specdims

Code for A. A. Patil, J. Bovy, G. Eadie, and S. Jaimungal, "Functional Data Analysis for Extracting the Intrinsic Dimensionality of Spectra: Application to Chemical Homogeneity in the Open Cluster M67", The Astrophysical Journal. 926, 51 (2022) ADS

AUTHOR

Main author: Aarya A. Patil

CITING THIS CODE

Aarya A. Patil et al. 2022 ApJ 926 51

INTRODUCTION

We apply Functional Principal Component Analysis (FPCA) to a large sample of APOGEE giants to extract the spectral structure instrinsic to the stars embedded in systematics, and determine its dimensionality. We then apply our Functional Principal Components (FPCs) to constrain chemical homogeneity in open cluster M67. This proves that the FPCs incorporate abundance information, and in turn helps validate chemical tagging. Thus, we have the opportunity to perform chemical tagging in the instrinsic spectral structure defined by our FPCs, which likely has information beyond a limited number of error-prone model-derived abundances.

fpca

One of the main contributions of this code is fpca.py, a general-purpose python module for performing FPCA. fpca is currently not yet available on PyPI, but it can be used by downloading the source code or cloning the GitHub repository and importing the module as follows:

from fpca import Fpca

fpca_train_dat = Fpca(data, 50, phi=basis, xerr=data_err)
fpca_train_dat.alpha_regression()
fpca_train_dat.solve_eigenproblem()

print(fpca_train_dat.psi_cap_t, fpca_train_dat.perc_var)

Here data and data_err represent the data you want to perform FPCA on and its error. 50 represents the number of basis functions. basis represents the basis functions you want to use; by deafult these are Legendre Polynomials. alpha_regression() provides the coefficients of regression for generating the functional approximation of data, whereas solve_eigenproblem provides FPCs.

Refer to the notebook fpca_test.ipynb to understand the basics of FPCA and the usage of fpca.

delfiSpec

delfiSpec is a module that provides useful functions to read, process and simulate APOGEE spectra.

This builds on top of apogee.

apogee_fpca

Code to compute FPCs of the APOGEE giants.

apogee_SNL

Code to perform Sequential Neural Likelihood on M67 APOGEE giants for inference of stellar parameters and abundances.

This requires pydelfi.

hierarch_t_distribution

Computing hierarchical distributions using the method Hogg, 2010 to constrain chemical homogeneity in M67.

gen_plots_tables

Code to generate plots and tables in the paper.