# Robust Period Estimation Using Mutual Information for Multiband Light Curves in the Synoptic Survey Era

## Abstract

The Large Synoptic Survey Telescope (LSST) will produce an unprecedented amount of light curves using six optical bands. Robust and efficient methods that can aggregate data from multidimensional sparsely sampled time-series are needed. Here, we present a new method for light curve period estimation based on quadratic mutual information (QMI). The presented method does not assume a particular model for the light curve nor its underlying probability density and it is robust to non-Gaussian noise and outliers. By combining the QMI from several bands the true period can be estimated even when no single-band QMI yields the period. Period recovery performance as a function of average magnitude and sample size is measured using 30,000 synthetic multiband light curves of RR Lyrae and Cepheid variables generated by the LSST Operations and Catalog simulators. The results show that aggregating information from several bands is highly beneficial in LSST sparsely sampled time-series, obtaining an absolute increase in period recovery rate up to 50%. We also show that the QMI is more robust to noise and light curve length (sample size) than the multiband generalizations of the Lomb–Scargle and AoV periodograms, recovering the true period in 10%–30% more cases than its competitors. A pythonmore »

- Authors:

- Austral Univ. of Chile, Valdivia (Chile); Millennium Inst. of Astrophysics (MAS), Santiago (Chile)
- Millennium Inst. of Astrophysics (MAS), Santiago (Chile); Univ. of Chile, Santiago (Chile)
- Univ. of Washington, Seattle, WA (United States)
- Harvard Univ., Cambridge, MA (United States)
- Univ. of Chile, Santiago (Chile)
- Computational Neuroengineering Lab. of Univ. of Florida (CNEL), Gainesville, FL (United States)

- Publication Date:

- Research Org.:
- Univ. of Washington, Seattle, WA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)

- OSTI Identifier:
- 1511031

- Grant/Contract Number:
- SC0011635

- Resource Type:
- Accepted Manuscript

- Journal Name:
- The Astrophysical Journal. Supplement Series (Online)

- Additional Journal Information:
- Journal Name: The Astrophysical Journal. Supplement Series (Online); Journal Volume: 236; Journal Issue: 1; Journal ID: ISSN 1538-4365

- Publisher:
- American Astronomical Society/IOP

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; data analysis methods; statistical methods; stars variables

### Citation Formats

```
Huijse, Pablo, Estévez, Pablo A., Förster, Francisco, Daniel, Scott F., Connolly, Andrew J., Protopapas, Pavlos, Carrasco, Rodrigo, and Príncipe, José C. Robust Period Estimation Using Mutual Information for Multiband Light Curves in the Synoptic Survey Era. United States: N. p., 2018.
Web. doi:10.3847/1538-4365/aab77c.
```

```
Huijse, Pablo, Estévez, Pablo A., Förster, Francisco, Daniel, Scott F., Connolly, Andrew J., Protopapas, Pavlos, Carrasco, Rodrigo, & Príncipe, José C. Robust Period Estimation Using Mutual Information for Multiband Light Curves in the Synoptic Survey Era. United States. doi:10.3847/1538-4365/aab77c.
```

```
Huijse, Pablo, Estévez, Pablo A., Förster, Francisco, Daniel, Scott F., Connolly, Andrew J., Protopapas, Pavlos, Carrasco, Rodrigo, and Príncipe, José C. Fri .
"Robust Period Estimation Using Mutual Information for Multiband Light Curves in the Synoptic Survey Era". United States. doi:10.3847/1538-4365/aab77c. https://www.osti.gov/servlets/purl/1511031.
```

```
@article{osti_1511031,
```

title = {Robust Period Estimation Using Mutual Information for Multiband Light Curves in the Synoptic Survey Era},

author = {Huijse, Pablo and Estévez, Pablo A. and Förster, Francisco and Daniel, Scott F. and Connolly, Andrew J. and Protopapas, Pavlos and Carrasco, Rodrigo and Príncipe, José C.},

abstractNote = {The Large Synoptic Survey Telescope (LSST) will produce an unprecedented amount of light curves using six optical bands. Robust and efficient methods that can aggregate data from multidimensional sparsely sampled time-series are needed. Here, we present a new method for light curve period estimation based on quadratic mutual information (QMI). The presented method does not assume a particular model for the light curve nor its underlying probability density and it is robust to non-Gaussian noise and outliers. By combining the QMI from several bands the true period can be estimated even when no single-band QMI yields the period. Period recovery performance as a function of average magnitude and sample size is measured using 30,000 synthetic multiband light curves of RR Lyrae and Cepheid variables generated by the LSST Operations and Catalog simulators. The results show that aggregating information from several bands is highly beneficial in LSST sparsely sampled time-series, obtaining an absolute increase in period recovery rate up to 50%. We also show that the QMI is more robust to noise and light curve length (sample size) than the multiband generalizations of the Lomb–Scargle and AoV periodograms, recovering the true period in 10%–30% more cases than its competitors. A python package with efficient Cython implementations of the QMI and other methods is provided.},

doi = {10.3847/1538-4365/aab77c},

journal = {The Astrophysical Journal. Supplement Series (Online)},

number = 1,

volume = 236,

place = {United States},

year = {2018},

month = {5}

}