement:
6 1. Using the range of channels without significant HI emission, we will measure the noise level σ in our spectrum. We will then take as V r,1 the largest velocity in the spectrum above the threshold of 1-σ. 2. In the second approach, we will take as V r,2 the highest velocity corresponding to one of the clear peaks in the spectrum. 3. Velocity to be used in our calculations is: V r = V r,1 +V r,2 2 σ Vr = V r,2 V r,1 2 (5) (6) Finally, from V r we will subtract 12.3 km/s to account for random motions of HI clouds along the line of sight as we are interested only in the contribution from Galactic rotation. The random velocity contribution was measured by McClure-Griffiths et al. (2007). We will talk more about each step as we keep working on our project. Please don t panic! 7. Galactic Standards: V and R For our calculations we will use the Galactic constants: R = 8.5kpc and V(R ) = 220kms 1 for Sun s distance from the Galactic center and its circular velocity (IAU recommended standard in 1985).