Dimensionality Reduction applied to Large Spectroscopic Surveys

Manuel Pichardo Marcano

Department of Physics and Astronomy

Lubbock
May 2018

When Cecilia Payne began her study of stellar spectra, scientists believed that the relative abundance of elements in the atmospheres of the Sun and the stars was similar to that in Earth’s crust. In 1889, geochemist Frank Wigglesworth Clarke’s The Relative Abundance of the Chemical Elements was the result of his comprehensive sampling of minerals from many parts of Earth’s crust. Many of the strong lines of the solar spectrum came from the elements most abundant on Earth. The pre-eminent American physicists at the time, Henry Norris Russell and Henry Rowland, believed that the elemental abundances on Earth and the Sun were substantially identical. Russell wrote [2] “The agreement of the solar and terrestrial lists is such as to confirm very strongly Rowland’s opinion that, if the Earth’s crust should be raised to the temperature of the Sun’s atmosphere, it would give a very similar absorption spectrum.” The spectra of the Sun and other stars were similar, so it appeared that the relative abundance of elements in the universe was like that in Earth’s crust.

Fingerprint of the Stars

N.A.Sharp, NOAO/NSO/Kitt Peak FTS/AURA/NSF

The Harvad "Computers"

Early Spectral Classification

Annie Jump Cannon Award in Astronomy
Leavitt Law

Harvard College Observatory, Plate Stacks.

OBAFGKM sequence

A theoretical breakthrough

Primarily a temperature sequence

Composition differences are minor

Stars are predominantly H and He

There is no joy more intense than that of coming upon a fact that cannot be understood in terms of currently accepted ideas." —Cecilia Payne

Nancy Grace Roman

"The Mother of Hubble”

Study heavy elements in stellar spectra:

First clue to the evolution of the Milky Way

Next Generation Spectroscopic Surveys

Era of data-rich astronomy

Explosion in size and complexity of data sets

Large Spectroscopic Surveys

The Challenges

Data size and complexity
- Data Compression
Noise:
- Filter Glitches, Skylines, Cosmic Rays
Feature Extraction:
- $T_{eff}$, log(g), [Fe/H]
Classification:.
- Automatic Classification

Dimensionality Reduction Methods

The Data

SEGUE: Sloan Extension for Galactic Understanding and Exploration

Principal Component Analysis of SDSS Stellar Spectra

Matrix

5000 stars X 2000

3850-9000 Å

82 Line Index (EW)

Atomic and molecular lines.

5 components:

95% of variance

Spectra Reconstruction

PCA Decomposition Results

Correlations eigencoefficients and stellar parameters:

First components related to $T_{eff}$
Smaller singular values related to log(g)

$T_{eff}$ Calibration

"A PCA approach to stellar effective temperatures" Muñoz Bermejo, J et. al 2013
Applied to Library of Synthetic Spectra

$$T_{eff} = T_0 + \sum ^C _{j=1} a_j PC_j + \sum ^C _{j=1} b_j PC_j^2 \, \, + \, \, ...$$

First Component and $T_{eff}$

2 Dimension

First Component and $T_{eff}$

3 Dimension

Classification: Unsupervised

Goal: Discover structure in the data

Plot Reduced-dimension representation
Linear Decomposition

PCA, ICA, NMF

Non-Linear Decomposition

Stochastic Neighbor Embedding (tSNE)

PCA

NMF

t-SNE

t-SNE

Conclusions

Dimensionality reduction methods like PCA and t-SNE can be used to efficiently target the future challenges with the huge increase of spectroscopic data soon available from future and ongoing all-sky surveys.

Future Work

More data
- Try with >5000 stars
- Giants, Dwarfs. Late type stars ...
Supervised Learning:
- PCA can be combined with ANN
Outliers:
- Take a closer look at outliers
Use Line Index:
- Matrix of Equivalent Width
- Radial Velocity, Distance, Emission lines ...

Gracias

Department of Physics and Astronomy

Printable version

Available online