sign in sign up
<<
Home , Beehive Cluster

Investigating the Beehive Cluster with Gaia Blaise Whitesell — Astronomy Capstone 2019

In this problem set, we will explore the capabilities of the publicly available data from Gaia DR2, which can be found at http://gea.esac.esa.int/archive/ or queried directly from within Python. We will focus on a single target: the Beehive cluster (M44, also known as Praesepe or NGC 2632). This is located at a distance of roughly 200 pc in the with coordinates (α, δ) = (130.1°, 19.67°). We will download Gaia data in the vicinity of the cluster, select only the belonging to the cluster, and then characterize the properties of those stars in the cluster.

1. Getting Data

For our analysis we need these columns from the Gaia DR2 database gaiadr2.gaia_source: source_id A numeric identifier for the object ra (degrees) dec Declination (degrees) parallax Parallax (mas) pmra Proper motion in right ascension (mas/yr) pmdec Proper motion in declination (mas/yr) phot_g_mean_mag Magnitude in Gaia G band (mags) bp_rp Gaia BP–RP color (mags) Select objects within 4 degrees of the cluster center. At the rough distance of the Beehive cluster, how many does that correspond to? We want to include objects at least that far in front and behind the cluster. Since we don’t know distances as precisely, we should expand the range by a factor of 3 or 4 to avoid missing cluster stars. What parallaxes (in mas) does this distance range correspond to? Use those parallax values as conditions to exclude objects far away from the cluster. Also add some conditions to select only good quality data. Let’s say less than 5% parallax error, and less than 0.05 mags uncertainty in the faintest band BP. (Within these constraints, the uncertainties in position and proper motion will also be low.) At the cluster distance, what does a 5% parallax uncertainty correspond to? Here is a sample SQL query including these conditions that can be executed in Python:

1 import os 2 from astropy.table import Table 3 from astroquery.gaia import Gaia 4 5 query= """ 6 SELECT source_id,ra,dec,parallax,pmra,pmdec,phot_g_mean_mag,bp_rp 7 FROM gaiadr2.gaia_source 8 WHERE 1 = CONTAINS(POINT('ICRS', ra, dec),

1 2

9 CIRCLE('ICRS', 130.1, 19.67, 4.0)) 10 AND parallax > 4 11 AND parallax < 7 12 AND parallax_over_error > 20 13 AND phot_bp_mean_flux_over_error > 20; 14 """ 15 filename= 'beehive.dat' 16 if not os.path.isfile(filename): 17 Gaia.launch_job_async(query, output_file=filename, 18 dump_to_file=True, verbose=True) 19 results= Table.read(filename) Hints: Depending on server demand, the query may take several minutes to complete. This implementation only launches the query if the filename doesn’t exist, so you can rerun the code and use data already downloaded. The columns of the table can be accessed like so: results['source_id']. • How many objects did your query return?

2. Determining Cluster Membership

Plot a sky projection of the points in your data sample, with right ascension on the x-axis and declination on the y-axis. Hints: The distribution should be circular. If yours is not, make sure you have an equal aspect ratio on your plot (e.g. .set_aspect('equal')). Reduce the size of the points (e.g. s=1) so it is possible to see where they are denser. Finally, reverse the x-axis (e.g. .invert_xaxis()) to match how the cluster appears on the sky. • Are there more stars at the center? p Now we want to slice our data by angular distance from the center. Calculate r = x2 + y2, where x and y are the offsets from the center in α and δ. Hints: Remember the cos(δ) term! Also remember that NumPy trig functions take arguments in radians (e.g. np.cos(np.radians(dec)) if you have dec in degrees). Try three slices: (r < 1°), (1° < r < 3°), and (3° < r < 4°). For each of these slices, make a histogram of the distances to the stars in the slice. You will need to calculate distance from parallax. Hints: Use an appropriate number of bins; ten is certainly too few. Also ensure that all three histograms use the same bins. If you plot the histograms separately, make sure the axis limits are the same on each. If you plot the histograms on the same axis, be careful that one doesn’t get lost behind another. • Does the histogram of the central field look different from that of the outer field? • How does the middle region compare? • Based on the distribution of stars in the center region, calculate an estimate of the distance to the cluster. 3

Make a scatter plot of the α and δ components of proper motion, displaying your slices in different colors. Hints: You will probably need to zoom in to see structure. Choose appropriate axis limits. It may be helpful to make a second plot on a smaller scale. • Do the stars at the center have a distribution different from that of the field? Explain why. Choose reasonable upper and lower bounds for each component to select stars most likely to be part of the cluster. To determine the spatial extent of the cluster, we will make a projected density profile. (The parallax uncertainties are not low enough to compare line-of-sight distances from the center with projected distances from the center on the scale of the cluster.) Convert your angular distance from the cluster center to a physical distance in parsecs, and bin the data into 0.5 pc bins. Plot the resulting density profile, with projected radius on the x-axis and number of stars per square on the y-axis. Hints: To find the number density, calculate the number of stars in each bin as well as the volume of each bin. Remember to slice the data to only include objects with proper motions within the bounds you determined. Are linear or logarithmic axes appropriate for this plot? Based on your plot, estimate a reasonable cutoff value in projected distance corresponding to the radius of the cluster. Slice your dataset to include only objects within this projected radius. We can’t directly slice to include only objects with parallaxes placing them within this distance from the center, because the parallax errors are higher. A typical parallax error is about 3 pc. To avoid excluding too many cluster stars due to parallax error, use a line-of-sight distance cutoff 3 pc greater than your projected distance cutoff. Slice your dataset to include only objects within that parallax range. Now you have conditions for cluster membership in projected distance, line-of-sight distance, and proper motion. • How many stars do you find to be part of the cluster? Go back and make another plot of the sky projection, this time highlighting the cluster stars. Compare the density of cluster objects to background objects in the center of the sample and on the edges of the sample. Do your results make sense? Does the background density appear uniform? Also make another distance histogram. Do the objects you found to be part of the cluster follow a Gaussian distribution along the line of sight? Hint: If your distribution has fat tails, you might be including too many background objects. Conversely, if the distribution looks like the tails have been chopped off, you might be excluding too many cluster objects. Adjust your radius cutoff value accordingly. • Describe the radius cutoff you used and how you chose it. 4

3. Cluster Properties

Once you are satisfied with your chosen conditions, use the resulting sample of cluster stars to determine properties of the cluster. • What is the center of your cluster sample? How does it compare to the given value of (α, δ) = (130.1°, 19.67°)? • Refine your estimate of the cluster distance. Is it similar to your first estimate? Do you think repeating the analysis with the new value would affect your results? • Calculate the mean proper motion (in mas/yr) and transverse spatial velocity of the cluster (in km/s), in (α, δ) components. Now construct a color-magnitude diagram of the cluster, calculating the absolute magnitude of each from its parallax. You will also need to correct G magnitude for extinction and BP–RP color for reddening. In the vicinity of the Beehive cluster, E(B–V) = 0.027 mags. The extinction coefficients for the Gaia bandpasses are AG = 2.74 E(B–V), ABP = 3.374 E(B–V), and ARP = 2.035 E(B–V). These offsets will not change the shape of the CMD, but will allow accurate comparison to theoretical stellar populations so we can determine properties of the cluster. Also plot where the would fall with MG, = 4.67, (BP–RP) = 0.82. • Describe what types of stars you see in the different parts of the color-magnitude diagram. • Compare to a published color-magnitude diagram such as Figure 2 on page 4 of Yang, Chen, & Zhao 2015. https://ui.adsabs.harvard.edu/abs/2015AJ....150..158Y/abstract Isochrones are provided for a range of possible ages and metallicities of the cluster. The necessary columns in the datafiles are G, G_BP, and G_RP, which are the magnitudes in each band. Overplot isochrones for young, 100 Myr populations of metallicities Z = 0.005, Z = 0.01, and Z = 0.02. • What is the approximate metallicity of the cluster? Overplot isochrones of your chosen metallicity for populations of ages 300 Myr, 1 Gyr, 3 Gyr, and 10 Gyr. • Approximately how old do you think the cluster is? Plot the cumulative luminosity profile L(R) for the cluster. Hints: This is a function of projected radius. When calculating the total light within a radius, you will need to sum the luminosities of each star and convert back to a magnitude. Never add magnitudes! A star with the same absolute magnitude as the Sun has a luminosity of 1 L . Bins of 0.5 pc are a reasonable choice.

• Does the luminosity appear to reach a finite limit? Calculate the total luminosity (in L ) and absolute magnitude of the cluster. • What is the half-light radius of the cluster, in arcminutes and in parsecs? 5

4. Advanced Investigation

We successfully fit an isochrone to our color-magnitude diagram for the cluster. This means we can predict properties of the cluster stars using properties of the nearest isochrone stars. Of course, this technique is only valid for stars near the isochrone. Using the masses of isochrone stars, we will calculate the masses of the cluster stars along the . Since the isochrone consists of discrete points, we must interpolate it first. Using a spline to fit the isochrone which best fits the stellar population, construct a numerical function of predicted BP–RP color given absolute G magnitude. Hint: You will need to restrict the isochrone to the main sequence and traverse in the direction of monotonically increasing G magnitude. Calculate the predicted color of each object in the region of your spline. • Is there a pattern to the residuals? • What objects might have colors different from the isochrone prediction? Next, perform another spline interpolation to construct a numerical function of stellar mass given absolute G magnitude. Then use this function to calculate the mass of each star along the isochrone. Hint: Slice the data to exclude objects that do not lie on the isochrone. • Calculate the total mass of main sequence stars in the cluster. Plot the mass function: log(N(M)) per bin of log(M). Also plot where the Sun would fall. • Fit a slope over the region you think your mass function is valid. • How does your mass function compare to a Salpeter IMF?