CT-6: Determining the age of a star cluster¶

The final phase of these computational tutorials is to determine the age of the star cluster you've chosen to study. Astronomers determine star cluster ages by finding the isochrone that best matches the observed star cluster data.

If you skipped CT-5, download these M67 observed data and isochrone data to use in the following analysis.

Import Libraries¶

In [5]:

#Set up astropy and astroquery 
from astropy.table import Table,Column
#from astropy.coordinates import SkyCoord, Distance, CartesianRepresentation
#from astropy import units as u
from astropy.io import ascii

Physical Constants¶

In [18]:

M67_reddening = 0.059
M67_distMod = 9.97

Read in tables¶

In [12]:

M67_iso = ascii.read('data/m67_isochrones.dat')
M67_iso

Out[12]:

Z	log(age/yr)	M_ini	M_act	logL/Lo	logTe	logG	mbol	U	B	V	R	I	J	H	K	int_IMF	stage
0.019	6.0	0.09	0.09	-1.3414	3.4341	3.422	8.123	14.3	13.336	11.982	10.328	8.411	6.121	5.566	5.157	1.46765435	0
0.019	6.0	0.1	0.1	-1.2408	3.4417	3.3975	7.872	13.845	12.906	11.571	9.966	8.085	5.877	5.316	4.924	1.57040203	0
0.019	6.0	0.1158868	0.1159	-1.1067	3.4516	3.3672	7.537	13.269	12.357	11.046	9.499	7.664	5.552	4.979	4.611	1.7140224	0
0.019	6.0	0.12	0.12	-1.0749	3.4539	3.3597	7.457	13.141	12.233	10.926	9.392	7.567	5.476	4.897	4.536	1.74782515	0
0.019	6.0	0.13960719	0.1396	-0.9418	3.4638	3.3319	7.124	12.617	11.72	10.438	8.954	7.167	5.157	4.554	4.219	1.89318299	0
0.019	6.0	0.14	0.14	-0.9392	3.464	3.3313	7.118	12.607	11.711	10.429	8.946	7.16	5.15	4.547	4.213	1.89584959	0
0.019	6.0	0.16	0.16	-0.8241	3.473	3.3102	6.83	12.178	11.282	10.027	8.582	6.823	4.877	4.244	3.935	2.0211525	0
0.019	6.0	0.20108072	0.2011	-0.6404	3.4906	3.296	6.371	11.523	10.59	9.354	7.973	6.28	4.455	3.757	3.491	2.22647381	0
0.019	6.0	0.23470959	0.2347	-0.6006	3.5001	3.3615	6.272	11.316	10.331	9.102	7.769	6.114	4.381	3.661	3.409	2.35701632	0
0.019	6.0	0.25695479	0.257	-0.5154	3.5092	3.3522	6.059	11.025	9.998	8.778	7.485	5.859	4.193	3.437	3.204	2.42988706	0
0.019	6.0	0.27576727	0.2758	-0.5026	3.5133	3.3864	6.027	10.95	9.891	8.663	7.394	5.795	4.173	3.411	3.183	2.48466825	0
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
0.019	10.0	1.06063998	0.9589	3.2166	3.5106	0.1976	-3.271	4.025	2.189	0.625	-1.057	-3.029	-5.088	-5.991	-6.298	3.15640569	7
0.019	10.0	1.0606401	0.9588	3.2206	3.51	0.1912	-3.282	4.029	2.209	0.643	-1.048	-3.025	-5.099	-6.003	-6.311	3.15640569	7
0.019	10.0	1.06064022	0.9587	3.2239	3.5096	0.186	-3.29	4.031	2.224	0.658	-1.04	-3.02	-5.108	-6.013	-6.322	3.15640569	7
0.019	10.0	1.06064034	0.9586	3.2284	3.5089	0.1789	-3.301	4.034	2.246	0.678	-1.028	-3.012	-5.12	-6.026	-6.336	3.15640569	7
0.019	10.0	1.06064057	0.9585	3.2329	3.5083	0.1717	-3.312	4.038	2.268	0.699	-1.016	-3.005	-5.133	-6.04	-6.351	3.15640569	7
0.019	10.0	1.06064081	0.9584	3.2393	3.5074	0.1617	-3.328	4.043	2.3	0.729	-1.0	-2.994	-5.15	-6.059	-6.372	3.15640593	7
0.019	10.0	1.06064117	0.9582	3.2469	3.5063	0.1496	-3.347	4.049	2.338	0.765	-0.979	-2.981	-5.171	-6.081	-6.397	3.15640593	7
0.019	10.0	1.06064153	0.958	3.255	3.5051	0.1367	-3.368	4.056	2.38	0.804	-0.958	-2.967	-5.193	-6.106	-6.423	3.15640593	7
0.019	10.0	1.06064212	0.9576	3.2762	3.502	0.1029	-3.421	4.077	2.495	0.912	-0.896	-2.926	-5.252	-6.17	-6.493	3.15640616	7
0.019	10.0	1.0606426	0.9573	3.2989	3.4986	0.0664	-3.477	4.101	2.621	1.032	-0.824	-2.876	-5.313	-6.238	-6.568	3.15640616	7
0.019	10.0	1.06064272	0.9572	3.2993	3.4985	0.0658	-3.478	4.101	2.623	1.034	-0.823	-2.875	-5.314	-6.24	-6.569	3.1564064	8

In [11]:

M67_obs = ascii.read('data/m67.tab', delimiter='\t')
M67_obs

Out[11]:

No	Ref	V	B-V	U-B	N
1	1367	13.59	0.57	0.06	2
3	1367	12.89	0.54	0.08	2
4	1367	12.77	0.95	0.69	1
5	1367	13.05	0.6	0.07	1
6	1367	12.82	0.55	0.03	1
7	1367	14.05	0.61	0.11	2
9	1367	13.45	0.56	0.07	2
11	1367	13.62	0.66	0.09	1
13	1367	14.29	0.62	0.07	1
14	1367	13.9	0.59	0.01	1
15	59	13.61	0.55	0.04	1
...	...	...	...	...	...
8912	1367	13.02	0.54	0.04	1
8936	1367	13.84	0.62	0.04	1
8947	1367	13.46	0.43	-0.09	1
8958	1367	14.42	0.5	-0.06	1
8962	1367	13.01	0.55	0.05	1
8982	1367	14.27	0.66	0.19	1
8983	1367	14.39	0.64	0.16	1
8993	1367	15.65	0.6	-0.02	2
8996	1367	15.04	0.6	0.1	3
9015	1367	12.56	0.61	0.03	1
9021	1367	12.29	1.17	1.08	1

Plotting Setup¶

In [13]:

%config InlineBackend.rc = {}
import matplotlib
import matplotlib.pyplot as plt
%matplotlib inline
import seaborn

Plot Color Magnitude Diagram¶

Here we will construct a color-magnitude diagram, by

In [33]:

fig = plt.figure (figsize=(10,8))
a2 = fig.add_subplot(111)
a2.scatter(M67_obs['B-V'],M67_obs['V'])
a2.set_title("Color Magnitude Diagram",fontsize=24)
a2.set_xlabel("B-V")
a2.set_ylabel("V")

Out[33]:

<matplotlib.text.Text at 0x1f6c4358>

Calculate Isocron fit¶

The magnitudes listed in the Isochrone table are Absolute Magnitudes. To compare them with your observed data in Step 3, you'll need to convert them to Apparent Magnitudes using the Distance Modulus. You recorded your cluster's Distance Modulus in CT-5.

To convert from Absolute to Apparent Magnitude, add the Distance Modulus to the Absolute Magnitudes (i.e., Apparent V Magnitude = Absolute V Magnitude + Distance Modulus ). If needed, check out these helpful hints for one way to do this.

In [20]:

V_M67 = M67_iso['V']+  M67_distMod

You'll also need to account for the Reddening (the effect of dust between us and the cluster). You recorded your cluster's Reddening in CT-5.

Add the Reddening value to the color [bmag-vmag] values (i.e., corrected color = [bmag-vmag]+reddening). If needed, check out these helpful hints for one way to do this.

In [21]:

CorrectedColor = M67_iso['B'] - M67_iso['V'] + M67_reddening

In [48]:

fig2 = plt.figure (figsize=(12,10))
a = fig2.add_subplot(111)
a.scatter(M67_obs['B-V'],M67_obs['V'],c='yellow',s=20)
a.scatter(CorrectedColor,V_M67,c=-M67_iso['log(age/yr)'],cmap='RdBu',s=20,edgecolor='none',marker='v')
a.set_title("Color Magnitude Diagram with Isocrons",fontsize=24)
a.set_xlabel("B-V")
a.set_ylabel("V")

Out[48]:

<matplotlib.text.Text at 0x22078f98>

In [ ]: