Tutorial 2: Generating Age Probability Distributions for Stars with Gaia Data

In the previous tutorial, we’ve calibrated the age–action spline model using a calibration sample of red giant branch stars with independent, asteroseismic ages.

Now, let’s use that spline model to generate age probabilities for other stars.

[1]:

import numpy as np
import matplotlib.pyplot as plt
import zoomies

%load_ext autoreload
%autoreload 2

Query Gaia

You will need to download the Gaia DR3 data for any stars you’re interested in. You can perform a mass query at https://gea.esac.esa.int/archive/ and read in the resulting table, or you can use astroquery to download the data right from your notebook, as we’ll do here:

[5]:

# Install astroquery if you haven't already!
from astroquery.gaia import Gaia
Gaia.MAIN_GAIA_TABLE = "gaiadr3.gaia_source"

[6]:

# Do your Gaia query or input a table of Gaia data

import astropy.units as u
from astropy.coordinates import SkyCoord

coord = SkyCoord(ra=280, dec=60, unit=(u.degree, u.degree), frame='icrs')
width = u.Quantity(0.5, u.deg)
height = u.Quantity(0.5, u.deg)

r = Gaia.query_object_async(coordinate=coord, width=width, height=height)

INFO: Query finished. [astroquery.utils.tap.core]

[7]:

# Filtering out stars without radial velocity
r = r[~r['radial_velocity'].mask]

Here’s the Gaia data for the couple of stars we’re interested in, as an astropy table:

[8]:

[8]:

Table length=2

dist	solution_id	designation	source_id	random_index	ref_epoch	ra	ra_error	dec	dec_error	parallax	parallax_error	parallax_over_error	pm	pmra	pmra_error	pmdec	pmdec_error	ra_dec_corr	ra_parallax_corr	ra_pmra_corr	ra_pmdec_corr	dec_parallax_corr	dec_pmra_corr	dec_pmdec_corr	parallax_pmra_corr	parallax_pmdec_corr	pmra_pmdec_corr	astrometric_n_obs_al	astrometric_n_obs_ac	astrometric_n_good_obs_al	astrometric_n_bad_obs_al	astrometric_gof_al	astrometric_chi2_al	astrometric_excess_noise	astrometric_excess_noise_sig	astrometric_params_solved	astrometric_primary_flag	nu_eff_used_in_astrometry	pseudocolour	pseudocolour_error	ra_pseudocolour_corr	dec_pseudocolour_corr	parallax_pseudocolour_corr	pmra_pseudocolour_corr	pmdec_pseudocolour_corr	astrometric_matched_transits	visibility_periods_used	astrometric_sigma5d_max	matched_transits	new_matched_transits	matched_transits_removed	ipd_gof_harmonic_amplitude	ipd_gof_harmonic_phase	ipd_frac_multi_peak	ipd_frac_odd_win	ruwe	scan_direction_strength_k1	scan_direction_strength_k2	scan_direction_strength_k3	scan_direction_strength_k4	scan_direction_mean_k1	scan_direction_mean_k2	scan_direction_mean_k3	scan_direction_mean_k4	duplicated_source	phot_g_n_obs	phot_g_mean_flux	phot_g_mean_flux_error	phot_g_mean_flux_over_error	phot_g_mean_mag	phot_bp_n_obs	phot_bp_mean_flux	phot_bp_mean_flux_error	phot_bp_mean_flux_over_error	phot_bp_mean_mag	phot_rp_n_obs	phot_rp_mean_flux	phot_rp_mean_flux_error	phot_rp_mean_flux_over_error	phot_rp_mean_mag	phot_bp_rp_excess_factor	phot_bp_n_contaminated_transits	phot_bp_n_blended_transits	phot_rp_n_contaminated_transits	phot_rp_n_blended_transits	phot_proc_mode	bp_rp	bp_g	g_rp	radial_velocity	radial_velocity_error	rv_method_used	rv_nb_transits	rv_nb_deblended_transits	rv_visibility_periods_used	rv_expected_sig_to_noise	rv_renormalised_gof	rv_chisq_pvalue	rv_time_duration	rv_amplitude_robust	rv_template_teff	rv_template_logg	rv_template_fe_h	rv_atm_param_origin	vbroad	vbroad_error	vbroad_nb_transits	grvs_mag	grvs_mag_error	grvs_mag_nb_transits	rvs_spec_sig_to_noise	phot_variable_flag	l	b	ecl_lon	ecl_lat	in_qso_candidates	in_galaxy_candidates	non_single_star	has_xp_continuous	has_xp_sampled	has_rvs	has_epoch_photometry	has_epoch_rv	has_mcmc_gspphot	has_mcmc_msc	in_andromeda_survey	classprob_dsc_combmod_quasar	classprob_dsc_combmod_galaxy	classprob_dsc_combmod_star	teff_gspphot	teff_gspphot_lower	teff_gspphot_upper	logg_gspphot	logg_gspphot_lower	logg_gspphot_upper	mh_gspphot	mh_gspphot_lower	mh_gspphot_upper	distance_gspphot	distance_gspphot_lower	distance_gspphot_upper	azero_gspphot	azero_gspphot_lower	azero_gspphot_upper	ag_gspphot	ag_gspphot_lower	ag_gspphot_upper	ebpminrp_gspphot	ebpminrp_gspphot_lower	ebpminrp_gspphot_upper	libname_gspphot
					yr	deg	mas	deg	mas	mas	mas		mas / yr	mas / yr	mas / yr	mas / yr	mas / yr																	mas				1 / um	1 / um	1 / um								mas					deg								deg	deg	deg	deg			electron / s	electron / s		mag		electron / s	electron / s		mag		electron / s	electron / s		mag							mag	mag	mag	km / s	km / s								d	km / s	K	log(cm.s**-2)	dex		km / s	km / s		mag	mag				deg	deg	deg	deg															K	K	K	log(cm.s**-2)	log(cm.s**-2)	log(cm.s**-2)	dex	dex	dex	pc	pc	pc	mag	mag	mag	mag	mag	mag	mag	mag	mag
float64	int64	object	int64	int64	float64	float64	float32	float64	float32	float64	float32	float32	float32	float64	float32	float64	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	int16	int16	int16	int16	float32	float32	float32	float32	int16	bool	float32	float32	float32	float32	float32	float32	float32	float32	int16	int16	float32	int16	int16	int16	float32	float32	int16	int16	float32	float32	float32	float32	float32	float32	float32	float32	float32	bool	int16	float64	float32	float32	float32	int16	float64	float32	float32	float32	int16	float64	float32	float32	float32	float32	int16	int16	int16	int16	int16	float32	float32	float32	float32	float32	int16	int16	int16	int16	float32	float32	float32	float32	float32	float32	float32	float32	int16	float32	float32	int16	float32	float32	int16	float32	object	float64	float64	float64	float64	bool	bool	int16	bool	bool	bool	bool	bool	bool	bool	bool	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	object
0.03294202574628697	1636148068921376768	Gaia DR3 2154901610573844864	2154901610573844864	241023460	2016.0	280.0656900806957	0.016397906	60.00257229273729	0.01832858	1.4395973611007848	0.017703537	81.31694	4.034647	-3.781376392246355	0.020791428	-1.4069714152136137	0.021559382	-0.13987689	-0.17148478	-0.16272342	0.06535884	0.28755578	0.00486031	-0.20837094	-0.15121393	-0.09816643	-0.008488968	313	9	312	1	1.5664704	355.76276	0.071118824	1.6831243	31	False	1.517273	--	--	--	--	--	--	--	36	26	0.03028327	39	16	0	0.0017206654	14.2530775	0	0	1.0627708	--	--	--	--	--	--	--	--	False	332	26596.06625197267	6.273805	4239.224	14.625323	34	13216.772791953359	14.825079	891.51447	15.035728	32	18934.12460635135	23.005768	823.0164	14.054783	1.2088591	0	0	0	1	0	0.9809456	0.41040516	0.5705404	-58.9981	3.5211964	2	20	1	16	5.3412848	--	--	848.42834	--	5250.0	4.0	0.0	111	--	--	--	13.703053	0.11823523	21	--	NOT_AVAILABLE	89.61278656239459	24.619597593406176	309.19731087572416	82.05259222492064	False	False	0	True	True	False	False	False	True	True	False	1.0310119e-13	5.149859e-13	0.9998932	5379.0903	5362.152	5393.7485	4.5733	4.5648	4.5806	0.0485	0.0305	0.0648	652.7858	646.5188	660.3986	0.1392	0.1265	0.15	0.1137	0.1033	0.1226	0.0603	0.0548	0.065	MARCS
0.034378304381720556	1636148068921376768	Gaia DR3 2154901988530967552	2154901988530967552	1404810341	2016.0	280.0194041542316	0.015531355	60.03298871744937	0.01771612	0.5369007191849855	0.017558102	30.578518	4.8870983	-4.8768787205310264	0.019893862	-0.31588292766908044	0.021310652	-0.10731452	-0.23620193	-0.11497756	0.05939605	0.29391325	-0.023874374	-0.18965203	-0.24747391	-0.037051436	0.10042425	280	0	277	3	0.33902383	288.02304	0.03911611	0.55264676	31	False	1.5930966	--	--	--	--	--	--	--	32	25	0.030482063	36	15	0	0.00040681817	32.448666	1	0	1.0133395	0.20663822	0.0930223	0.08154183	0.031603187	-136.6344	84.516	8.542825	8.555851	False	300	30990.814155148175	9.8583145	3143.622	14.459285	32	17775.656355814244	20.999525	846.47894	14.713978	33	19015.991510360494	19.759075	962.3928	14.050098	1.1871791	0	0	0	0	0	0.6638794	0.25469303	0.40918636	29.453352	10.561475	2	14	3	13	3.9535046	--	--	788.70197	--	6000.0	2.5	-0.75	111	--	--	--	14.051752	0.13647689	12	--	NOT_AVAILABLE	89.6401909216361	24.648574475550223	309.16325479158144	82.09051468241744	False	False	0	True	True	False	False	False	True	True	False	1.0282279e-13	5.135947e-13	0.9999208	6483.586	6460.9736	6514.4473	4.0976	4.0761	4.1173	-0.4975	-0.517	-0.479	1753.8871	1703.02	1810.7133	0.1891	0.1782	0.2041	0.1644	0.1548	0.1776	0.089	0.0838	0.0961	MARCS

Calculate Jz

You now need to calculate ln(Jz) (log of vertical action) for each Gaia star. The star must have a radial velocity. (Make sure you check the number of stars that have radial velocities from Gaia for the sample you’re interested in.)

TODO: You must input a table with at least two rows. It doesn’t work if you just input one row of Gaia data.

[9]:

# This function returns a table with three new
# columns for the action angles at the end: Jz, Jphi, and Jtheta

# This line may take a while for very large tables.

r_actions = zoomies.calc_jz(r)
r_actions

/opt/anaconda3/envs/zoomies_test_3/lib/python3.14/site-packages/gala/potential/potential/builtin/special.py:257: GalaFutureWarning: The MilkyWayPotential2022 class will be deprecated soon. Instead, use: MilkyWayPotential(version="v2") to get what is currently the MilkyWayPotential2022 class. Or, to always use the latest Milky Way model in Gala, you can call the class with no arguments MilkyWayPotential() or specify MilkyWayPotential(version="latest")
  warnings.warn(

Calculating actions with galpy...

[9]:

Table length=2

dist	solution_id	designation	source_id	random_index	ref_epoch	ra	ra_error	dec	dec_error	parallax	parallax_error	parallax_over_error	pm	pmra	pmra_error	pmdec	pmdec_error	ra_dec_corr	ra_parallax_corr	ra_pmra_corr	ra_pmdec_corr	dec_parallax_corr	dec_pmra_corr	dec_pmdec_corr	parallax_pmra_corr	parallax_pmdec_corr	pmra_pmdec_corr	astrometric_n_obs_al	astrometric_n_obs_ac	astrometric_n_good_obs_al	astrometric_n_bad_obs_al	astrometric_gof_al	astrometric_chi2_al	astrometric_excess_noise	astrometric_excess_noise_sig	astrometric_params_solved	astrometric_primary_flag	nu_eff_used_in_astrometry	pseudocolour	pseudocolour_error	ra_pseudocolour_corr	dec_pseudocolour_corr	parallax_pseudocolour_corr	pmra_pseudocolour_corr	pmdec_pseudocolour_corr	astrometric_matched_transits	visibility_periods_used	astrometric_sigma5d_max	matched_transits	new_matched_transits	matched_transits_removed	ipd_gof_harmonic_amplitude	ipd_gof_harmonic_phase	ipd_frac_multi_peak	ipd_frac_odd_win	ruwe	scan_direction_strength_k1	scan_direction_strength_k2	scan_direction_strength_k3	scan_direction_strength_k4	scan_direction_mean_k1	scan_direction_mean_k2	scan_direction_mean_k3	scan_direction_mean_k4	duplicated_source	phot_g_n_obs	phot_g_mean_flux	phot_g_mean_flux_error	phot_g_mean_flux_over_error	phot_g_mean_mag	phot_bp_n_obs	phot_bp_mean_flux	phot_bp_mean_flux_error	phot_bp_mean_flux_over_error	phot_bp_mean_mag	phot_rp_n_obs	phot_rp_mean_flux	phot_rp_mean_flux_error	phot_rp_mean_flux_over_error	phot_rp_mean_mag	phot_bp_rp_excess_factor	phot_bp_n_contaminated_transits	phot_bp_n_blended_transits	phot_rp_n_contaminated_transits	phot_rp_n_blended_transits	phot_proc_mode	bp_rp	bp_g	g_rp	radial_velocity	radial_velocity_error	rv_method_used	rv_nb_transits	rv_nb_deblended_transits	rv_visibility_periods_used	rv_expected_sig_to_noise	rv_renormalised_gof	rv_chisq_pvalue	rv_time_duration	rv_amplitude_robust	rv_template_teff	rv_template_logg	rv_template_fe_h	rv_atm_param_origin	vbroad	vbroad_error	vbroad_nb_transits	grvs_mag	grvs_mag_error	grvs_mag_nb_transits	rvs_spec_sig_to_noise	phot_variable_flag	l	b	ecl_lon	ecl_lat	in_qso_candidates	in_galaxy_candidates	non_single_star	has_xp_continuous	has_xp_sampled	has_rvs	has_epoch_photometry	has_epoch_rv	has_mcmc_gspphot	has_mcmc_msc	in_andromeda_survey	classprob_dsc_combmod_quasar	classprob_dsc_combmod_galaxy	classprob_dsc_combmod_star	teff_gspphot	teff_gspphot_lower	teff_gspphot_upper	logg_gspphot	logg_gspphot_lower	logg_gspphot_upper	mh_gspphot	mh_gspphot_lower	mh_gspphot_upper	distance_gspphot	distance_gspphot_lower	distance_gspphot_upper	azero_gspphot	azero_gspphot_lower	azero_gspphot_upper	ag_gspphot	ag_gspphot_lower	ag_gspphot_upper	ebpminrp_gspphot	ebpminrp_gspphot_lower	ebpminrp_gspphot_upper	libname_gspphot	Jz	Jphi	Jr
					yr	deg	mas	deg	mas	mas	mas		mas / yr	mas / yr	mas / yr	mas / yr	mas / yr																	mas				1 / um	1 / um	1 / um								mas					deg								deg	deg	deg	deg			electron / s	electron / s		mag		electron / s	electron / s		mag		electron / s	electron / s		mag							mag	mag	mag	km / s	km / s								d	km / s	K	log(cm.s**-2)	dex		km / s	km / s		mag	mag				deg	deg	deg	deg															K	K	K	log(cm.s**-2)	log(cm.s**-2)	log(cm.s**-2)	dex	dex	dex	pc	pc	pc	mag	mag	mag	mag	mag	mag	mag	mag	mag		km kpc / s	km kpc / s	km kpc / s
float64	int64	object	int64	int64	float64	float64	float32	float64	float32	float64	float32	float32	float32	float64	float32	float64	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	int16	int16	int16	int16	float32	float32	float32	float32	int16	bool	float32	float32	float32	float32	float32	float32	float32	float32	int16	int16	float32	int16	int16	int16	float32	float32	int16	int16	float32	float32	float32	float32	float32	float32	float32	float32	float32	bool	int16	float64	float32	float32	float32	int16	float64	float32	float32	float32	int16	float64	float32	float32	float32	float32	int16	int16	int16	int16	int16	float32	float32	float32	float32	float32	int16	int16	int16	int16	float32	float32	float32	float32	float32	float32	float32	float32	int16	float32	float32	int16	float32	float32	int16	float32	object	float64	float64	float64	float64	bool	bool	int16	bool	bool	bool	bool	bool	bool	bool	bool	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	float32	object	float64	float64	float64
0.03294202574628697	1636148068921376768	Gaia DR3 2154901610573844864	2154901610573844864	241023460	2016.0	280.0656900806957	0.016397906	60.00257229273729	0.01832858	1.4395973611007848	0.017703537	81.31694	4.034647	-3.781376392246355	0.020791428	-1.4069714152136137	0.021559382	-0.13987689	-0.17148478	-0.16272342	0.06535884	0.28755578	0.00486031	-0.20837094	-0.15121393	-0.09816643	-0.008488968	313	9	312	1	1.5664704	355.76276	0.071118824	1.6831243	31	False	1.517273	--	--	--	--	--	--	--	36	26	0.03028327	39	16	0	0.0017206654	14.2530775	0	0	1.0627708	--	--	--	--	--	--	--	--	False	332	26596.06625197267	6.273805	4239.224	14.625323	34	13216.772791953359	14.825079	891.51447	15.035728	32	18934.12460635135	23.005768	823.0164	14.054783	1.2088591	0	0	0	1	0	0.9809456	0.41040516	0.5705404	-58.9981	3.5211964	2	20	1	16	5.3412848	--	--	848.42834	--	5250.0	4.0	0.0	111	--	--	--	13.703053	0.11823523	21	--	NOT_AVAILABLE	89.61278656239459	24.619597593406176	309.19731087572416	82.05259222492064	False	False	0	True	True	False	False	False	True	True	False	1.0310119e-13	5.149859e-13	0.9998932	5379.0903	5362.152	5393.7485	4.5733	4.5648	4.5806	0.0485	0.0305	0.0648	652.7858	646.5188	660.3986	0.1392	0.1265	0.15	0.1137	0.1033	0.1226	0.0603	0.0548	0.065	MARCS	3.530247057416689	-1627.3115601530285	24.777721413012102
0.034378304381720556	1636148068921376768	Gaia DR3 2154901988530967552	2154901988530967552	1404810341	2016.0	280.0194041542316	0.015531355	60.03298871744937	0.01771612	0.5369007191849855	0.017558102	30.578518	4.8870983	-4.8768787205310264	0.019893862	-0.31588292766908044	0.021310652	-0.10731452	-0.23620193	-0.11497756	0.05939605	0.29391325	-0.023874374	-0.18965203	-0.24747391	-0.037051436	0.10042425	280	0	277	3	0.33902383	288.02304	0.03911611	0.55264676	31	False	1.5930966	--	--	--	--	--	--	--	32	25	0.030482063	36	15	0	0.00040681817	32.448666	1	0	1.0133395	0.20663822	0.0930223	0.08154183	0.031603187	-136.6344	84.516	8.542825	8.555851	False	300	30990.814155148175	9.8583145	3143.622	14.459285	32	17775.656355814244	20.999525	846.47894	14.713978	33	19015.991510360494	19.759075	962.3928	14.050098	1.1871791	0	0	0	0	0	0.6638794	0.25469303	0.40918636	29.453352	10.561475	2	14	3	13	3.9535046	--	--	788.70197	--	6000.0	2.5	-0.75	111	--	--	--	14.051752	0.13647689	12	--	NOT_AVAILABLE	89.6401909216361	24.648574475550223	309.16325479158144	82.09051468241744	False	False	0	True	True	False	False	False	True	True	False	1.0282279e-13	5.135947e-13	0.9999208	6483.586	6460.9736	6514.4473	4.0976	4.0761	4.1173	-0.4975	-0.517	-0.479	1753.8871	1703.02	1810.7133	0.1891	0.1782	0.2041	0.1644	0.1548	0.1776	0.089	0.0838	0.0961	MARCS	49.70225373350188	-2209.7850153513127	83.49405970242807

Age-Jz Relation Calibrated on RGB ages

We previously calibrated an age–vertical action spline model in Tutorial 1, and saved it in the "RGB_spline_model" directory. Let’s read that model back in here.

Alternatively, you can download the folder from Zenodo: 10.5281/zenodo.10048927

[10]:

spline_direct = "../RGB_spline_model/"

# Reading the pre-calibrated spline model back in
RGB_spline = zoomies.read(directory=spline_direct)

The KinematicAgeSpline.evaluate_ages() function evaluates dynamical ages for the ln(Jz) values in our table.

[11]:

# this function evaluates age predictions for a set of ln(Jz) values.

eval_grid, starRGB_eval_pdf = RGB_spline.evaluate_ages(np.log(r_actions['Jz']), eval_grid=np.linspace(0, 14, 1000))

100%|████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 2/2 [00:00<00:00, 1515.01it/s]

This is the age probabiltiy distribution for the first star in our Gaia table:

[12]:

plt.plot(eval_grid, starRGB_eval_pdf[0])

plt.xlabel('Age gyr')
plt.ylabel('PDF')
plt.title('lnJz = ' + str((np.log(r_actions['Jz'][0]))))

[12]:

Text(0.5, 1.0, 'lnJz = 1.2613678564329032')

../_images/tutorials_get_age_predictions_19_1.png

And here it is for the second star:

[13]:

# this is the age prediction for the second star in the table

plt.plot(eval_grid, starRGB_eval_pdf[1])

plt.xlabel('Age gyr')
plt.ylabel('PDF')

plt.title('lnJz = ' + str((np.log(r_actions['Jz'][1]))))

[13]:

Text(0.5, 1.0, 'lnJz = 3.906050278824991')

../_images/tutorials_get_age_predictions_21_1.png

[ ]: