Abstract

Gaia measures the five astrometric parameters for stars in the Milky Way, but only four of them (positions and proper motion, but not parallax) are well measured beyond a few kpc from the Sun. Modern spectroscopic surveys such as APOGEE cover a large area of the Milky Way disk and we can use the relation between spectra and luminosity to determine distances to stars beyond Gaia's parallax reach. Here, we design a deep neural network trained on stars in common between Gaia and APOGEE that determines spectro-photometric distances to APOGEE stars, while including a flexible model to calibrate parallax zero-point biases in Gaia DR2. We determine the zero-point offset to be -52.3 +/- 2.0uas when modeling it as a global constant, but also train a multivariate zero-point offset model that depends on G, G_BP - G_RP color, and T_eff and that can be applied to all 139 million stars in Gaia DR2 within APOGEE's color--magnitude range. Our spectro-photometric distances are more precise than Gaia at distances ≈2kpc from the Sun. We release a catalog of spectro-photometric distances for the entire APOGEE DR14 data set which covers Galactocentric radii 2kpc<≈R<≈19kpc; ≈150,000 stars have <10% uncertainty, making this a powerful sample to study the chemo-dynamical structure of the disk. We use this sample to map the mean [Fe/H] and 15 abundance ratios [X/Fe] from the Galactic center to the edge of the disk. Among many interesting trends, we find that the bulge and bar region at R<≈5kpc clearly stands out in [Fe/H] and most abundance ratios.

Getting Started

This repository is to make sure all figures and results are reproducible by anyone easily for this paper.

If Github has issue (or too slow) to load the Jupyter Notebooks, you can go http://nbviewer.jupyter.org/github/henrysky/astroNN_gaia_dr2_paper/tree/master/

To get started, this paper uses astroNN developed by us and tested with astroNN 1.1.0 (Not yet released). Python 3.6 or above and reasonable computational resource is required. Extensive documentation at http://astroNN.readthedocs.io and quick start guide at http://astronn.readthedocs.io/en/latest/quick_start.html

astroNN Apogee DR14 Distance data is available as apogee_dr14_nn_dist.fits

Some notebooks make use of milkyway_plot to plot on milkyway and gaia_tools to do query.

Some notebooks make use of data from Deep learning of multi-element abundances from high-resolution spectroscopic data [arXiv:1804.08622][ADS] and its data product available at https://github.com/henrysky/astroNN_spectra_paper_figures

To continuum normalize arbitrary APOGEE spectrum, see: http://astronn.readthedocs.io/en/latest/tools_apogee.html#pseudo-continuum-normalization-of-apogee-spectra

A legacy version of data file available as apogee_dr14_nn_dist_0562.fits in which 56.2uas offset is applied directly to train, and its data model will not be provided.

Jupyter Notebook

Incomplete list of notebook

• Datasets_Data_Reduction.ipynb

  You should check out this notebook first as it describes how to reproduce the exactly same datasets used in the paper
• Training.ipynb

  It provides the code used to train astroNN_no_offset_model, astroNN_constlant_model and astroNN_multivariate_model

  It provides a minimal model code (in pure Tensorflow and pure PyTorch) to help you understand what is the core logic of the model
• Offset_Gaia.ipynb

  It describes the result of Gaia offset
• Inference.ipynb

  It describes inference, NN performance and NN uncertainty. And how to generate distances for the whole APOGEE DR14.
• Jacobian.ipynb

  It describes jacobian analysis.
• MW_Science.ipynb

  It describes some MilkyWay Science plots
• nn_figure1_draw_io

  Source for Figure 1 in paper for the NN model, can be opened and edited by draw.io

Neural Net Models and Quantity Conversion

It is recommend to use model ends with _reduced for example, using astroNN_constant_model_reduced instead of astroNN_constant_model

• astroNN_no_offset_model is a astroNN's ApogeeBCNN() class model to infer Ks-Band fakemag without offset model.
• astroNN_constant_model is a astroNN's ApogeeDR14GaiaDR2BCNN() class model to infer Ks-Band fakemag with a constant offset model
• astroNN_constant_model_reduced is a astroNN's ApogeeBCNN() class model extracted from astroNN_constant_model
• astroNN_multivariate_model is a astroNN's ApogeeDR14GaiaDR2BCNN() class model to infer Ks-Band fakemag with a multivariate offset model
• astroNN_multivariate_model_reduced is a astroNN's ApogeeBCNN() class model extracted from astroNN_multivariate_model

To load the model, open python outside your_astroNN_model

from astroNN.models import load_folder

# replace the name of the NN folder you want to open
neuralnet = load_folder('astroNN_model')
# neuralnet is an astroNN neural network object, to learn more;
# http://astronn.readthedocs.io/en/latest/neuralnets/basic_usage.html

# To get what the output neurones are representing
print(neuralnet.targetname)

To convert NN Ks-band fakemag (a pseudo luminosity scale) and its uncertainty to astrometric quantities, you can

from astroNN.gaia import fakemag_to_pc, fakemag_to_parallax

# outputs carry astropy unit
parsec, parsec_uncertainty = fakemag_to_pc(nn_fakemag, ks_magnitude, nn_fakemag_uncertainty)
# outputs carry astropy unit
parallax, parallax_uncertainty = fakemag_to_parallax(nn_fakemag, ks_magnitude, nn_fakemag_uncertainty)

# OR you can provide input without uncertainty
# output carries astropy unit
parsec = fakemag_to_pc(fakemag, ks_magnitude)
# output carries astropy unit
parallax = fakemag_to_parallax(fakemag, ks_magnitude)

To convert NN Ks-band fakemag (a pseudo luminosity scale) to log10 solar luminosity, you can

from astroNN.gaia import fakemag_to_logsol

logsol = fakemag_to_logsol(fakemag, band='Ks')

astroNN Apogee DR14 Distance & Data Model

apogee_dr14_nn_dist.fits is compiled prediction with astroNN_constant_model_reduced on the whole Apogee DR14. The code used to generate this file is described in Inference.ipynb

To load it with python and to initialize orbit with galpy (requires galpy>=1.4 and astropy>3)

from astropy.io import fits

# read the data file
f = fits.getdata("apogee_dr14_nn_dist.fits")

# ========= see our paper for the most accurate descriptive data model ========= #

# APOGEE and NN data, contains -9999. for unknown/bad data
apogee_id = f['apogee_id']  # APOGEE's apogee id
location_id = f['location_id']  # APOGEE DR14 location id
ra_apogee = f['ra_apogee']  # J2000 RA
dec_apogee = f['dec_apogee']  # J2000 DEC
fakemag = f['fakemag']  # NN Ks-band pseudo luminosity prediction
fakemag_error = f['fakemag_error']  # NN Ks-band pseudo luminosity uncertainty
nn_parsec = f['dist']  # NN inverse parallax in parsec
nn_parsec_uncertainty = f['dist_error']  # NN inverse parallax total uncertainty in parsec
nn_parsec_model_uncertainty = f['dist_model_error']  # NN inverse parallax model uncertainty in parsec
nn_plx = f['nn_parallax']  # NN parallax in mas
nn_plx_uncertainty = f['nn_parallax_error']  # NN parallax uncertainty in mas
nn_plx_model_uncertainty = f['nn_parallax_model_error']  # NN parallax model uncertainty in mas
weighted_dist = f['weighted_dist']  # inv var weighted NN & Gaia distance in parsec
weighted_dist_uncertainty = f['weighted_dist_error']  # inv var weighted NN & Gaia distance uncertainty in parsec

# Gaia DR2 Data, contains -9999. for unknown/bad data
ra = f['ra']  # RA J2015.5
dec = f['dec']  # DEC J2015.5
pmra = f['pmra']  # RA proper motion
pmra_error = f['pmra_error']  # RA proper motion error
pmdec = f['pmdec']  # DEC proper motion
pmdec_error = f['pmdec_error']  # DEC proper motion error
pmdec = f['pmdec']  # DEC proper motion
phot_g_mean_mag = f['phot_g_mean_mag']  # g-band magnitude
bp_rp = f['bp_rp']  # bp_rp colour

Moreover, you can use galpy (>=1.5) to setup Orbit to easily do unit conversion or integrating orbits

# To convert to 3D position and 3D velocity
from astroNN.apogee import allstar
from galpy.orbit import Orbit
import astropy.units as u
import astropy.coordinates as coord
from astropy.coordinates import CartesianDifferential

f_allstardr14 = fits.getdata(allstar(dr=14))

# because the catalog contains -9999.
non_n9999_idx = ((pmra !=-9999.) & (pmdec !=-9999.) & (nn_parsec !=-9999.))
c = coord.SkyCoord(ra=ra[non_n9999_idx]*u.degree,
                   dec=dec[non_n9999_idx]*u.degree,
                   distance=nn_parsec[non_n9999_idx]*u.pc,
                   pm_ra_cosdec=pmra[non_n9999_idx]*u.mas/u.yr,
                   pm_dec=pmdec[non_n9999_idx]*u.mas/u.yr,
                   radial_velocity=f_allstardr14['VHELIO_AVG'][non_n9999_idx]*u.km/u.s,
                   galcen_distance=8.125*u.kpc, # https://arxiv.org/abs/1807.09409 (GRAVITY Collaboration 2018)
                   z_sun=20.8*u.pc, # https://arxiv.org/abs/1809.03507 (Bennett & Bovy 2018)
                   galcen_v_sun=CartesianDifferential([11.1, 245.7, 7.25]*u.km/u.s))

# galpy Orbit object, need galpy >= 1.5
os = Orbit(c)
x, y, z = os.x(), os.y(), os.z()    # 3D position
vx, vy, vz = os.vx(), os.vy(), os.vz()    # 3D velocity

Using Neural Net on arbitrary APOGEE spectra

To do inference on an arbitrary APOGEE spectrum to get distance,

1. Open python under the repository folder but outside the neural net folder
2. Copy and paste the following code to do inference with neural net in this paper on 2M19060637+4717296

from astropy.io import fits
from astroNN.apogee import visit_spectra, apogee_continuum
from astroNN.gaia import extinction_correction, fakemag_to_pc
from astroNN.models import load_folder

# arbitrary spectrum
f = fits.open(visit_spectra(dr=14, apogee='2M19060637+4717296'))
spectrum = f[1].data
spectrum_err = f[2].data
spectrum_bitmask = f[3].data

# using default continuum and bitmask values to continuum normalize
norm_spec, norm_spec_err = apogee_continuum(spectrum, spectrum_err,
                                            bitmask=spectrum_bitmask, dr=14)

# load neural net, it is recommend to use model ends with _reduced
# for example, using astroNN_constant_model_reduced instead of astroNN_constant_model
neuralnet = load_folder('astroNN_constant_model_reduced')

# inference, if there are multiple visits, then you should use the globally
# weighted combined spectra (i.e. the second row)
pred, pred_err = neuralnet.test(norm_spec)

# correct for extinction
K = extinction_correction(f[0].header['K'], f[0].header['AKTARG'])

# convert prediction in fakemag to distance
pc, pc_error = fakemag_to_pc(pred[:, 0], K, pred_err['total'][:, 0])
print(f"Distance: {pc} +/- {pc_error}")

Authors

• Henry Leung - henrysky

  Student, Department of Astronomy and Astrophysics, University of Toronto

  Contact Henry: henrysky.leung [at] utoronto.ca
• Jo Bovy - jobovy

  Professor, Department of Astronomy and Astrophysics, University of Toronto

License

This project is licensed under the MIT License - see the LICENSE file for details