Surveying Transient Host Galaxies with ASAS-SN

Home , SN 2011fe, Supernova Legacy Survey

DISSERTATION

Presented in Partial Fulﬁllment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Jonathan Scott Brown Jr.

Graduate Program in Astronomy

The Ohio State University 2018

Dissertation Committee: Professor Krzysztof Z. Stanek, Advisor Professor Christopher S. Kochanek Professor Paul Martini Copyright by

Jonathan Scott Brown Jr.

2018 Abstract

The technological advances of the recent years have allowed for the proliferation of relatively inexpensive charge-coupled devices (CCDs) and other imaging hardware that has revolutionized modern astronomy. The burgeoning ﬁeld of transient astronomy is perhaps the largest benefactor of these advances, and as a result, high cadence, all-sky surveys are becoming a reality. New transient phenomena are discovered and studied in depth on a regular basis, and the datasets of “normal” transients are becoming richer by the day. However, transient phenomena are intimately connected to their environment, and understanding this connection can provide insight that the study of transient phenomenology alone cannot. In this dissertation, I leverage the statistical power of modern all-sky surveys to investigate the nature of transients, the properties of their host galaxies, as well as the techniques and tools we use to study both.

ii Dedication

To motorcycle maintenance.

iii Acknowledgments

I am indebted to the OSU Department of Astronomy for encouraging such a lively and collegial environment in which to learn and grow as a scientist, as well as the OSU Graduate School for providing support to conduct my research. I’d especially like to thank the members of my committee. I am immensely grateful for Professor Krzysztof Z. Stanek’s mentorship and his ability to identify what is important, and how to explain it in a way that people can connect to. I am also grateful for his witty title suggestions. I am thankful to Professor Christopher S.

Kochanek for his truly rapid and informative feedback on any questions I’ve had. I must also thank him for the many trips to the LBT, and for being a counterweight to Professor Stanek’s wit. I am grateful to Professor Paul Martini for his role early on in my graduate student career, especially for his guidance on writing and editing. I thank Professor Richard W. Pogge and Kevin Croxall for introducing me to spectroscopy with MODS, which ultimately paved the way for the rest of my time here at OSU. I owe David Will many thanks for a near seamless computing experience for the 5 years I’ve spent here. I thank Oﬃce 4k members both past and present, including honorary member Greg Simmonian for his frequent banter and occasional admonishment. In particular, I’d like to thank Tom Holoien for being a

iv great friend (but don’t think for a second I’ve forgotten about Sevastopol), colleague, and brewery enthusiast. Always remember, as far as the oﬃcial fantasy football record is concerned, we are equals. Job Oﬃce, thank you all for making this past year much less stressful than it otherwise would have been. I am also immensely grateful to the members of the department that came before me, especially Ben

Shappee and Brett Andrews, whose own eﬀorts made much of my research possible.

Finally, I owe many thanks to my friends from that school up north; you’ve each been an inspiration in one form or another, so thanks n’at.

v Vita

December 11, 1990 ...... Born – Burlington, VT, USA

B.S., Astronomy & Astrophysics 2013 – 2015...... University of Michigan

Graduate Teaching Associate 2013 – 2016...... The Ohio State University

M.S., Astronomy 2016...... The Ohio State University

Graduate Research Associate 2016 – 2017...... The Ohio State University

Presidential Fellow 2017 – 2018...... The Ohio State University

Allan Markowitz Award in Observational Astronomy 2018...... The Ohio State University

Publications

Research Publications

1. J. S. Brown, C. S. Kochanek, T. W.-S. Holoien, K. Z. Stanek, K. Auchettl, B. J. Shappee, J. L. Prieto, N. Morrell, E. Falco, J. Strader, L. Chomiuk, R. Post, S. Villanueva Jr., S. Mathur, S. Dong, P. Chen, and S. Bose, “The ultraviolet spectroscopic evolution of the low-luminosity tidal disruption event iPTF16fnl”, Monthly Notices of the Royal Astronomical Society, 473, 1130, (2018)

vi 2. T. W.-S. Holoien, J. S. Brown, K. Z. Stanek, C. S. Kochanek, B. J. Shappee, J. L. Prieto, S. Dong, J. Brimacombe, D. W. Bishop, S. Bose, J. F. Beacom, D. Bersier, P. Chen, L. Chomiuk, E. Falco, D. Godoy-Rivera, N. Morrell, G. Pojmanski, J. V. Shields, J. Strader, M. D. Stritzinger, T. A. Thompson, P. R. Wo´zniak, G. Bock, P. Cacella, E. Conseil, I. Cruz, J. M. Fernandez, S. Kiyota, R. A. Koﬀ, G. Krannich, P. Marples, G. Masi, L. A. G. Monard, B. Nicholls, J. Nicolas, R. S. Post, G. Stone, and W. S. Wiethoﬀ, “The ASAS-SN bright supernova catalogue - III. 2016”, Monthly Notices of the Royal Astronomical Society, 471, 4966, (2017)

3. C. S. Kochanek, M. Fraser, S. M. Adams, T. Sukhbold, J. L. Prieto, T. M¨uller, G. Bock, J. S. Brown, S. Dong, T. W.-S. Holoien, R. Khan, B. J. Shappee, and K. Z. Stanek, “Supernova progenitors, their variability and the Type IIP Supernova ASASSN-16fq in M66”, Monthly Notices of the Royal Astronomical Society, 467, 3347, (2017)

4. T. W.-S. Holoien, J. S. Brown, K. Z. Stanek, C. S. Kochanek, B. J. Shappee, J. L. Prieto, S. Dong, J. Brimacombe, D. W. Bishop, U. Basu, J. F. Beacom, D. Bersier, P. Chen, A. B. Danilet, E. Falco, D. Godoy-Rivera, N. Goss, G. Pojmanski, G. V. Simonian, D. M. Skowron, T. A. Thompson, P. R. Wo´zniak, C. G. Avila,´ G. Bock, J.-L. G. Carballo, E. Conseil, C. Contreras, I. Cruz, J. M. F. Andújar, Z. Guo, E. Y. Hsiao, S. Kiyota, R. A. Koff, G. Krannich, B. F. Madore, P. Marples, G. Masi, N. Morrell, L. A. G. Monard, J. C. Munoz-Mateos, B. Nicholls, J. Nicolas, R. M. Wagner, and W. S. Wiethoff, “The ASAS-SN bright supernova catalogue - II. 2015”, Monthly Notices of the Royal Astronomical Society, 467, 1098, (2017)

5. M. M. Fausnaugh, C. J. Grier, M. C. Bentz, K. D. Denney, G. De Rosa, B. M. Peterson, C. S. Kochanek, R. W. Pogge, S. M. Adams, A. J. Barth, T. G. Beatty, A. Bhattacharjee, G. A. Borman, T. A. Boroson, M. C. Bottorﬀ, J. E. Brown, J. S. Brown, M. S. Brotherton, C. T. Coker, S. M. Crawford, K. V. Croxall, S. Eftekharzadeh, M. Eracleous, M. D. Joner, C. B. Henderson, T. W.-S. Holoien, K. Horne, T. Hutchison, S. Kaspi, S. Kim, A. L. King, M. Li, C. Lochhaas, Z. Ma, F. MacInnis, E. R. Manne-Nicholas, M. Mason, C. Montuori, A. Mosquera, D. Mudd, R. Musso, S. V. Nazarov, M. L. Nguyen, D. N. Okhmat, C. A. Onken, B. Ou-Yang, A. Pancoast, L. Pei, M. T. Penny, R. Poleski, S. Rafter, E. Romero-Colmenero, J. Runnoe, D. J. Sand, J. S. Schimoia, S. G. Sergeev, B. J. Shappee, G. V. Simonian, G. Somers, M. Spencer, D. A. Starkey, D. J. Stevens, J. Tayar, T. Treu, S. Valenti, J. Van Saders, S. Villanueva Jr., C. Villforth, Y. Weiss, H. Winkler, and W. Zhu, “Reverberation Mapping of Optical Emission Lines in Five Active Galaxies”, The Astrophysical Journal, 840, 97, (2017)

6. J. S. Brown, T. W.-S. Holoien, K. Auchettl, K. Z. Stanek, C. S. Kochanek, B. J.

vii Shappee, J. L. Prieto, and D. Grupe, “The Long Term Evolution of ASASSN-14li”, Monthly Notices of the Royal Astronomical Society, 466, 4904, (2017)

7. L. Pei, M. M. Fausnaugh, A. J. Barth, B. M. Peterson, M. C. Bentz, G. De Rosa, K. D. Denney, M. R. Goad, C. S. Kochanek, K. T. Korista, G. A. Kriss, R. W. Pogge, V. N. Bennert, M. Brotherton, K. I. Clubb, E. Dalla Bontà, A. V. Filippenko, J. E. Greene, C. J. Grier, M. Vestergaard, W. Zheng, S. M. Adams, T. G. Beatty, A. Bigley, J. E. Brown, J. S. Brown, G. Canalizo, J. M. Comerford, C. T. Coker, E. M. Corsini, S. Croft, K. V. Croxall, A. J. Deason, M. Eracleous, O. D. Fox, E. L. Gates, C. B. Henderson, E. Holmbeck, T. W.-S. Holoien, J. J. Jensen, C. A. Johnson, P. L. Kelly, S. Kim, A. King, M. W. Lau, M. Li, C. Lochhaas, Z. Ma, E. R. Manne-Nicholas, J. C. Mauerhan, M. A. Malkan, R. McGurk, L. Morelli, A. Mosquera, D. Mudd, F. Muller Sanchez, M. L. Nguyen, P. Ochner, B. Ou-Yang, A. Pancoast, M. T. Penny, A. Pizzella, R. Poleski, J. Runnoe, B. Scott, J. S. Schimoia, B. J. Shappee, I. Shivvers, G. V. Simonian, A. Siviero, G. Somers, D. J. Stevens, M. A. Strauss, J. Tayar, N. Tejos, T. Treu, J. Van Saders, L. Vican, S. Villanueva Jr., H. Yuk, N. L. Zakamska, W. Zhu, M. D. Anderson, P. Arévalo, C. Bazhaw, S. Bisogni, G. A. Borman, M. C. Bottorff, W. N. Brandt, A. A. Breeveld, E. M. Cackett, M. T. Carini, D. M. Crenshaw, A. De Lorenzo-Cáceres, M. Dietrich, R. Edelson, N. V. Efimova, J. Ely, P. A. Evans, G. J. Ferland, K. Flatland, N. Gehrels, S. Geier, J. M. Gelbord, D. Grupe, A. Gupta, P. B. Hall, S. Hicks, D. Horenstein, K. Horne, T. Hutchison, M. Im, M. D. Joner, J. Jones, J. Kaastra, S. Kaspi, B. C. Kelly, J. A. Kennea, M. Kim, S. C. Kim, S. A. Klimanov, J. C. Lee, D. C. Leonard, P. Lira, F. MacInnis, S. Mathur, I. M. McHardy, C. Montouri, R. Musso, S. V. Nazarov, H. Netzer, R. P. Norris, J. A. Nousek, D. N. Okhmat, I. Papadakis, J. R. Parks, J.-U. Pott, S. E. Rafter, H.-W. Rix, D. A. Saylor, K. Schnülle, S. G. Sergeev, M. Siegel, A. Skielboe, M. Spencer, D. Starkey, H.-I. Sung, K. G. Teems, C. S. Turner, P. Uttley, C. Villforth, Y. Weiss, J.-H. Woo, H. Yan, S. Young, and Y. Zu, “Space Telescope and Optical Reverberation Mapping Project. V. Optical Spectroscopic Campaign and Emission-line Analysis for NGC 5548”, The Astrophysical Journal, 837, 131, (2017)

8. T. W.-S. Holoien, K. Z. Stanek, C. S. Kochanek, B. J. Shappee, J. L. Prieto, J. Brimacombe, D. Bersier, D. W. Bishop, S. Dong, J. S. Brown, A. B. Danilet, G. V. Simonian, U. Basu, J. F. Beacom, E. Falco, G. Pojmanski, D. M. Skowron, P. R. Wo´zniak, C. G. Avila,´ E. Conseil, C. Contreras, I. Cruz, J. M. Fernández, R. A. Koff, Z. Guo, G. J. Herczeg, J. Hissong, E. Y. Hsiao, J. Jose, S. Kiyota, F. Long, L. A. G. Monard, B. Nicholls, J. Nicolas, and W. S. Wiethoff, “The ASAS-SN bright supernova catalogue - I. 2013-2014”, Monthly Notices of the Royal Astronomical Society, 464, 2672, (2017)

9. T. W.-S. Holoien, C. S. Kochanek, J. L. Prieto, D. Grupe, P. Chen, D.

viii Godoy-Rivera, K. Z. Stanek, B. J. Shappee, S. Dong, J. S. Brown, U. Basu, J. F. Beacom, D. Bersier, J. Brimacombe, E. K. Carlson, E. Falco, E. Johnston, B. F. Madore, G. Pojmanski, and M. Seibert, “ASASSN-15oi: a rapidly evolving, luminous tidal disruption event at 216 Mpc”, Monthly Notices of the Royal Astronomical Society, 463, 3813, (2016)

10. J. S. Brown, B. J. Shappee, T. W.-S. Holoien, K. Z. Stanek, C. S. Kochanek, and J. L. Prieto, “Hello darkness my old friend: the fading of the nearby TDE ASASSN-14ae”, Monthly Notices of the Royal Astronomical Society, 462, 3993, (2016)

11. G. J. Herczeg, S. Dong, B. J. Shappee, P. Chen, L. A. Hillenbrand, J. Jose, C. S. Kochanek, J. L. Prieto, K. Z. Stanek, K. Kaplan, T. W.-S. Holoien, S. Mairs, D. Johnstone, M. Gully-Santiago, Z. Zhu, M. C. Smith, D. Bersier, G. D. Mulders, A. V. Filippenko, K. Ayani, J. Brimacombe, J. S. Brown, M. Connelley, J. Harmanen, R. Itoh, K. S. Kawabata, H. Maehara, K. Takata, H. Yuk, and W. Zheng, “The Eruption of the Candidate Young Star ASASSN-15QI”, The Astrophysical Journal, 831, 133, (2016)

12. J. L. Prieto, T. Krühler, J. P. Anderson, L. Galbany, C. S. Kochanek, E. Aquino, J. S. Brown, S. Dong, F. Förster, T. W.-S. Holoien, H. Kuncarayakti, J. C. Maureira, F. F. Rosales-Ortega, S. F. Sánchez, B. J. Shappee, and K. Z. Stanek, “MUSE Reveals a Recent Merger in the Post-starburst Host Galaxy of the TDE ASASSN-14li”, The Astrophysical Journal, 830, L32, (2016)

13. J. S. Brown, P. Martini, and B. H. Andrews, “A recalibration of strong- line oxygen abundance diagnostics via the direct method and implications for the high-redshift universe”, Monthly Notices of the Royal Astronomical Society, 458, 1529, (2016)

14. S. Dong, B. J. Shappee, J. L. Prieto, S. W. Jha, K. Z. Stanek, T. W.-S. Holoien, C. S. Kochanek, T. A. Thompson, N. Morrell, I. B. Thompson, U. Basu, J. F. Beacom, D. Bersier, J. Brimacombe, J. S. Brown, F. Bufano, P. Chen, E. Conseil, A. B. Danilet, E. Falco, D. Grupe, S. Kiyota, G. Masi, B. Nicholls, F. Olivares E., G. Pignata, G. Pojmanski, G. V. Simonian, D. M. Szczygiel, and P. R. Wo´zniak, “ASASSN-15lh: A highly super-luminous supernova”, Science, 351, 257, (2016)

15. T. W.-S. Holoien, C. S. Kochanek, J. L. Prieto, K. Z. Stanek, S. Dong, B. J. Shappee, D. Grupe, J. S. Brown, U. Basu, J. F. Beacom, D. Bersier, J. Brimacombe, A. B. Danilet, E. Falco, Z. Guo, J. Jose, G. J. Herczeg, F. Long, G. Pojmanski, G. V. Simonian, D. M. Szczygiel, T. A. Thompson, J. R. Thorstensen, R. M. Wagner, and P. R. Wo´zniak, “Six months of multiwavelength follow-up of the

ix tidal disruption candidate ASASSN-14li and implied TDE rates from ASAS-SN”, Monthly Notices of the Royal Astronomical Society, 455, 2918, (2016)

16. T. W.-S. Holoien, J. L. Prieto, D. Bersier, C. S. Kochanek, K. Z. Stanek, B. J. Shappee, D. Grupe, U. Basu, J. F. Beacom, J. Brimacombe, J. S. Brown, A. B. Davis, J. Jencson, G. Pojmanski, and D. M. Szczygiel, “ASASSN-14ae: a tidal disruption event at 200 Mpc”, Monthly Notices of the Royal Astronomical Society, 445, 3263, (2014)

17. J. S. Brown, K. V. Croxall, and R. W. Pogge, “Direct Method Gas- phase Oxygen Abundances of Four Lyman Break Analogs”, The Astrophysical Journal, 792, 140, (2014)

18. C. A. Onken, M. Valluri, J. S. Brown, P. J. McGregor, B. M. Peterson, M. C. Bentz, L. Ferrarese, R. W. Pogge, M. Vestergaard, T. Storchi-Bergmann, and R. A. Riﬀel, “The Black Hole Mass of NGC 4151. II. Stellar Dynamical Measurement from Near-infrared Integral Field Spectroscopy”, The Astrophysical Journal, 791, 37, (2014)

19. J. S. Brown, M. Valluri, J. Shen, and V. P. Debattista, “On the Oﬀset of Barred Galaxies from the Black Hole M BH -σ Relationship”, The Astrophysical Journal, 778, 151, (2013)

Fields of Study

Major Field: Astronomy

x Table of Contents

Abstract ...... ii

Dedication ...... iii

Acknowledgments ...... iv

Vita ...... vi

List of Tables ...... xvi

List of Figures ...... xvii

Chapter 1: Introduction ...... 1

1.1 FundamentalGalaxyProperties ...... 1

1.2 TheAll-SkyAutomatedSurveyforSupernovae ...... 5

1.2.1 TidalDisruptionEvents ...... 6

1.2.2 TypeIaSupernovae...... 7

1.3 ScopeoftheDissertation...... 9

Chapter 2: Precise Abundances in Star Forming Galaxies ...... 11

2.1 Introduction...... 11

2.2 ObservationsandReduction ...... 14

2.2.1 ObservingProcedures ...... 14

xi 2.2.2 DataReduction...... 15

2.3 Analysis ...... 16

2.3.1 StellarContinuumSubtraction ...... 16

2.3.2 LineFluxMeasurment ...... 17

2.3.3 AbundanceDetermination ...... 18

2.4 Results...... 21

2.4.1 Excitation...... 21

2.4.2 OxygenAbundances ...... 22

2.5 Discussion...... 24

2.5.1 ExcitationConditionsofLBAs ...... 24

2.5.2 LBAs and the Fundamental Metallicity Relation ...... 26

2.6 Summary ...... 30

Chapter 3: A Recalibration of Oxygen Abundance Diagnostics .... 44

3.1 Introduction...... 44

3.2 Data...... 47

3.2.1 SampleSelection ...... 47

3.2.2 StackingProcedure ...... 49

3.2.3 ChoiceofStackingParameters...... 50

3.2.4 StellarContinuumSubtraction ...... 54

3.2.5 LineFluxMeasurement ...... 54

3.3 Analysis ...... 55

3.3.1 Abundances...... 55

3.3.2 EmpiricalCalibrations ...... 57

3.4 Results...... 59

xii 3.4.1 N2Method ...... 60

3.4.2 O3N2Method...... 61

3.4.3 N2O2Method...... 62

3.4.4 WhichCalibrationIsBest? ...... 64

3.5 Discussion...... 65

3.5.1 Application of New Calibrations to Local Galaxies ...... 65

3.5.2 The M⋆–Z–SFRRelation ...... 68

3.5.3 Application of New Calibrations to High Redshift Galaxies.. 72

3.6 Summary ...... 78

Chapter 4: Late-time Observations of the Tidal Disruption Event ASASSN-14ae ...... 98

4.1 Introduction...... 98

4.2 Observations...... 99

4.2.1 SpectroscopicObservations...... 99

4.2.2 Swift Observations ...... 101

4.2.3 ASAS-SNPre-DiscoveryUpperLimit ...... 102

4.3 EvolutionoftheLate-TimeEmission ...... 102

4.3.1 SpectralAnalysis ...... 102

4.3.2 Photometry ...... 107

4.4 Conclusions ...... 109

Chapter 5: The Late-time Evolution of the Tidal Disruption Event ASASSN-14li ...... 119

5.1 Introduction...... 119

5.2 Observations...... 121

xiii 5.2.1 SpectroscopicObservations...... 121

5.2.2 Swift Observations ...... 123

5.2.3 ASAS-SNPre-DiscoveryUpperLimits ...... 125

5.3 EvolutionoftheLate-TimeEmission ...... 126

5.3.1 EvolutionoftheOpticalSpectra ...... 126

5.3.2 EvolutionoftheUVOTPhotometry ...... 129

5.3.3 EvolutionoftheX-rayEmission...... 133

5.4 Conclusions ...... 136

Chapter 6: The Ultraviolet Evolution of the Tidal Disruption Event iPTF16fnl ...... 154

6.1 Introduction...... 154

6.2 Observations...... 156

6.2.1 ArchivalHostData ...... 156

6.2.2 ASAS-SNDetection ...... 157

6.2.3 HST/STISToOObservations ...... 158

6.2.4 Swift Observations ...... 159

6.2.5 Ground-BasedMonitoring ...... 160

6.3 Analysis ...... 161

6.3.1 SpectroscopicAnalysis ...... 161

6.3.2 PhotometricAnalysis...... 170

6.4 Conclusions ...... 175

Chapter 7: The Speciﬁc Type Ia Supernova Rate from Three Years of ASAS-SN ...... 190

7.1 Introduction...... 190

xiv 7.2 Data...... 191

7.2.1 TheSNIaSample ...... 191

7.2.2 ArchivalHostData ...... 196

7.3 Analysis ...... 197

7.4 Conclusions ...... 203

References ...... 215

xv List of Tables

Table2.1 LBAEmissionLineIntensities ...... 40

Table2.2 Electron Temperatures&Densities ...... 41

Table2.3 DerivedAbundances...... 42

Table 2.4 Direct and Strong-Line Oxygen Abundances ...... 43

Table 3.1 Wavelength Fit and Mask Ranges of Measured Lines...... 95

Table3.2 LineFluxes ...... 96

Table3.3 Calibrationresults...... 97

Table4.1 Observations...... 117

Table 4.2 Measurements of Hα ProﬁleProperties ...... 118

Table5.1 LBT/MODS1observations...... 150

Table 5.2 Measurements of Hα Properties ...... 151

Table5.3 ASASSN-14liX-rayProperties ...... 152

Table 5.4 Swift Observations...... 153

Table6.1 ArchivalPhotometryofMrk0950 ...... 187

Table6.2 InferredMagnitudesofMrk0950 ...... 187

Table 6.3 Swift Observations...... 188

Table 6.4 Host and Reddening Corrected Swift Observations. . . . 189

xvi List of Figures

Figure2.1 MODS1spectraofaLymanBreakAnalog...... 32

Figure2.2 MODS1spectraofaLymanBreakAnalog...... 32

Figure2.3 MODS1spectraofaLymanBreakAnalog...... 33

Figure2.4 MODS1spectraofaLymanBreakAnalog...... 33

Figure 2.5 BPT diagram showing ioninzation conditions of LBAs. . . . . 34

Figure 2.6 Excitation diagnostics of LBAs in relation to SDSS galaxies. . 35

Figure 2.7 Diagnostic emission line ratios of LBAs in relation to H IIregions. 36

Figure2.8 Wolf-RayetfeaturesinLBAs...... 37

Figure 2.9 Oxygen abundance measurements versus stellar mass for the LBAs...... 38

Figure 2.10 LBAs shown on the Fundamental Metallicity Relation. .... 39

Figure3.1 StackedSDSScompositespectrum...... 81

Figure 3.2 Diagnostic ratios versus stellar mass for SDSS galaxies. . . . . 82

Figure 3.3 BTP and excitation plots of SDSS galaxies and the stacked spectra...... 83

Figure 3.4 N2 versus direct method oxygen abundance...... 84

Figure 3.5 O3N2 versus direct method oxygen abundance...... 85

Figure 3.6 N2O2 versus direct method oxygen abundance...... 86

Figure 3.7 Grids showing the binning and oxygen abundance residuals. . 87

Figure 3.8 MZR derived from the new N2 calibration...... 88

xvii Figure 3.9 MZR derived from the new O3N2 calibration...... 89

Figure 3.10 MZR derived from the new N2O2 calibration...... 90

Figure 3.11 N2 oxygen abundance at ﬁxed stellar mass...... 91

Figure 3.12 N2O2 oxygen abundance at ﬁxed stellar mass...... 92

Figure 3.13 Dependence of oxygen abundance on ∆log(SSFR) as a function ofstellarmass...... 93

Figure 3.14 New calibrations applied to high redshift galaxies...... 94

Figure4.1 OpticalspectraofASASSN-14ae...... 112

Figure 4.2 Late-time spectrum and residual after host subtraction. . . . . 113

Figure 4.3 Luminosity and equivalent with evolution of Hα...... 114

Figure 4.4 SwiftUVOTphotometryofASASSN-14ae...... 115

Figure 4.5 Late-time Hα limitsforvariousTDEs...... 116

Figure5.1 OpticalspectraofASASSN-14li...... 142

Figure 5.2 Swift and ground-based photometry of ASASSN-14li...... 143

Figure5.3 BlackbodyﬁtstotheTDEemission...... 144

Figure5.4 LuminosityevolutionofASASSN-14li...... 145

Figure5.5 RadiusevolutionofASASSN-14li...... 146

Figure5.6 X-rayspectraofASASSN-14li...... 147

Figure 5.7 Late-time Hα limitsforvariousTDEs...... 148

Figure5.8 E+AgalaxieswithUVexcess...... 149

Figure6.1 TheUVevolutionofiPTF16fnl...... 178

Figure 6.2 Line proﬁle evolution of iPTF16fnl...... 179

Figure 6.3 The UV spectra of iPTF16fnl compared to ASASSN-14li and SDSSquasars...... 180

Figure 6.4 The optical spectral evolution of iPTF16fnl...... 181

xviii Figure 6.5 The photometric evolution of iPTF16fnl...... 182

Figure 6.6 The temperature evolution of iPTF16fnl...... 183

Figure6.7 TheradiusevolutionofiPTF16fnl...... 184

Figure 6.8 The luminosity evolution of iPTF16fnl...... 185

Figure 6.9 The spectral energy distribution of iPTF16fnl...... 186

Figure 7.1 SN Ia absolute magnitude versus luminosity distance...... 205

Figure 7.2 ASAS-SN completeness versus apparent magnitude...... 206

Figure7.3 ASAS-SNSNIaluminosityfunction...... 207

Figure 7.4 Charts showing the distribution of SN Ia subtypes and and host galaxyphotometry...... 208

Figure7.5 ComparisontoGalspecresults...... 209

Figure 7.6 SN Ia host galaxies in the M SFRplane...... 210 ⋆ − Figure 7.7 SN Ia distance and absolute magnitude versus host galaxy stellarmass...... 211

Figure 7.8 Cumulative distributions of host galaxy stellar masses. . . . . 212

Figure 7.9 Normalized speciﬁc SN Ia rate versus host galaxy stellar mass. 213

Figure 7.10 The ratio of the SN Ia rate in actively star forming galaxies to that in passive galaxies, as a function of host galaxy stellarmass. . . 214

xix Chapter 1: Introduction

1.1. Fundamental Galaxy Properties

Identifying and quantifying correlations between fundamental parameters gives us insight into the physical processes governing the evolution of the objects under investigation. In the ΛCDM paradigm, galaxies accrete mass primarily via hierarchical mergers with other galaxies. This formulation reproduces the physical properties of galaxies we observe in the nearby universe (Kauﬀmann & Haehnelt 2000; Hopkins & Beacom 2006a). Thus, the mass of a galaxy reveals the gross characteristics of its history. Similarly, the metallicity of a galaxy is a fundamental characteristic which is intimately related to its formation and subsequent chemical evolution. Studying how the mass and metallicity of galaxies correlate across a wide range of physical parameters informs us about how today’s galaxies coalesced and evolved over cosmic time.

The relation between a galaxy’s stellar mass (M⋆) and gas phase oxygen abundance (sometimes referred to as metallicity) make up the mass-metallicity relation (MZR). The MZR was ﬁrst investigated by Lequeux et al. (1979). Subsequent studies often focused on the more readily measured correlation between luminosity and oxygen abundance (the LZ relation; e.g., Garnett & Shields 1987; Skillman, Kennicutt & Hodge 1989; Zaritsky, Kennicutt & Huchra 1994). With data from Sloan Digital Sky Survey (SDSS; York et al. 2000) for a very large number of galaxies, Tremonti et al. (2004) showed the MZ relation persists across at least

1 3 orders of magnitude in mass and an order of magnitude in oxygen abundance. This trend was extended 2.5 orders of magnitude lower in mass and another order of magnitude lower in oxygen abundance by Lee et al. (2006). There have been a number of following studies that have investigated possible variations in the MZR as a function of redshift (e.g. Erb et al. 2006), star formation rate (e.g. Andrews & Martini 2013), morphology and environment (e.g. Ellison et al. 2008a,b), or a combination of these factors (e.g. Mannucci et al. 2010; Lara-L´opez et al. 2010).

In addition to the local MZR and its dependence on SFR, the same correlations can be studied in high redshift galaxies in order to probe galaxy formation and evolution in the early universe (Shapley et al. 2005; Erb et al. 2006; Maiolino et al. 2008; Steidel et al. 2014; Zahid et al. 2014a; Sanders et al. 2015). Furthermore, the correlation between M⋆, Z, and SFR in the early universe, and how that relates to the correlations observed in the local universe, constrains how the population of galaxies has evolved over cosmic time (Zahid et al. 2014b; Maier et al. 2014; Izotov et al. 2015).

Accurate and precise metallicity measurements are vital to gain physical insights from both local correlations and evolution over cosmic time. The most reliable oxygen abundances are determined with the “direct method”, or “Te method” (Dinerstein 1990). Under the right conditions, the electron temperature of ionized gas can be directly measured from the temperature sensitive intensity ratios of collisionally excited forbidden lines (e.g. [O III] λ4363/[O III] λ5007). As oxygen is one of the primary coolants in the ISM, the temperature is anti-correlated with abundance. The density of the gas can be measured from density sensitive lines

(e.g. [S III] λ6717/λ6731). For a given temperature and density the emissivity of a given ionic species can be computed, which can then be used to determine relative abundances.

2 The direct method is subject to some biases. Temperature ﬂuctuations and gradients in H II regions produce a bias towards lower metallicities (Peimbert 1967; Kobulnicky, Kennicutt & Pizagno 1999) . This bias also applies to integrated (as well as stacked) spectra of galaxies. Hotter regions have brighter auroral lines, which can bias the direct method toward higher electron temperatures and correspondingly lower metallicities. Additionally, the assumption of a Maxwell-Boltzmann electron energy distribution has recently come into question (Nicholls, Dopita & Sutherland 2012; Dopita et al. 2013). If electron energies are instead well described by a κ-distribution, this may contribute to the well known temperature discrepancy problem (Garcia-Rojas & Esteban 2006; Garc´ıa-Rojas & Esteban 2007; Nicholls, Dopita & Sutherland 2012; Blanc et al. 2015), although this is less of a concern for relative comparisons of direct method abundances. Even with the potential for these systematic eﬀects, the direct method is widely regarded as the standard for nebular abundances.

In order to estimate the metallicities of galaxies without the use of the auroral lines, so-called “strong-line” diagnostics were developed based on the more easily measured nebular emission lines (Pagel et al. 1979; Alloin et al. 1979). There have been many eﬀorts to calibrate these diagnostics via theoretical (e.g., McGaugh 1991; Zaritsky, Kennicutt & Huchra 1994; Dopita et al. 2000; Charlot & Longhetti 2001; Kewley & Dopita 2002; Kobulnicky & Kewley 2004; Tremonti et al. 2004; Stasi´nska 2006) and empirical means (e.g., Pilyugin 2003; Pettini & Pagel 2004; Pilyugin & Thuan 2005; Pilyugin, V´ılchez & Thuan 2010; Pilyugin, Grebel & Mattsson 2012; Marino et al. 2013; Bianco et al. 2015).

Perhaps the most common of these diagnostics is R ([O II] λ3727 + 23 ≡ [O III] λλ4959, 5007)/Hβ (Edmunds & Pagel 1984; McCall, Rybski & Shields

1985; Dopita & Evans 1986; Zaritsky, Kennicutt & Huchra 1994). R23 encodes

3 some information about the overall oxygen abundance, but the ratio is ultimately determined by the excitation of the [O II] and [O III] lines. This leads to the double valued nature of R23, which complicates its use as an abundance diagnostic.

Fortunately there are other nebular lines that encode information about the gas phase oxygen abundance, and nitrogen is the most accessible of these. Nitrogen has both primary origin, where the amount of nitrogen produced in stars and returned to the ISM is independent of metallicity, and secondary origin, where the amount of nitrogen produced is proportional to metallicity (Alloin et al. 1979; Vila Costas & Edmunds 1993; Consid`ere et al. 2000). In the high metallicity regime, nitrogen is secondary and the nitrogen abundance increases faster than the oxygen abundance. Furthermore, some strong line ratios are temperature sensitive since, for instance, the [O II] λ 3727 A˚ line requires a signiﬁcantly higher energy to excite than the

[N II] λ6583 A˚ line (Pilyugin, V´ılchez & Thuan 2010). As a result, nitrogen based diagnostics can serve as indicators of the oxygen abundance.

Many strong-line calibrations are often inconsistent with one another. Kewley & Ellison (2008) show the extent to which the various strong line calibrations disagree and provide a framework for mapping one strong line metallicity onto another. Many of the strong-line calibrations diﬀer simply because they use diﬀerent calibration samples, but the situation is more complicated than sample selection. Some calibrations utilize grids from photoionization simulations (McGaugh 1991; Zaritsky, Kennicutt & Huchra 1994; Kewley & Dopita 2002), while others use unique samples of H II regions (e.g., Marino et al. 2013) which themselves are often heterogeneous compilations of samples from the literature (e.g., Pettini & Pagel 2004; Pilyugin, V´ılchez & Thuan 2010).

4 Empirical abundance diagnostics have the benefit of being calibrated on direct method measurements, but due to selection effects the calibration samples are often biased toward low metallicity H II regions (Jones, Riess & Scolnic 2015). The application of these calibrations to integrated spectra of moderately star forming galaxies requires significant extrapolation from the H II regions that compose most calibration samples. Furthermore, most empirical calibrations will result in erroneous metallicities if, for instance, the ionization conditions of the galaxies in question differ significantly from the calibration sample (Dopita et al. 2000; Kewley & Dopita 2002; Steidel et al. 2014).

1.2. The All-Sky Automated Survey for Supernovae

The survey strategies employed in most of these studies suffer from observational biases and incompleteness problems that the All-Sky Automated Survey for Supernovae (ASAS-SN; Shappee et al. 2013) was designed to minimize. ASAS-SN monitors the entire night sky at a relatively high cadence. The discovery and rapid propagation of nearby, bright transients to the astronomical community allows for detailed followed-up with both ground and space based instrumentation. ASAS-SN has been influential in the discovery of a wide variety of transients including novel SNe (e.g., Dong et al. 2016; Godoy-Rivera et al. 2017; Holoien et al. 2016c; Shappee et al. 2016), tidal disruption events (TDEs; Holoien et al. 2014, 2016b,a; Brown et al. 2016a, 2017), flares in active galactic nuclei (AGN; Shappee et al. 2014), stellar outbursts (Holoien et al. 2014; Schmidt et al. 2014, 2016; Herczeg et al. 2016), and cataclysmic variable stars (CVs; Kato et al. 2014b,a, 2015, 2016). Additionally, ASAS-SN data has played a crucial role in constraining the pre-discovery and early-time light curves of several other interesting objects (e.g., Bose et al. 2017).

5 1.2.1. Tidal Disruption Events

When a star passes through the center of a galaxy, it may be disrupted by the central supermassive black hole (SMHB) in a “tidal disruption event” (TDE). After the disruption of a main sequence star, approximately half of the stellar debris will remain on bound orbits and asymptotically return to pericenter at a rate proportional to t−5/3 (Rees 1988; Evans & Kochanek 1989; Phinney 1989). For

8 3/2 −1/2 MBH > 10 M⊙ (R∗/R⊙) (M∗/M⊙) , rp falls roughly within the Schwarzschild ∼ 8 radius and the star is simply absorbed. For black holes less massive than 10 M⊙, ∼ the characteristics of the observed emission are heavily dependent on the disrupted star (e.g. MacLeod, Guillochon & Ramirez-Ruiz 2012; Kochanek 2016a), the post-disruption evolution of the accretion stream (e.g. Kochanek 1994; Strubbe & Quataert 2009; Guillochon & Ramirez-Ruiz 2013; Piran et al. 2015; Shiokawa et al. 2015), and complex radiative transfer eﬀects (e.g. Gaskell & Rojas Lobos 2014; Strubbe & Murray 2015; Roth et al. 2016), making TDEs exceptional probes of both SMBH physics and environment (e.g. Magorrian & Tremaine 1999; Ulmer 1999; Wegg & Bode 2011; Metzger & Stone 2016; Li et al. 2015; Ricarte et al. 2016).

While the first TDEs were discovered as X-ray transients (e.g. Grupe, Thomas & Leighly 1999; Komossa & Bade 1999; Komossa & Greiner 1999), the increasing number of wide-field optical transient surveys (including ASAS-SN) have led to an increase in the number of optical TDE candidates, and some previous studies have even examined the spectral characteristics of TDEs both near peak and at later times (e.g. van Velzen et al. 2011; Cenko et al. 2012; Gezari et al. 2012; Arcavi et al. 2014; Chornock et al. 2014; Holoien et al. 2014; Gezari et al. 2015; Vinkó et al. 2015; Holoien et al. 2016a,b,a). However, the majority of these studies were focused on either characterizing the immediate evolution of the flare, or studying the underlying host galaxies. As a result, the spectroscopic follow-up observations

6 were conducted on either very short or very long timescales after the flares occurred, and consequently provided only weak constraints on the late-time spectral evolution. van Velzen et al. (2011) examined the flaring state characteristics of TDE1 and TDE2, but since their study was based primarily on archival data, they were not able to study the spectroscopic evolution of the flares in detail. Gezari et al. (2012) presented moderately late-time ( 250 days) follow-up spectroscopy of the ∼ H-deficient TDE PS1-10jh, but broad He II λ4686 emission was still visible well above the host continuum in their late-time spectrum. In contrast, Gezari et al. (2015) presented host galaxy spectra taken years after the flare had faded. Similarly, Arcavi et al. (2014) and French, Arcavi & Zabludoff (2016b) presented late-time spectra of several recent TDEs, but in each case the spectrum was either dominated by the flare, or the observations were conducted years after the flare had faded, leaving the transition from a flare dominated state to a host galaxy dominated state relatively unobserved. The spectroscopic characteristics of some peculiar optical transients have been studied during the transition to the host dominated regime (e.g. PTF10iya; Cenko et al. 2012, PS1-11af; Chornock et al. 2014, Dougie; Vinkó et al. 2015, and ASASSN-15oi; Holoien et al. 2016a). With the exception of the TDEs discovered by ASAS-SN, most of these TDE candidates are relatively distant, which has made the characterization of their spectroscopic evolution difficult.

1.2.2. Type Ia Supernovae

Type Ia supernovae (SNe Ia), which arise from the thermonuclear detonation of carbon-oxygen white dwarfs (WDs), are a fundamental pillar of modern astronomy, cosmology, and physics. These events are unambiguously classiﬁed with low resolution optical spectra (Filippenko 1997), and evolve in such a way that their intrinsic luminosities (and thus distances) are precisely known (Phillips 1993; Hamuy

7 et al. 1995; Riess, Press & Kirshner 1996). The widespread interest in SNe Ia has been primarily driven by their luminosity and homogeneity, which makes them excellent probes of the large scale universe and cosmic evolution (e.g., Riess et al. 1998; Perlmutter et al. 1999). Given the pivotal role of SNe Ia in our understanding of the fundamental constants of our universe, and the tension with other independent cosmological experiments (e.g., Planck Collaboration et al. 2016), it is paramount that we fully understand their physical origin.

Unfortunately, our picture of SNe Ia is not as constrained as one might hope; even the physical systems that give rise to the explosions are not well characterized. The two competing theories both involve a carbon-oxygen WD in a close binary. In the single-degenerate (SD) scenario (Whelan & Iben 1973; Nomoto 1982), the binary companion is a non-degenerate star which steadily transfers mass onto the WD until a thermonuclear runaway occurs. In the double-degenerate (DD) scenario (Tutukov & Yungelson 1979; Iben & Tutukov 1984; Webbink 1984; Thompson 2011; Dong et al. 2015), a merger or collision of two white dwarfs in a binary provides the necessary conditions for explosive burning of the carbon-oxygen fuel. Observational evidence disfavors the presence of a SD companion in the most well studied cases (e.g., SN 2011fe Nugent et al. 2011; Chomiuk et al. 2012; Shappee et al. 2013). On the other hand, there are theoretical diﬃculties with producing a SN Ia from the DD scenario (e.g., Shen et al. 2012).

One avenue for progress is the characterization of the delay-time distribution (DTD) of SNe Ia, or the SN Ia rate as a function of time after an episode of star formation. By constraining the rate at which SNe Ia occur after an episode of star formation, certain progenitor scenarios can be ruled out. The SN Ia DTD is broadly consistent with a t−1 form; equivalently, there is evidence for a population of SNe Ia that occur promptly after star formation (t 108 yr), and a delayed component ∼ 8 that occurs at much later times (t > 109 yr) (Mannucci et al. 2005; Scannapieco ∼ & Bildsten 2005; Sullivan et al. 2006; Brandt et al. 2010; Maoz et al. 2011; Maoz, Mannucci & Brandt 2012). Observationally, lower mass galaxies produce more SNe Ia per unit stellar mass than high mass galaxies (e.g., Mannucci et al. 2005; Sullivan et al. 2006; Li et al. 2011a; Graur & Maoz 2013).

While the discovery and follow-up of rare objects is informative, there is one aspect of ASAS-SN that has yet to be exploited. ASAS-SN is largely agnostic with regard to host galaxy properties and thus provides a quasi-unbiased census of SNe in the nearby universe. Some SNe are invariably missed due to their location on the sky, being near bright stars or behind the Sun, and extinction (both Galactic and extragalactic) will also result in some incompleteness. However, for the optically accessible, bright SNe (mV < 17), ASAS-SN is more sensitive to small galaxies and nuclear regions than most previous SN surveys (Holoien et al. 2017a,b,c). Furthermore, the brightness and sample size of the ASAS-SN survey has allowed us to spectroscopically follow-up and classify all of our discoveries, which eliminates a signiﬁcant source of bias that has aﬀected many previous SN surveys.

1.3. Scope of the Dissertation

In Chapter 2 I present a study of the gas phase chemical abundances of a sample of compact star forming galaxies. I discuss the various methods of measuring gas phase abundances and address potential pitfalls associated with the various methods. In Chapter 3 I develop an improved set of diagnostics that can be used to measure gas phase abundances in galaxies spanning a wide range of physical properties. In Chapters 4 and 5 I present two complementary studies examining the late-time evolution of TDEs, and discuss how their late-time behavior can aﬀect the appearance of their host galaxies. In Chapter 6 I show the results of the ﬁrst

9 study of the UV spectroscopic evolution of a nearby tidal disruption event. Finally, in Chapter 7 I use the statistical power of three years of ASAS-SN discoveries to constrain the relative SN Ia rate across an unprecedentedly wide range of host galaxy properties.

10 Chapter 2: Precise Abundances in Star Forming Galaxies

2.1. Introduction

While general trends between galactic parameters are both interesting and useful, objects that deviate from the observed relations offer a unique perspective, as it is these objects which allow for the direct indentification of important physical mechanisms driving galactic evolution. The “Lyman Break Analogs” (LBA) project (Heckman et al. 2005) identified a class of galaxies that appear to deviate from the local galaxy population and more closely resemble high-redshift Lyman Break Galaxies (LBGs; for a review see Giavalisco 2002). These objects were initially

9 −2 identiﬁed as nearby (z < 0.3), compact (IFUV > 10 L⊙ kpc ), and UV bright

10.3 (LFUV > 10 L⊙) objects, mimicking the physical conditions in LBGs seen at much higher redshifts. Thus, if LBAs are true analogs of LBGs, they provide us with an opportunity to study a mode of star formation that may have been dominant in the early universe in a much more detailed way than the very distant LBGs allow. After the identiﬁcation of LBAs, subsequent work (Hoopes et al. 2007; Basu-Zych et al. 2007a; Overzier et al. 2008, 2009, 2010; Gon¸calves et al. 2010) used the Hubble Space Telescope (HST), Spitzer, VLA, Sloan Digital Sky Survey (SDSS), Galaxy

This chapter is adapted from “Direct Method Gas Phase Oxygen Abundances of 4 Lyman Break Analogs”, Brown, Croxall, & Pogge, ApJ, 792, 140, (2014).

11 Evolution Explorer (GALEX), and the Keck II telescope to investigate the physical properties of these systems, as well as the degree to which they may resemble LBGs.

The gas-phase oxygen abundance of these objects was estimated by Overzier et al. (2009, 2010) using the N2 and O3N2 empirical calibrations from Pettini & Pagel (2004, hereafter PP04). After applying the N2 relation to SDSS galaxies and LBAs, Overzier et al. (2010) showed the oﬀset of the LBAs from the MZ relation of local star forming galaxies is inversely correlated with mass, with the least massive LBAs falling > 0.2 dex below the locus of SDSS galaxies. Low metallicity objects ∼ are of particular interest, as they oﬀer a view of how the earliest stars and galaxies formed (e.g. Kunth & Ostlin¨ 2000; Skillman et al. 2013). Fortunately the empirical abundance calibrations incorporate many low mass, low metallicity blue compact galaxies (BCGs) in the hope of extending the calibrations to the lowest metallicities possible. However, we have no a priori reason to expect that a locally calibrated empirical abundance relation ought to apply to a class of exotic objects experiencing an episode of relatively extreme, concentrated star formation, as is found in the centers of these LBAs.

Typical LBAs exhibit star formation rates an order of magnitude higher than local dwarf galaxies. Additionally, most LBAs have morphologies and kinematics consistent with recent interactions (Overzier et al. 2009, 2010; Gon¸calves et al. 2010). Clearly these objects depart from the physical parameter space occupied by local H II regions and dwarf galaxies used to calibrate the empirical relations. Are the empircally estimated oxygen abundances of LBAs being systematically aﬀected by their extreme physical conditions? For instance, Pilyugin, V´ılchez & Thuan (2010) showed that many of the line ratios used in the typical strong-line abundance indicators (Pagel et al. 1979; Alloin et al. 1979) are complex functions of electron temperature. They show that deriving an abundance calibration from a sample

12 of relatively cool H II regions and applying it to relatively hot H II regions could yield erroneous abundance estimates. Alternatively, if locally calibrated empirical relations return reliable abundance estimates when applied to LBAs, this would also be of interest, as this is not immediately obvious given the extreme physical nature of these objects.

Fortunately, we are not required to rely on empirical calibrations alone for these objects. With a measure of the electron temperature (Te), we can determine the oxygen abundance directly using the Te or “direct” method (Dinerstein 1990). The electron temperature can be determined from temperature sensitive intensity ratios of collisionally excited forbidden lines. Generally speaking, as metallicity increases, the temperature of the nebula decreases, as there are more ions available to cool the gas. In relatively low metallicity nebulae, a measure of the electron temperature is typically obtained using the [O III] λ4363/λλ(4959 + 5007) line ratio. However, somewhat problematically, the auroral oxygen line [O III] λ4363 A˚ is intrinsically faint, making it notoriously diﬃcult to measure in distant and/or faint objects (though see Hoyos et al. (2005); Kakazu, Cowie & Hu (2007); Amor´ın, P´erez-Montero & V´ılchez (2010); Amor´ın et al. (2012) for instances of the direct method being applied at relatively high redshifts).

We have measured [O III] λ4363 A˚ in four of the objects from the Overzier et al. (2009) sample using the newly commissioned Multi-Object Double Spectrograph #1

(MODS1) on the 8.4m Large Binocular Telescope (LBT). We use the [O III] line ﬂuxes to determine an electron temperature, yielding a gas-phase oxygen abundance measurement that we can compare to the values derived via empirical techniques.

In Section 2.2 we describe the observations and data reduction. Section 2.3 describes the analysis of the data, including the subtraction of the underlying

13 stellar continuum. In Section 2.4 we present the results of our analysis. Lastly, in Section 2.5 we discuss where LBAs ﬁt in the bigger picture of galaxy formation and evolution; Section 2.6 provides a summary. Throughout this paper we assume

−1 −1 H0 = 70 km s Mpc , Ωλ = 0.7, and ΩM = 0.3. With these cosmological parameters, a redshift of z =0.2 corresponds to an age of the universe of 11 Gyr. ∼

2.2. Observations and Reduction

2.2.1. Observing Procedures

We observed 4 of the LBAs identiﬁed in Overzier et al. (2009) using MODS1 on the LBT (Pogge et al. 2010) between September 2011 and January 2013. All targets were observed in longslit mode with a 1′′.0 slit imaged onto two 3072 8192 format × e2v CCDs with 15µm pixels. MODS1 uses a dichroic that splits the light into separately optimized red and blue channels at 5650 A.˚ The blue CCD covers a ∼ wavelength range of 3200 – 5650 A,˚ with a 400 l mm−1 grating (spectral resolution ∼ of 2.4 A),˚ while the red CCD covers a wavelength range of 5650 – 10000 A,˚ with a ∼ 250 l mm−1 grating (spectral resolution of 3.4 A).˚

Each target was observed with three 600s exposures for a total of 1800s, with the exception of J005527, which was observed with four 1200s exposures for a total of 4800s. The position angle of the slit approximated the parallactic angle at the midpoint of the observation so as to minimize slit losses due to differential atmospheric refraction. If the arc lamp or flat field data was not available on the night of the observation, we used the calibration data obtained within 1-2 days of our observations. Given the stability of MODS1 over the course of an observing run, this is sufficiently recent to provide accurate calibrations. We obtained bias frames and Hg(Ar), Ne, Xe, and Kr calibration lamp images, which we used for wavelength

14 calibration. Night sky lines were used to correct for the small ( 1 A)˚ residual ∼ ﬂexure. Standard stars were observed with a 5x60′′spectrophotometric slit mask used for ﬂux calibration. The standard stars are from the HST Primary Calibrator list, which is composed of well observed northern-hemisphere standards from the lists of Oke (1990) and Bohlin, Colina & Finley (1995).

Target selection was done such that priority was given to the objects from Overzier et al. (2009) with the lowest oxygen abundance estimates, and hence most oﬀset from the MZ relation, that were visible at the time of observation. Our ﬁnal sample has a mean redshift z =0.205 with standard deviation σ =0.053. h i z

2.2.2. Data Reduction

The basic 2D data reduction was performed in Python using the modsCCDRed suite of programs1. We used modsCCDRed to bias subtract, flat field, and illumination correct the raw data frames. We then coadded the frames and removed cosmic rays with L.A. Cosmic2 (van Dokkum 2001), taking extra care to ensure any emission features were not misidentified as cosmic rays.

We performed sky subtraction and 1D extraction using the modsIDL pipeline3. This pipeline has been developed speciﬁcally for MODS and makes use of the XIDL packages4. Figure 2.1 shows our reduced spectra compared with spectra from the SDSS. The MODS1 spectra achieve a higher S/N than the SDSS spectra across a wider wavelength range. The inset shows a zoomed view of the metallicity sensitive

[O III] λ4363 A˚ auroral emission line. For each target, the MODS1 spectra show a high signiﬁcance detection of the line. In some cases, the eﬀects of stellar absorption

1http://www.astronomy.ohio-state.edu/MODS/Software/modsCCDRed/ 2http://www.astro.yale.edu/dokkum/lacosmic/ 3http://www.astronomy.ohio-state.edu/MODS/Software/modsIDL/ 4http://www.ucolick.org/ xavier/IDL/ ∼ 15 near the Balmer lines can be seen. Note the lack of detection of the auroral nitrogen emission line, consistent with the previously estimated low metallicity of these objects from empirical bright line methods.

2.3. Analysis

2.3.1. Stellar Continuum Subtraction

Many of the emission lines are blended with underlying stellar absorption features. To obtain accurate line ﬂux measurements it is necessary to remove the underlying stellar component before extracting line ﬂuxes.

Prior to modeling the underlying stellar component of the LBAs, we correct for foreground Galactic exinction using the dust maps from Schlegel, Finkbeiner &

Davis (1998) and the reddening law from O’Donnell (1994) with RV =3.1. We then shift each spectra to the rest frame using the redshifts from the SDSS and resample our spectra to 1 A˚ per pixel.

We model the underlying stellar component of each target using the STARLIGHT stellar population synthesis code (Cid Fernandes et al. 2005, 2011). STARLIGHT uses a Markov Chain Monte Carlo approach to ﬁtting a combination of spectra from a stellar library to an observed spectrum. We adopted the stellar library from Bruzual & Charlot (2003) and assumed a Chabrier IMF (Chabrier 2003). We chose base spectra that cover a wide range in both metallicity (0.0004 Z 0.03) and age (1 Myr τ 10 Gyr). In general, our galaxies lack any strong ≤ ≤ ≤ ≤ stellar absorption features which could be used to place strong constraints on the underlying stellar population. However we are able to model the general shape of the continuum, as well as remove any absorption features near our metallicity-sensitive lines. In particular, the [O III] λ4363 A˚ line lies in close proximity to Hγ, and so we

16 need to take extra care to make sure the [O III] λ4363 A˚ flux in not degraded by Balmer absorption. In general, we find that our galaxies are best fit with a young (τ < 20 Myr) stellar population of roughly solar metallicity, with a velocity dispersion ∼ σ 200 km s−1. We regard this strictly as a qualitative assement; our targets ∼ can be equally well fit with a wide range of ages, metallicities, and kinematics. In general, we find the effects of our detailed model fit on the strengths of the stellar absorption features to be minimal. Accounting for stellar absorption, we find, on average, EW(Hβ(ABS)) = 2.70 A,˚ which is small compared to our mean EW(Hβ) = 111 A.˚ See Table 2.6 for further details. −

2.3.2. Line Flux Measurment

We assume the that emission lines in our targets are approximately Gaussian. We fit a library of atomic lines to each spectrum using MPFIT5 (Markwardt 2009), an IDL implementation of the robust non-linear least squares fitting routine MINPACK-1. We assume the lines all have the same FWHM in velocity space and allow for variation in the intensity of each line as well as a small translation in wavelength (< 1 A).˚ We test the robustness of our flux measurements and find that when using ∼ other flux extraction methods (e.g. direct integration), we obtain good agreement between the two methods to within a percent or so. We normalize our fluxes to Hβ and deredden the spectra using the Balmer decrement. Our final value of C(Hβ) is an error-weighted average of the values obtained using Hα/Hβ,Hβ/Hγ, and Hα/Hγ and their appropriate intensity ratios assuming Case B recombination. See Table 2.6 for a list of relevent line intensities used in our subsequent analysis. We adopt the

5http://purl.com/net/mpﬁt

17 following notation:

R2 = I[O II]λλ3727, 29/IHβ (2.1)

R3 = I[O III]λλ4959,5007/IHβ (2.2)

R23 = R2 + R3 (2.3)

P = R3/R23 (2.4) for the principal diagnostic emission line ratios.

2.3.3. Abundance Determination

We detect [O III] λ4363 A˚ in each of the galaxies, with the minimum detection at S/N = 8.8 and an average S/N = 15.9; well above the S/N typically required for obtaining an electron temperature from [O III] λ4363 A˚ (e.g. Croxall et al. 2009). We assume the electrons in the H II region follow a Maxwell– Boltzmann equilibrium energy distribution. In the low density Boltzmann regime,

[O III] λ4363/λλ(4959 + 5007) is goverened by the relative level populations of the

[O III] ion, and, due to the spacing of the energy levels, the relative level population is very sensitive to the electron temperature of the ionized region. Since the derived ionic abundances are a strong function of electron temperature, a measurement of

[O III] λ4363/λλ(4959 + 5007) allows us to compute the total oxygen abundance directly, rather than having to rely on empirical methods.

The assumption of a Maxwell–Boltzmann distribution of electron energies has recently come into question. Speciﬁcally, even diﬀerent temperature sensitive line ratios used to directly measure the electron temperature (e.g. [O III]

λ4363/λλ4959,5007, [S II] λλ4069, 76/λλ6717, 31, [N II] λ5755/λλ6548,84, and

[O II] λλ7318, 24/λλ3726,9) sometimes yield inconsistent results. Nicholls, Dopita & Sutherland (2012) proposed that these discrepancies could be explained if the

18 distribution of electron energies follows a κ-distribution, rather than a Maxwell– Boltzmann distribution. However, we are only concerned with relative comparisons for a given electron temperature measurement method. Thus, we do not expect systematic effects arising from our assumed energy distribution to significantly influence our results.

Osterbrock & Ferland (2006) describes how to compute Te and ne in ionized nebulae. In this paper, we measure the electron temperature (Te) and density (ne) using the im_temden IDL routines from the Moustakas code repository6. This set of routines uses well-known line ratios to compute the electron temperature and/or electron density of a given region. We assume a three zone ionization region, composed of a high ionization region (with T = T T ([O III])), an e 3 ≡ e intermediate ionization region (T T ([Ar III])), and a low ionization region (with e ≡ e T = T T ([O II])). We measure T from [O III] λ4363/λλ(4959 + 5007) and e 2 ≡ e 3 compute T2 using the relation

t2 =0.264+0.835t3 (2.5)

(where t = T/104) from Pilyugin et al. (2009). Due to the substantial noise from sky contamination and relative weakness of the [O II] λλ7320,30 lines, we don’t achieve a strong detection of these lines in all of our targets. In the two cases where we are able to make a robust measurement of the lines, we ﬁnd reasonable agreement between the calcuated T2 using the relation above and the T2 we measure from the

[O II] line ratios. We compute the electron density ne using the density sensitive line ratio [S III] λ6717/λ6731. For objects with densities less than 100 cm−3, we adopt a value of 100 cm−3, as lower densities are consistent with 100 cm−3. While J005527 shows signs of slightly higher electron density, we are still well inside the

6https://github.com/moustakas/impro

19 low density regime for each of our targets. Table 2.6 lists the measured temperatures and densities for each LBA in our sample. Given the redshift of these objects, several [S III] lines (e.g. [S III] λλ9069,9532) are unobservable with MODS1, and so we exclude sulphur from our abundance determinations.

We then take our electron temperatures and densities and use Moustakas’ im_nlevel routine to compute the relative populations and emissivities for the diﬀerent ions using an n-level atom calculation. For simplicity, in the low ionization zone we adopt the reasonable canonical assumptions that Te([N II]) = Te([O II]) = T2 where T2 is the theoretical value derived from our measured T3. Similarly, for the high ionization region we assume Te([Ne III]) = Te([O III]) = T3. Lastly, in the intermediate ionization region, we assume Te([Ar III])=0.83T3 +0.17 from Garnett (1992). We obtain a density for each ion using

i N(X ) Iλi jHβ + = (2.6) N(H ) IHβ jλi In order to compute the total abundance of a given element, we sum the observable ionic states. In the case of oxygen, we assume O O0 +O+ +O++ = (2.7) H H+ We compute both total and ionic abundances for O, N, Ne, and Ar. We compute ionization correction fractions (ICFs) for N, Ne, and Ar. Adopting the ICFs from Thuan, Izotov & Lipovetsky (1995): O ICF(N) = (2.8) O+

O ICF(Ne) = (2.9) O++

Ar ICF(Ar) = = [0.15 + x(2.39 2.64x)]−1 (2.10) Ar++ − 20 where x =O+/O. The abundance estimates (and associated uncertainties) for each object is presented in Table 2.6.

2.4. Results

2.4.1. Excitation

In Figure 2.5 we show the standard diagnostic Baldwin, Phillips, Terlevich (BPT) diagram (Baldwin, Phillips & Terlevich 1981) used to distiguish between ionization regions heated primarily by star-formation and regions heated primarily by AGN. Star forming SDSS galaxies7 from the MPA-JHU catalog are shown as gray contours,

H II regions8 from Pilyugin, Grebel & Mattsson (2012) are shown as black points, and our LBAs are shown as the large cyan dots. The dashed and solid red lines are from Kauffmann et al. (2003b) and Kewley et al. (2006) and denote the boundaries between star forming galaxies and AGN. Our results are consistent with those presented in previous studies; the LBAs fall squarely in the star-formation dominated region of the BPT diagram. We find that J005527 (red circle) is offset to the right in Figure 2.5 relative to our other LBAs and the H II regions from Pilyugin, Grebel

& Mattsson (2012), indicative of enhanced [N II] emission.

Figure 2.6 shows the excitation conditions of our LBAs based on the relative oxygen line ratios. We plot the star forming SDSS galaxies (gray contours), the

H II regions from Pilyugin, Grebel & Mattsson (2012) (black dots), and our 4 LBAs

(cyan dots). The left panel compares the relative [O II] and [O III] line ratios. The dotted lines show constant R23; from bottom left to top right log(R23) = 0., 0.5, 1.0. As seen in Figure 2.5, the LBAs and H II regions from Pilyugin, Grebel & Mattsson

(2012) have higher [O III] emission compared to the SDSS galaxies. The right panel

7Available at http://www.mpa-garching.mpg.de/SDSS/DR7/ 8Available at http://vizier.cfa.harvard.edu/viz-bin/VizieR?-source=J/MNRAS/424/2316

21 shows P = R3/R23 as a function of log(R23). Again, the LBAs display excitation conditions which are typical of H II regions, but quite unusual for star forming SDSS galaxies.

In Figure 2.7 we show line diagnostic diagrams from Pilyugin, V´ılchez & Thuan

(2010). The LBAs display line ratios that are remarkably similar to “warm” H II regions. Again, the red circle marks the location of J005527, which shows signs of enhanced nitrogen relative to the other LBAs, even though it still remains well within the parameter space occupied by H II regions.

Figure 2.8 shows the region around 4660 A,˚ where we detect characteristic Wolf-Rayet features (e.g. Bresolin, Garnett & Kennicutt 2004; Brinchmann, Kunth

& Durret 2008) in each of our 4 targets. The most common features are C IV

λ4658 A,˚ and He II λ4686 A.˚ J005527 displays the strongest Wolf-Rayet signatures, speciﬁcally N III λ4640 A˚ and a broad bump from 4600–4700 A,˚ in addition to the ∼ C IV and He II emission lines. These high ionization features are associated with very young stellar populations, as they are typically visible for only a few million years following an episode of signiﬁcant star formation.

2.4.2. Oxygen Abundances

Our oxygen abundances are presented in Table 2.6. We are able to reproduce the oxygen abundances from Overzier et al. (2009) to within a few percent using the PP04 O3N2 method on the SDSS spectra. We have included the original N2 and O3N2 calibrations from PP04 as well as newer CALIFA-Te calibrations from Marino et al. (2013) that use a larger sample of H II regions with direct oxygen abundances. The calibrations from Marino et al. (2013) are generally shallower than

22 those presented in PP04, but in the abundance range we are concerned with, the CALIFA and PP04 calibrations produce nearly identical results.

Due to the location of the LBAs in the transition zone of the R23 index, the popular theoretical strong-line calibrations are rather insensitive to the oxygen abundance of these objects (e.g. Pilyugin & Thuan 2005; Pe˜na-Guerrero, Peimbert & Peimbert 2012). Furthermore, the numerous theoretical calibrations are known to systematically deviate from each other (see Kewley & Ellison 2008). For these reasons, we consider here only the empirical strong-line methods, which are deﬁned almost entirely by H II regions with direct abundance determinations.

Given the scatter in the emprirical calibrations of 0.3 dex and the uncertainties ∼ in our direct abundances, the two results are roughly consistent in the sense that both indicate that these LBAs have low oxygen abundances for their mass relative to the MZ relation. The N2 estimates generally give higher O/H values than both the O3N2 estimates and our direct abundances (see Table 2.6). This is qualitatively consistent with Kewley & Ellison (2008), who show that the N2 method tends to yield O/H values that are slightly higher than the O3N2 method at low oxygen abundances (12+log(O/H)< 8.2). However, with four objects in our sample this is ∼ not statistically significant, and so we refrain from drawing any inferences regarding the systematic effects between strong-line calibrations and direct abundances in LBAs. Importantly, the LBAs remain significantly below the locus of SDSS galaxies regardless of the abundance method used. With this in mind, and for the sake of simplicity and consistency with previous studies, we restrict our discussion of strong-line estimates to the N2 empirical calibration from PP04.

Figure 2.9 shows the oxygen abundances of our LBAs relative to the SDSS galaxies. In order to minimize systematic eﬀects, it is necessary to only compare the

23 oxygen abundances of objects when using the same diagnostic (e.g. direct method abundance of SDSS galaxies versus direct method abundance of LBAs). Our direct method measurements of the LBAs are shown as cyan dots. Due to the difficulty of measuring the auroral lines, we do not have direct method abundances for a statistically significant number of individual SDSS galaxies. We do however have the best fit relation to the direct method oxygen abundance of stacked SDSS spectra from Andrews & Martini (2013), which we have included in Figure 2.9 as the thick black line.

The SDSS galaxies (gray contours) have masses from MPA-JHU catalogue (see Kauffmann et al. (2003a); Salim et al. (2007)) and have had the oxygen abundances estimated using the N2 calibration from PP04. The LBA N2 estimates of oxygen abundance are shown as orange and green dots for the SDSS and MODS1 data respectively; the offset from the locus of individual SDSS contours is clear and consistent with Overzier et al. (2010). While the relation from Andrews & Martini (2013) systematically deviates from the N2 oxygen abundance estimates (as expected), our direct method oxygen abundances of the LBAs still fall well below that of the stacked SDSS spectra. Thus it appears that systematic effects in the strong-line calibrations cannot explain the offset of the LBAs from the MZ relation; these LBAs have low oxygen abundance given their mass.

2.5. Discussion

2.5.1. Excitation Conditions of LBAs

Empirical abundance calibrations are typically based on samples of H II regions with well-determined electron temperatures and thus directly measured abundances. However, the direct method is subject to a number of observational biases. For

24 instance, metal poor objects generally have higher electron temperatures, brighter auroral lines, and more easily determined abundances. This results in a preferential selection of low metallicity objects in empirical calibrations. Furthermore, most large scale surveys of emission line galaxies, like the SDSS, are composed of predominantly low-excitation galaxies relative to the H II regions on which the empirical calibrations are based (see Figure 2.6). Moustakas et al. (2010) cautions against haphazardly extrapolating empirical relations to lower excitation regimes occupied by the majority of galaxies in large surveys, as doing so could result in erroneous abundance determinations.

Looking at Figure 2.7, the emission line ﬂux ratios of all 4 of our LBAs are remarkably similar to those of the “warm” H II ratios from Pilyugin, V´ılchez &

Thuan (2010). Additionally, even though J005527 displays fairly strong [N II] emission compared to the other LBAs in our sample, it remains in an excitation regime fairly typical of local H II regions. This supports the idea that locally determined empirical calibrations ought to return reasonable abundance estimates for LBAs. This is a crucial step in justifying the application of locally calibrated empirical relations to LBAs and LBGs. However, caution must still be exercised when extrapolating these relations to high redshifts, as recent work has suggested that the LBG population as a whole evolves rapidly with redshift (Stanway & Davies 2014).

It is readily apparent that LBAs are undergoing an episode of signiﬁcant star formation. Within a few million years of the initial burst, large numbers of Wolf-Rayet stars, supernova remnants, and other extremely hot objects could conspire to produce an abnormally hard ionization spectrum. If we suppose that the gas surrounding these hot objects was subject to a harder ionization spectrum than what is observed in local H II regions, we would expect to see relatively

25 enhanced ionic emission features. High energy photons have a smaller cross section for interaction. As a result, these high energy photons have a longer mean free path, resulting in larger partially ionized regions. In general, this results in enhanced ionic emission. In the case of ionized nitrogen, an anomalously hard ionization spectrum would produce enhanced [N II] emission and result in systematically high abundance estimates when using a locally calibrated empirical relation.

Berg, Skillman & Marble (2011) showed that enhanced nitrogen abundance (relative to oxygen) could also bias strong-line estimates towards high oxygen abundance. However, the excitation conditions of our LBAs are quite diﬀerent from what is expected in the evolved Wolf-Rayet galaxies from Berg, Skillman & Marble

(2011). Furthermore, our LBAs do not show abnormally high [N II]/[O II] ratios. If the high N2 method estimates observed in some of our targets were the result of an abnormally hard ionization spectrum, we would not expect the O3N2 method to yield a high abundance estimate, as such a radiation ﬁeld would have a similar eﬀect on both N+ and O++ emission.

2.5.2. LBAs and the Fundamental Metallicity Relation

LBAs have masses typical of entire galaxies and thus it is interesting to note that their excitation conditions fall in a region that is sparsely populated by the SDSS star forming galaxies, but well occupied by the H II regions from Pilyugin, Grebel &

Mattsson (2012). It seems that the LBAs more closely resemble giant H II regions in terms of photoionization conditions than typical SDSS galaxies. What is the primary physical process causing the LBAs to be so signiﬁcantly oﬀset from SDSS galaxies?

The deﬁning characteristic of LBAs is their compact UV emission arising from recent star formation, and indeed, the typical star formation rate for an LBA is an

26 order of magnitude higher than a typical SDSS galaxy (Overzier et al. 2009). Such high rates of star formation imply a recent replenishment of star forming material in the LBA systems. This inﬂux of gas could be due to a tidal interaction (e.g. Peeples, Pogge & Stanek 2009), or perhaps a recent merger. Generally these events will result in dilution of the interstellar gas and a corresponding reduction in the observed metallicity.

Peeples, Pogge & Stanek (2009) compute the expected dilution which might result from the funneling of gas from large galactocentric radius into the center of a galaxy. They find that for a galaxy with a reasonable metallicity gradient and gas surface density profile, gas flowing inward from within 20 kpc would result in a metallicity dilution ∆(O/H) = 0.5 dex, which is remarkably close to the MZ − relation offsets observed for their morphologically disturbed galaxies. The LBAs in our sample also tend to be offset from the SDSS MZ relation of Andrews & Martini (2013) by a comparable amount, suggesting that LBAs may have recently experienced an inflow of unenriched gas. This is consistent with the disturbed morphology of LBAs seen in the HST images from Overzier et al. (2009, 2010) and the dispersion dominated kinematics (e.g. σ/v > 1) presented in Gon¸calves et al. (2010).

A global inﬂow of star forming material could also result in an intense burst of star formation (Rupke, Veilleux & Baker 2008; Kewley et al. 2010). It is often assumed that the timescale for the enrichment of the interstellar medium (ISM) is short compared to the overall galaxy evolution timescale. However, the photoionization conditions of LBAs indicate that we are observing the actual burst of star formation take place. The LBAs have not had time to convert the infalling gas into stars and have those stars chemically enrich their ISM. If the burst of star formation in LBAs is indeed being powered by relatively low metallicity gas, we

27 would expect that their residuals from the MZ relation correlate with star formation rate.

The Fundamental Metallicity Relation (FMR; Mannucci et al. 2010; Andrews & Martini 2013) parametrizes the correlation of residuals from the MZ relation and star formation rate by introducing the parameter µ such that µ = log M∗ α log(SFR). α α − The sample of galaxies compiled by Mannucci et al. (2010) consists of > 140000 SDSS galaxies at z 0, 182 objects from 0.5

The exact value of α is quite sensitive to the abundance diagnostic used. Yates, Kauffmann & Guo (2012) found α =0.19 when using the oxygen abundances from Tremonti et al. (2004), and Andrews & Martini (2013) found α = 0.66 when using direct method abundances, both of which are significantly different from the α = 0.32 presented in Mannucci et al. (2010). Additionally, the determination of α merely minimizes the scatter for a given abundance diagnostic; two strong-line calibrations will generally not share the same FMR.

Determining where an object sits on the FMR requires knowledge of the SFR in addition to the mass and metallicity of the object. Overzier et al. (2009) adopts SFR calibrations from Calzetti et al. (2009) and computes various SFRs using Hα,Hα + 24µm, and FUV luminosities. The Hα ﬂux is associated with only the most recent star formation activity, whereas the FUV calibration is sensitive to the integrated star formation activity over the previous 1 Gyr. The appearance of the LBAs is dominated by the current burst of star formation activity, so we adopt the Hα + 24µm SFRs (Kennicutt et al. 2007; Calzetti et al. 2007).

28 The Hα + 24µm calibration is not without its own systematic effects. For example, an AGN could preferentially heat dust and result in 24µm flux above that which would arise from star formation alone. However, none of the Overzier et al. (2009) LBAs appear to host a Type 1 (unobscured) AGN. While the presence of Type 2 (obscured) AGN is not ruled out, it seems unlikely given where these LBAs lie on the diagnostic diagrams (Overzier et al. 2009). If an AGN were present, it is likely to only have a very small effect.

Figure 2.10 shows the oxygen abundances of the SDSS star forming galaxies and the LBAs as a function of µα, where we have adopted the values of α = 0.30 and α = 0.66 corresponding to the N2 index and direct method respectively from Andrews & Martini (2013). The cyan dots show our LBAs with direct method oxygen abundances; the thick black line shows the linear ﬁt to the FMR for stacked SDSS spectra from Andrews & Martini (2013). The N2 estimates of oxygen abundance for our LBAs are shown as orange and green dots for the SDSS and MODS1 data respectively. The gray contours are the star forming SDSS galaxies from the MPA-JHU catalogue (see Kauﬀmann et al. (2003a) and Salim et al. (2007) for mass determinations and Brinchmann et al. (2004) for star formation rate determinations). The oxygen abundances of the SDSS galaxies are estimated from the PP04 N2 calibration. We see that plotting oxygen abundance as a function of both mass and star formation rate does indeed reduce the scatter between the LBAs and SDSS data for a given abundance estimation method (direct or emprical).

It is important to keep in mind that a comparison of where the direct abundance measurements fall on the FMR relative to the contoured SDSS data is largely meaningless, since we do not expect the diﬀerent abundance diagnostics to produce consistent results. However, the fact that incorporating SFR drastically reduces the scatter for a given abundance diagnostic suggests that the high SFR, low oxygen

29 abundance, and disturbed morphology of these LBAs could be explained by a recent inﬂow of relatively unenriched gas and is consistent with the existence of a FMR that the LBAs appear to follow.

2.6. Summary

It is believed that LBAs (z 0.2) are true analogs of LBGs (z > 3), and thus ∼ ∼ laboratories for studying one of the dominant modes of star formation in the early universe in exquisite detail. Before applying locally calibrated empirical relations to these LBAs, it is important to investigate whether or not the locally calibrated empirical relations based on single, bright H II regions in normal galaies still hold for the physical conditions present in LBAs.

The empirically-derived oxygen abundances of LBAs show them to be metal deﬁcient for their mass, falling > 0.2 dex below the MZ relation deﬁned by local ∼ star forming galaxies. We have presented direct abundance measurements of 4 LBAs using MODS1 on the LBT to detect [O III] λ4363 A˚ in each target, allowing for a direct measurement of the electron temperature and thus a robust determination of the gas phase oxygen abundance. We have shown that:

LBAs display excitation conditions that are unusual for SDSS galaxies, but are • quite typical of H II regions from Pilyugin, Grebel & Mattsson (2012).

The N2 empirical calibration is generally valid for the LBAs presented here. • Objects with particularly hard ionizing spectra may have biased strong-line abundance estimates, but the eﬀect is likely to be smaller than the scatter in the empirical calibrations.

30 LBAs are offest from the MZ relation of local star forming glaxies in the sense • that they have lower oxygen abundances for a given mass. However, when their abnormally high star formation rates are taken into account, we find that they do not appear to deviate significantly from the FMR. This, coupled with their disturbed morphologies, is consistent with an interaction driven gas inflow paradigm.

We can improve our understanding of LBAs in a statistical sense by increasing the size of the sample studied. Here we have presented observations of only 4 of the 31 LBAs in the Overzier et al. (2009) sample. With instruments like MODS1, precise spectroscopic observations of LBAs are quite feasible and can be done with a modest amount of telescope time. An increased number of LBAs with robustly determined abundances would allow us to place tighter constraints on the systematic effects between locally calibrated strong-line abundance estimates and direct method abundances. Lastly, it has been suggested that both the MZ relation and FMR are a consequence of the relation between gas phase oxygen abundance and stellar-to-gas mass ratio (the Universal Metallicity Relation; Zahid et al. 2014b). They argue that once the ISM of a galaxy has been enriched to a point such that the amount of oxygen being locked up in low mass stars is comparable to the oxygen produced by massive stars, the oxygen abundance asymptotically approachs a value which is independent of redshift. If the LBAs have indeed experienced a significant inflow of gas mass relative to their stellar mass, they could potentially serve as key testing grounds for the Universal Metallicity Relation.

31 200 J092600 100 80 γ H SDSS 150 60 λ

] [OIII] 4363

40 α H −1

3727 20 100 λ Å

−2 4313 4353 4393 4433 β [OII] 50 H cm −1 0 100 Hγ erg s 80 MODS1

−17 150 60 [OIII] λ4363 40 α [10 3727 H λ 100 λ 20 f MgII λ2798 β

[OII] 4313 4353 4393 4433 50 H [SII] λ6716,31 0 3000 5000 7000 9000 REST WAVELENGTH [Å]

Fig. 2.1.— Comparison of our MODS1 spectra with SDSS spectra (1/4).

200 J004054 100 80 SDSS 150 60 Hγ

] 40 [OIII] λ4363 −1 100 20 Å

0 α H −2 4313 4353 4393 4433 3727 λ 50 β H cm [OII] −1 0 100 Hγ erg s 80 MODS1 α

−17 150 60 [OIII] λ4363 H 40 [10 3727 λ 100 λ 20 f MgII λ2798 [SII] λ6716,31 β

[OII] 4313 4353 4393 4433 50 H 0 3000 5000 7000 9000 REST WAVELENGTH [Å]

Fig. 2.2.— Comparison of our MODS1 spectra with SDSS spectra (2/4).

32 200 J020356 100 80 γ SDSS 150 60 H λ

] [OIII] 4363

40 α H −1

3727 20 100 λ Å

−2 4313 4353 4393 4433 β [OII] 50 H cm −1 0 Hγ 100 erg s MODS1

80 α

−17 150 λ H 60 [OIII] 4363

λ β [10 MgII 2798 3727 40 H λ 100 λ [SII] λ6716,31 f 20

[OII] 4313 4353 4393 4433 50 0 3000 5000 7000 9000 REST WAVELENGTH [Å]

Fig. 2.3.— Comparison of our MODS1 spectra with SDSS spectra (3/4).

200 J005527 100 80 Hγ SDSS 150 60 λ

] [OIII] 4363 40 α H −1 3727 100 λ 20 Å

−2 4313 4353 4393 4433 β [OII] 50 H cm −1 0 Hγ 100 erg s MODS1

80 α

−17 150 λ H 60 [OIII] 4363 [10 3727 40 λ 100 λ λ

f [SII] 6716,31 MgII λ2798 20 β

[OII] 4313 4353 4393 4433 50 H 0 3000 5000 7000 9000 REST WAVELENGTH [Å]

Fig. 2.4.— Comparison of our MODS1 spectra with SDSS spectra (4/4).

33 1.0 ) β 0.5 5007 / H

λ 0.0

log([OIII] −0.5

−1.0 −2.0 −1.5 −1.0 −0.5 0.0 log([N II] λ 6583 / Hα)

Fig. 2.5.— BPT diagram composed of star forming SDSS galaxies (gray contours), H II regions from Pilyugin, Grebel & Mattsson (2012) (black points), and the LBAs from our sample (cyan/red circles). The uncertainties in the line ratios for the LBAs are smaller than the plotting symbols. The dashed and solid red lines are from Kauﬀmann et al. (2003b) and Kewley et al. (2006) and denote the boundaries between star forming galaxies and AGN. The red circle represents J005527, which seems to exhibit enhanced nitrogen relative to the other LBAs.

34 1.0 1.0

0.8 ) β 0.5

23 0.6 / R 3727 / H 3 λ 0.0

P = R 0.4 log([OII]

−0.5 0.2

−1.0 0.0 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 λ β log([OIII] 5007 / H ) log(R23)

Fig. 2.6.— Excitation diagnostic plots for SDSS galaxies (gray contours), H II regions from Pilyugin, Grebel & Mattsson (2012) (black points), and the LBAs from our sample (cyan points). The uncertainties in the line ratios for the LBAs are smaller than the plotting symbols. The left panel shows [O II] λλ3727,29 as a function of [O III] λ5007. Dotted lines show constant R23; from bottom left to top right log(R23) = 0., 0.5, 1.0. In general, the LBAs display higher excitation conditions more similar to H II regions than the SDSS star forming galaxies. The right panel shows P = R3/R23 as a function of log(R23). Again, the LBAs occupy an excitation regime closer to that of H II regions than star forming SDSS galaxies.

35 1.0 1.5 ) ) 1.0 β β 0.5 0.5 0.0 0.0 −0.5 −0.5 log ([O II]/H log ([O III]/H −1.0 −1.0

) 0.5 0.5 β 0.0 0.0 −0.5 −0.5 −1.0 −1.5 −1.0

log ([N II]/H −1.5 −2.0 log ([N II]/[O II]) 0.5 0.0

) 0.0 β −0.5 −0.5 −1.0 −1.0

log ([S II]/H −1.5 log ([S II]/[O II]) −2.0 −1.5 7.0 7.5 8.0 8.5 9.0 7.0 7.5 8.0 8.5 9.0 12+log(O/H) 12+log(O/H)

Fig. 2.7.— Diagnostic emission-line ratios as a function of oxygen abundance for our LBAs and a comparison set of local H II regions from Pilyugin, Grebel & Mattsson (2012). The LBAs from our sample are shown as cyan points, with the location of J005527 marked with a red circle; the H II regions with well measured metallicities from Pilyugin, Grebel & Mattsson (2012) are shown as black points. The error bars in the lower right of each plot represent an uncertainty in the oxygen abundance of 0.07 dex. J005527 displays relatively stronger [N II] emission compared to the other LBAs, but remains well within the parameter space occupied by the H II regions. The LBA line ratios are remarkably similar to those of the “warm” H II regions from Pilyugin, V´ılchez & Thuan (2010), suggesting that the excitation conditions in LBAs are actually quite similar to that of typical H II regions.

36 1.4 J092600 λ 1.2 C IV λ4658 He II 4686 1.0 0.8 0.6 1.4 J004054 λ 1.2 C IV λ4658 He II 4686 1.0 0.8 0.6 1.4 J020356 1.2 C IV λ4658 1.0 Arbitrary Flux 0.8 0.6 1.4 J005527 C IV λ4658 1.2 He II λ4686 N III λ4640 1.0 0.8 0.6 4500 4550 4600 4650 4700 4750 4800 Rest Wavelength [Å]

Fig. 2.8.— Wolf-Rayet features identified near 4660 A˚ . The most prominent features are the C IV line at 4658 A˚ and He II at 4686 A.˚ J005527 displays a broad bump from 4600 – 4700 A˚ as well as N III emission, both of which are characteristic of a Wolf-Rayet galaxy. The noise spike and drop in flux seen in the J020356 panel is due to the coincidental location of the dichroic cutoff for this particular target.

37 9.0 MODS1 Direct MODS1 N2 SDSS N2 8.8

8.6

8.4 12 + log(O/H)

8.2

8.0

8.5 9.0 9.5 10.0 10.5 11.0

log(M∗/M ) ⊙ Fig. 2.9.— Gas phase oxygen abundance as a function of mass for various abundance diagnostics. The cyan points show our direct method oxygen abundance for the 4 LBAs in our sample, with masses taken from Overzier et al. (2009). The thick black line denotes the logarithmic best ﬁt to the stacked SDSS direct oxygen abundances from Andrews & Martini (2013). The orange and green points show the PP04 N2 oxygen abundance estimates from the SDSS and MODS1 spectra respectively. The gray contours are the star forming SDSS galaxies from the MPA-JHU catalogue with oxygen abundances estimated from the PP04 N2 calibration. Regardless of the diagnostic used, the LBAs display low oxygen abundances for their mass relative to the MZ relation.

38 8.5 MODS1 Direct MODS1 N2 8.4 SDSS N2

8.3

8.2 12 + log(O/H) 8.1

8.0

8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4 µ α α = log(M∗/M ) − log(SFR) ⊙ Fig. 2.10.— Gas phase oxygen abundance as a function of µα, where α is chosen depending on the abundance diagnostic. We adopt the appropriate α from Andrews & Martini (2013); for the direct method we use α =0.66, and for the N2 method we use α =0.30. The color scheme is the same as that from 2.9. Masses and Hα +24µm star formation rates for the LBAs are taken from Overzier et al. (2009); star formation rates for the SDSS galaxies are from the MPA-JHU catalogue. The thick black line denotes the linear best ﬁt to the FMR of direct method stacked SDSS galaxies from Andrews & Martini (2013). The incorporation of star formation rate reduces the degree to which the LBAs are oﬀset from typical SDSS star forming galaxies.

39 Ion J092600 J004054 J020356 J005527

[O II] λ3727 1.576 0.044 1.662 0.044 2.684 0.063 2.082 0.111 ± ± ± ± He I λ3820 0.005 0.009 0.008 0.007 0.006 0.014 0.016 0.010 ± ± ± ± [Ne III] λ3869 0.468 0.016 0.485 0.018 0.315 0.012 0.308 0.015 ± ± ± ± Hγ λ4340 0.480 0.016 0.472 0.022 0.481 0.015 0.468 0.018 ± ± ± ± [O III] λ4363 0.076 0.005 0.073 0.017 0.025 0.007 0.022 0.004 ± ± ± ± [He II] λ4686 0.015 0.005 0.008 0.004 0.004 0.011 0.016 0.005 ± ± ± ± Hβ λ4861 1.000 0.037 1.000 0.044 1.000 0.033 1.000 0.056 ± ± ± ± [O III] λ4959 1.831 0.060 1.939 0.076 1.193 0.038 1.179 0.053 ± ± ± ± [O III] λ5007 5.338 0.169 5.825 0.220 3.496 0.104 3.509 0.141 ± ± ± ± Hα λ6563 2.927 0.094 2.878 0.117 2.930 0.096 2.861 0.128 ± ± ± ±

40 [N II] λ6583 0.119 0.014 0.105 0.021 0.246 0.016 0.431 0.027 ± ± ± ± [S II] λ6717 0.161 0.014 0.158 0.023 0.308 0.018 0.232 0.024 ± ± ± ± [S II] λ6731 0.121 0.014 0.107 0.024 0.226 0.017 0.198 0.023 ± ± ± ± [O II] λ7320 0.022 0.009 0.049 0.026 0.022 0.023 0.035 0.005 ± ± ± ± [O II] λ7330 0.017 0.009 0.013 0.032 0.008 0.027 0.030 0.004 ± ± ± ± Hβ Information

C(Hβ) 0.041 0.024 0.178 0.034 0.149 0.019 0.236 0.041 ± ± ± ± EW(Hβ(ABS))(A)˚ 2.40 2.00 3.40 2.00 3.80 2.00 3.50 2.00 ± ± ± ± EW(Hβ) (A)˚ 118 187 69 70 − − − −

Note. — Units are such that Hβ = 1.

Table 2.1. LBA Emission Line Intensities −3 Target Te(OII) [K] Te(OIII) [K] Ne(SII) [cm ]

J092600 1.189 0.11843 104 1.324 0.01609 104 100 ± × ± × J004054 1.262 0.05396 104 100 41 ··· ± × J020356 1.040 0.04571 104 100 ··· ± × J005527 1.390 0.05420 104 1.000 0.02756 104 312 ± × ± ×

Table 2.2. Electron Temperatures & Densities Parameter J092600 J004054 J020356 J005527

O0/H+( 105) 0.302 0.025 0.357 0.067 1.162 0.111 × ± ± ··· ± O+/H+( 105) 1.787 0.035 2.155 0.040 6.042 0.100 5.588 0.187 × ± ± ± ± O++/H+( 105) 8.283 0.176 10.234 0.277 11.309 0.245 12.829 0.380 × ± ± ± ± 12+log(O/H) 8.02 0.06 8.11 0.08 8.24 0.05 8.29 0.08 ± ± ± ± N/H+( 105) × ··· ··· ··· ··· N+/H+( 105) 0.109 0.012 0.101 0.027 0.342 0.023 0.645 0.041 × ± ± ± ± ICFN 5.805 0.152 5.839 0.170 2.872 0.065 3.504 0.141 ± ± ± ± 12+log(N/H) 6.80 0.05 6.77 0.09 6.99 0.03 7.35 0.03 ± ± ± ± 42 log(N/O) -1.22 0.26 -1.33 0.47 -1.25 0.16 -0.94 0.17 ± ± ± ± Ne++/H+( 105) 1.719 0.058 2.063 0.068 2.748 0.107 3.158 0.154 × ± ± ± ± ICF Ne 1.252 0.035 1.245 0.044 1.534 0.041 1.526 0.057 ± ± ± ± 12+log(Ne/H) 7.33 0.14 7.41 0.15 7.62 0.16 7.68 0.20 ± ± ± ± log(Ne/O) -0.68 0.09 -0.70 0.10 -0.61 0.10 -0.61 0.13 ± ± ± ± Ar++/H+( 105) 0.032 0.004 0.039 0.010 0.061 0.004 × ± ± ··· ± ICF Ar 2.069 0.207 2.089 0.209 1.621 0.162 ± ± ··· ± 12+log(Ar/H) 5.82 0.42 5.91 0.73 5.99 0.32 ± ± ··· ± log(Ar/O) -2.19 0.38 -2.20 0.66 -2.30 0.28 ± ± ··· ±

Table 2.3. Derived Abundances Method J092600 J004054 J020356 J005527

Direct (this work) 8.02 0.06 8.11 0.08 8.24 0.05 8.29 0.08 ± ± ± ± Strong Line Estimates – This Work

PP04N2 8.127 8.107 8.251 8.375 PP04O3N2 8.056 8.026 8.215 8.293 CALIFAN2 8.105 8.081 8.251 8.363 CALIFAO3N2 8.082 8.062 8.189 8.240 43

Overzier Estimates

PP04O3N2 8.09 8.03 8.21 8.28

Note. — The scatter in these empirical calibrations is 0.3 in 12+log(O/H); see Pettini ∼ & Pagel (2004) and Marino et al. (2013) for details.

Table 2.4. Direct and Strong-Line Oxygen Abundances Chapter 3: A Recalibration of Oxygen Abundance Diagnostics

3.1. Introduction

Galaxies are continually undergoing chemical enrichment. Gas is condensed into stars, processed into heavier elements, and returned to the interstellar medium. This gas, enriched by the products of stellar nucleosynthesis and/or supernova ejecta, is reincorporated into new generations of stars, where it is enriched once again. A galaxy may also accrete low metallicity gas from the intergalactic medium, which both dilutes the ISM and provides fuel for a new generation of stars to form. This interplay between star formation, chemical enrichment, and accretion of new material is a central component of galaxy evolution.

An episode of star formation increases a galaxy’s stellar mass and enriches the ISM. A substantial body of work has shown that there are correlations between stellar mass (M⋆), star formation rate (SFR), and gas phase oxygen abundance.

The correlation between M⋆ and gas phase oxygen abundance is called the Mass-Metallicity Relation (MZR; Lequeux et al. 1979; Tremonti et al. 2004). The MZR extends from low mass, extremely metal deﬁcient galaxies like Leo P (Skillman

This chapter is adapted from “A Recalibration of Strong Line Oxygen Abundance Diagnostics via the Direct Method and Implications for the High Redshift Universe”, Brown, Martini, & Andrews,

MNRAS, 458, 1529, (2016).

44 et al. 2013) up to massive galaxies with 2-3 times the solar oxygen abundance (Tremonti et al. 2004; Moustakas et al. 2011).

The MZR often serves as a benchmark for models of galaxy evolution because the details of the MZR are direct probes of the underlying physics. For instance, Tremonti et al. (2004) describe how the shape of the MZR requires galactic winds to efficiently remove metals from low mass galaxies. Subsequent cosmological models (e.g. Davé, Finlator & Oppenheimer 2006; Oppenheimer & Davé2006; Finlator & Davé2008; Davé, Finlator & Oppenheimer 2011; Davé, Oppenheimer & Finlator 2011) incorporated winds into their cosmological models in order to better understand the origin of the MZR. In the context of their momentum driven wind models, the mass loading parameter η M˙ /M˙ is proportional to the inverse of ≡ outflow ⋆ the velocity dispersion of the halo, which scales with the halo mass to the one third − power, η 1/σ M 1/3 (Murray, Quataert & Thompson 2005; Oppenheimer & ∝ h ∝ h Davé2006). Once the star formation has reached an equilibrium with the inflowing and outflowing gas, the metallicity is Z = y/(1+ η) where y is the effective yield. In the limit that η 1, the slope of the MZR is ultimately related to how M scales ≫ ⋆ with M , since log(Z) log(η) 1 log(M ). h ∝− ∝ 3 h

There is good observational evidence for a second parameter that affects the relationship between M⋆ and Z such that galaxies with higher star formation rates have lower metallicities at fixed stellar mass (the M⋆–Z–SFR relation; Ellison et al. 2008a; Mannucci et al. 2010; Lara-López et al. 2010). This relation is also apparent in high signal-to-noise ratio stacked spectra of SDSS galaxies (Andrews & Martini 2013). However, it has intriguingly not been seen in the CALIFA sample of 150 nearby galaxies studied with integral field spectroscopy by Sánchez et al. (2013).

45 The exact form of the SFR dependence is less clear, but if the fuel for star formation is lower metallicity gas accreted from the IGM, this would produce an anticorrelation between gas phase metallicity and SFR. The form of the secondary dependence of the MZR on SFR offers insights into several open questions, such as how star formation is regulated, and how the processes that govern galactic inflows and outflows operate in detail Davé, Finlator & Oppenheimer (2011); Davé, Oppenheimer & Finlator (2011); Lilly et al. (2013). Accurate measurements of the gas phase oxygen abundance are cruicial for investigating these relationships, but in practice, dectecting the auroral lines (e.g. [O III] λ4363) requires a significant investment of observational resources for even the brightest, most metal poor galaxies and H II regions. At present, most spectroscopy comes from low to moderate SNR, and direct method abundances are typically not practical.

Recently, several studies have shown that stacking the spectra of a suﬃciently large number of galaxies can boost the S/N of the auroral lines to a detectable level (Liang et al. 2007; Andrews & Martini 2013). We use the stacking technique presented in Andrews & Martini (2013) to obtain direct method oxygen abundances for galaxies spanning a wide range in M⋆ and SFR. Our stacking method mitigates the potential for bias by binning galaxies we expect to have similar metallicities based on the small intrinsic scatter of the MZR and M⋆–Z–SFR relation. We then recalibrate the popular strong line abundance diagnostics with the direct method oxygen abundances, and apply the new calibrations to data taken from the literature.

46 We adopt the following notation for the principal diagnostic emission line ratios:

N2 = [N II] λ6583/Hα (3.1)

O3N2 = [O III] λ5007/Hβ/[N II] λ6583/Hα (3.2)

N2O2 = [N II] λ6583/[O II] λ3727 (3.3)

R2 = [O II] λ3727/Hβ (3.4)

R3 = [O III] λλ4959, 5007/Hβ (3.5)

R23 = R2 + R3 (3.6)

P = R3/R23 (3.7)

Section 3.2 describes our selection and stacking process. Section 3.3 describes our empirical calibrations of (O/H)Te . In Section 3.4 we present our newly derived calibrations. In Section 3.5 we apply our calibrations to various samples of galaxies and discuss the implications for the M⋆–Z–SFR relation. Finally, we brieﬂy summarize our results in Section 3.6.

3.2. Data

3.2.1. Sample Selection

Our sample of galaxies is derived from the SDSS Data Release 7 (DR7; Abazajian et al. (2009)). We begin with the MPA/JHU catalog of galaxies with stellar masses (Kauﬀmann et al. 2003b), SFRs (Brinchmann et al. 2004; Salim et al. 2007), and oxygen abundances (Tremonti et al. 2004, hereafter T04). We discard AGN dominated galaxies with the standard Baldwin-Philips-Terlevich (BPT) diagram (Baldwin, Phillips & Terlevich 1981) and the criterion for star forming galaxies from

47 Kauﬀmann et al. (2003a):

log([O III] λ5007/Hβ) < 0.61[log([N II] λ6583/Hα) 0.05]−1 +1.3 (3.8) −

Our S/N requirements are the same as those presented in Andrews & Martini

(2013). We restrict our sample to galaxies with Hβ,Hα, and [N II] λ6583 detected at > 5σ. For galaxies with [O III] λ5007 detected at > 3σ, we apply the selection criteria shown in Equation 3.8. In order to include galaxies with high metallicity

(and inherently weak [O III] λ5007) we include galaxies with [O III] λ5007 detected at < 3σ but log([N II] λ6583/Hα) < 0.4.

We also take signiﬁcant care to inspect low mass galaxies (log[M∗] < 8.6) and remove galaxies with poor photometric deblending (ﬂagged with DEBLEND_NOPEAK or DEBLENDED_AT_EDGE) or otherwise spurious stellar mass determinations. These selection cuts leave a total of 208,529 galaxies in our sample.

We emphasize that a limitation of this analysis is that the data were obtained with single fibers centered on resolved galaxies, and therefore not all of the light is included in the 3′′ diameter fiber aperture. For reference, 3′′ corresponds to 2.2 kpc at the median redshift (z = 0.078) of our sample. The missing fraction due to this aperture bias will depend on redshift for galaxies of similar sizes, and will depend on mass and star formation rate due to the flux-limited nature of the sample. This aperture bias is important because galaxies exhibit radial abundance gradients (e.g. Searle 1971; Kennicutt, Bresolin & Garnett 2003; Bresolin et al. 2009b,a; Berg et al. 2013; Sánchez et al. 2014) that will cause abundances measured in the central region of a galaxy to overestimate the total abundance. Tremonti et al. (2004) investigated this aperture bias for SDSS observations and found metallicity variations of 0.05 to 0.11 dex with redshift for galaxies of similar absolute z band magnitudes. Kewley, − Jansen & Geller (2005) studied aperture effects with the Nearby Field Galaxy

48 Survey and recommended that ﬁber spectroscopy include at least > 20% of the galaxy light (typically z > 0.04 for SDSS observations) to minimize systematic and random errors, and this corresponds to most of our sample. Based on these studies, we estimate that aperture biases are comparable to the scatter in the inferred O/H for galaxies of similar stellar mass and star formation rate.

Another limitation of single-fiber observations is they simply present an incomplete picture of the properties of galaxies. One example is that while Sánchez et al. (2013) found a very tight relationship between integrated stellar mass and metallicity with integral field data from CALIFA (Sánchez et al. 2012), they did not find any dependence of metallicity on star formation rate at fixed stellar mass. Another example is the analysis by Belfiore et al. (2015) of nebular data for 14 galaxies with P-MaNGA, the prototype instrument for the ongoing MaNGA survey (Bundy et al. 2015). Those authors found a substantial spread in O/H values at fixed N/O for regions within individual galaxies, which is in contrast to the stronger correlation exhibited by the central regions from single-fiber observations.

3.2.2. Stacking Procedure

The auroral lines of [N II], [O II], and [O III] are generally weak and typically undetectable in most SDSS galaxy spectra. However, previous studies (e.g. Liang et al. 2007; Andrews & Martini 2013) have demonstrated that stacking spectra to reduce the contribution of random fluctuations in the measured flux is a viable way to obtain sufficient S/N to measure the auroral lines.

The stacking method relies on the fact that the random noise in a composite spectrum of N galaxies scales roughly as 1/√N; it is advantageous for our bins to contain a large number of galaxies in order to reduce the noise in the spectrum as

49 much as possible. However, we also want each bin to span a very small range in actual (O/H) so that we are stacking qualitatively similar galaxies. The chosen bin widths are a compromise between these two goals.

Before stacking the spectra, we follow the same reduction process described in Andrews & Martini (2013). Starting with the spectra that have been processed with the SDSS pipeline (Stoughton et al. 2002), we correct for Galactic reddening using the extinction values from Schlegel, Finkbeiner & Davis (1998). We then shift each spectrum to the rest frame using redshifts from the MPA/JHU catalog. We interpolate each spectrum onto a wavelength grid spanning 3700A–7360˚ A˚ with spacing ∆λ = 1A.˚ In order to compare galaxies at various distances we normalize each spectrum to the stellar continuum with the mean continuum flux from 4400A–4450˚ A.˚ Thus when we measure the line flux we effectively measure the equivalent width of the line. At fixed M⋆, normalizing to the stellar continuum is acceptable since the luminosities of the galaxies are essentially the same. Figure 3.1 demonstrates the benefit of stacking. In the raw SDSS spectrum of a single galaxy (gray line), the weak auroral lines are undetectable. They become fairly evident after stacking (blue line). After removing nearby stellar continuum features (red line), the previously undetectable auroral lines are prominent features in the final spectrum (black line).

3.2.3. Choice of Stacking Parameters

Our goal is to derive improved strong line calibrations, so one of the parameters we use to assign galaxies to a stack is similar strong line ratios. However, the strong line ratios show considerable dependence on more parameters than just metallicity, such as incident spectral shape, ionization parameter, and gas density (Dopita et al. 2000; Kewley & Dopita 2002; Dopita et al. 2013). For example, Steidel et

50 al. (2014) demonstrated that variations in line ratios due to a factor of ﬁve change in metallicity could be reproduced with only a factor of two change in ionization parameter. Figure 2 clearly demonstrates that there is a substantial range in stellar mass and star formation rate at a constant value of the N2, O3N2, N2O2, or R23 strong line diagnostics.

As in Andrews & Martini (2013), we assume that galaxies with similar stellar masses and star formation rates have similar physical conditions, and therefore similar values of the other parameters that impact the connection between strong line ratio and metallicity. We consequently only stack galaxies with similar stellar masses and star formation rates to minimize the dispersion in galaxy properties in each stack. Good support for this approach comes from an investigation of stacking by Andrews & Martini (2013). They compared electron temperatures and abundances for galaxies with individual auroral line detections to stacks of the same sample of galaxies and found good agreement within the measurement uncertainties.

We have performed a bootstrap analysis as an additional validation of this approach. For this analysis we chose four bins of diﬀerent star formation rates at the same stellar mass. We resampled each bin 100 times and processed them with our analysis pipeline to derive the metallicity. We found the median of the bootstrap metallicity distribution agreed well with the stack value for each bin. The spread in the metallicity distribution ( 0.15 dex) was somewhat larger than the formal ∼ metallicity uncertainties, but smaller than the variations in the strong line ratios at ﬁxed stellar mass and star formation rate ( 0.2 dex). ∼

We have chosen to use both stellar mass and star formation rate because there is good evidence that metallicity depends on star formation rate at ﬁxed mass (Ellison et al. 2008; Mannucci et al. 2010; Lara-Lopez et al. 2010). In addition, we

51 expect galaxies with different star formation rates at fixed mass may differ in other parameters (incident spectral shape, etc.). While the integral field study by Sánchez et al. (2013) did not find that metallicity depends on star formation rate at fixed mass, we emphasize that our decision to stack in both quantities is also motivated by how other physical parameters vary with star formation rate.

It is also well known that stellar mass and star formation rate are well correlated, a correlation known as the star forming main sequence (Brinchmann et al. 2004; Salim et al. 2007; Noeske et al. 2007; Whitaker et al. 2012; Zahid et al. 2012b; Kashino et al. 2013). In order to characterize this dependence, Salim et al. (2014) showed that the parameter ∆log(SSFR)

∆log(SSFR) = log(SSFR) log(SSFR) (3.9) −h iM⋆ is more eﬀective than both SFR and SSFR at identifying low and high oxygen abundance outliers across a wide range in M . The quantity log(SSFR) is the ⋆ h iM⋆ median log(SSFR) of galaxies at M⋆. Thus ∆log(SSFR) is deﬁned relative to the

−1 star forming main sequence rather than an arbitrary value (e.g. 1 M⊙ yr ).

Binning in ∆log(SSFR) rather than SFR is also beneficial for calibrating the relationship between the strong line ratios and (O/H)Te . Figure 3.2 shows that at a fixed strong line ratio, there is significant scatter in M⋆. Since M⋆ and SFR are correlated, absolute SFR does not necessarily correspond to a lower oxygen abundance at a fixed strong line value. Furthermore, since ∆log(SSFR) is a reflection of the SFR density, galaxies with similar ∆log(SSFR) ought to have similar ionization conditions. The same does not hold true for galaxies with similar SFR but different stellar masses, since a relatively low mass, compact star forming galaxy will have more intense ionization conditions than a more massive galaxy with relatively diffuse star formation.

52 Our choice of bin widths was largely ad hoc. It is clear from Figure 11 of

Andrews & Martini (2013) that there is some scatter in (O/H)Te at ﬁxed M⋆ and

∆log(SSFR). Our primary motives were to (1) resolve the M⋆–Z–SFR relationship,

(2) include enough galaxies in metal rich stacks to measure (O/H)Te , and (3) limit the total number of stacks to keep the stacking procedure, stellar continuum subtraction, and abundance determination computationally feasible. We ran various trials and found our results to be insensitive to bin widths.

The left panel of Figure 3.3 shows where M⋆–∆log(SSFR) stacks fall on the BPT diagram relative to the galaxies in our sample (gray contours) and individual

H II regions from Pilyugin, Grebel & Mattsson (2012) (black points). The stacks with high ∆log(SSFR) are undergoing relatively intense star formation, and their line ratios closely resemble those of individual H II regions. The passively star forming stacks track the overall distribution of galaxies, which is not traced by the individual H II regions.

Naively we expect that galaxies undergoing more intense star formation have many more ionizing photons per atom. While the excitation parameter P is marginally dependant on abundance, the right panel of Figure 3.3 suggests our naive expectation is correct; stacks with high ∆log(SSFR) show systematically higher values of P . Incorporating ∆log(SSFR) accounts for some of the strong line ratios’ sensitivity to ionization conditions.

Lastly, it is easily shown that many strong line ratios (e.g. N2) are biased by SFR since they include Hα ﬂux. By grouping galaxies with similar ∆log(SSFR), which is equivalent to SFR at ﬁxed M⋆, our chosen stacking methodology minimizes this bias.

53 3.2.4. Stellar Continuum Subtraction

Many emission lines used in this study (particularly [O III] λ4363) fall in wavelength regimes where stellar absorption features are present. Therefore it is necessary to fit and remove the underlying stellar population contribution to the stacked spectra. Following Andrews & Martini (2013), we use the STARLIGHT spectral synthesis code (Cid Fernandes et al. 2005, 2011) and a library of 300 empirical MILES spectral templates (Sánchez-Blázquez et al. 2006; Cenarro et al. 2007; Vazdekis et al. 2010; Falcón-Barroso et al. 2011) to generate a synthetic spectrum representative of the underlying stellar population for each of our stacks. We adopt the Cardelli, Clayton & Mathis (1989) extinction law and mask the locations of all bright emission lines.

For strong lines redward of 4000A˚ (Hβ, [O III] λλ4959, 5007A,˚ Hα, [N II] λλ6548,

6583A,˚ and [S II] λλ6716, 6731A)˚ we model the stellar continuum using template fits to the entire spectral range (3700A–7360˚ A).˚ We fit the continuum near weaker emission lines, auroral lines, and strong lines blueward of 4000A˚ using template fits to the continuum within a few 100A˚ of each line since this provides a significant reduction in the rms of the continuum around the line (Andrews & Martini 2013). See Table 3.1 for details regarding each emission line’s fit region.

3.2.5. Line Flux Measurement

Following Andrews & Martini (2013), we fit the emission lines of the stacked spectra using the specfit routine (Kriss 1994) in the IRAF/STSDAS package. We use the simplex χ2 minimization algorithm to simultaneously fit a flat continuum and Gaussian profile to each emission line. Andrews & Martini (2013) found this to be a robust method consistent with other flux measurement techniques. Uncertainties are derived from the χ2 of the fit returned by specfit. We deredden the spectra using

54 the extinction law from Cardelli, Clayton & Mathis (1989) and the assumption of

4 case B recombination (Hα/Hβ= 2.86 for Te = 10 K). Andrews & Martini (2013) estimate the systematic error introduced by adopting a ﬁxed Hα/Hβ ratio to be

< 0.07 dex. Finally, with the exception of [O II] λ3727 A,˚ our diagnostic emission ∼ lines are anchored to nearby Balmer lines, and are thus insensitive to reddening.

3.3. Analysis

3.3.1. Abundances

We compute the chemical abundances of the stacks using the same procedure as Andrews & Martini (2013); here we present a brief overview and direct the reader to that paper for further details.

We assume a simple two-zone model composed of a high ionization region

(traced by [O III]) and a low ionization region (traced by [O II], [N II], and [S II]). Previous works have assumed simple relationships between the temperatures of the high and low ionization regions (the T T relation Campbell, Terlevich & Melnick 2 − 3 1986; Garnett 1992; Pagel et al. 1992; Izotov et al. 2006; Pilyugin et al. 2009). We assume a linear T T relation normalized such that we get the best agreement 2 − 3 in stacks for which we are able to measure the temperature of both ionization zones (see below). We use a Monte Carlo technique to derive uncertainties in our measurements.

We measure the electron temperature and density using the IRAF/STSDAS nebular.temden routine (Shaw & Dufour 1995), which is based on the 5 level atom from De Robertis, Dufour & Hunt (1987). We use the [S III] λ6717/λ6731 ratio to measure the electron density. We use the auroral oxygen ratios

55 ([O II] λ7320+7330/λλ(3726+3729) and [O III] λ4363/λλ(4959 + 5007)) to measure T2 and T3 respectively. Andrews & Martini (2013) discuss at length the diﬀerences between the canonical T T relation and that observed for their stacks 2 − 3 and ﬁnd that in general their stacks fall below the Campbell, Terlevich & Melnick

(1986) relation (in the sense of low T2 at fixed T3). This offset from the predicted relation has been previously seen (Pilyugin, V´ılchez & Thuan 2010). The fact that this offset disappears for galaxies with relatively high SFRs (which are likely to have contributions from relatively young stellar populations) indicates that the offset is likely due to the differences between the single stellar spectra used by Stasińska

(1982) and the composite H II region spectrum that ionizes the gas in a galaxy.

The ionic abundances of O+ and O++ are calculated using the electron temperature, electron density, the ﬂux ratios of the strong lines relative to Hβ, and the IRAF/STSDAS nebular.ionic routine (De Robertis, Dufour & Hunt 1987; Shaw & Dufour 1995). Atomic data plays a critical role in direct method temperature determinations (Kennicutt, Bresolin & Garnett 2003). For example, Berg et al.

(2015) noted a substantial difference in S III temperatures when using updated collision strengths. The O III temperatures are largely unaffected by the updated atomic data, so we utilize the nebular.temden routine without modification. The uncertainties in the abundances of individual ionic species are determined with the same Monte Carlo simulations used to determine the uncertainties in electron temperatures. The ionic abundance uncertainties are used to analytically calculate the uncertainty in the total abundances.

We assume the total oxygen abundance is given by

O O+ O++ = + . (3.10) H H+ H+ 56 Historically, the temperature of the high ionization region, T3, is measured using the direct method and T is then inferred using the T T relation. At high masses, we 2 2 − 3 are unable to measure T3 but often have a measurement of T2. We use the stacks where both T and T are measured to infer a T T relation that results in the 2 3 2 − 3 best agreement between measured and inferred T3. As in Andrews & Martini (2013), this is done using a systematic shift ( 0.1 dex) in the log(O/H) of the stacks for ∼ which T2 was measured and used to infer T3.

3.3.2. Empirical Calibrations

There are many abundance diagnostic ratios. Our choice of ratios to consider is motivated by three factors: (1) our calibration(s) should be empirical, (2) the distribution of line ratios for individual galaxies in a stack ought to be reasonably peaked around the mean value, and (3) the calibration ought to be valid for the majority of our stacks.

The most commonly used oxygen abundance diagnostics are N2 and O3N2 (Denicoló, Terlevich & Terlevich 2002; Pettini & Pagel 2004; Marino et al. 2013), N2O2 (Dopita et al. 2000; Kewley & Dopita 2002), and R23 (Pagel et al. 1979; McGaugh 1991; Pilyugin 2003; Kobulnicky & Kewley 2004) . Figure 3.2 shows the distribution of individual galaxies in the M⋆–diagnostic planes for these diagnostics. In panel “(a)” of Figure 3.2, the distribution of galaxies is such that galaxies with similar M⋆ and ∆log(SSFR) follow a relatively tight sequence in the M⋆–N2 plane. Similar behavior is seen in panel “(b)” (O3N2) and, to a somewhat lesser extent, panel “(c)” (N2O2). In panel “(d)” at fixed M⋆ and ∆log(SSFR), the values of R23 follow a relatively broad distribution; the scatter in R23 at fixed M⋆ and ∆log(SSFR) can be comparable to the entire range spanned by the diagnostic. In this instance, the degree to which the average strong line value of a given stack is representative of

57 the galaxies within that stack is less meaningful than with other diagnostics. This is a primary concern when stacking galaxies (see Footnote 14 of Salim et al. (2014) for an example of how binning can lead to the wrong impression).

An additional concern with strong line abundance diagnostics is the eﬀect of ionization parameter variations on the diagnostic ratios (Kewley & Dopita 2002; Steidel et al. 2014). The ionization parameter Γ is given by

Φ Φ Γ (3.11) ≡ nH ≈ ne where nH is the number density of hydrogen atoms and Φ is the density of hydrogen ionizing photons. Changes in the ionization parameter can be due to either variations in the temperature of the ionizing continuum (i.e. a galaxy composed of systematically hotter stars than average) and/or variations in the physical conditions of star forming regions (i.e. higher stellar densities and/or lower gas densities than average). In order to eliminate these biases, it would be advantageous to use a diagnostic that is insensitive to ionization parameter variations (e.g. N2O2, Kewley & Dopita 2002), though our choice of ∆log(SSFR) as a second parameter should at least somewhat account for diﬀerences in ionization parameter (see the right panel of Figure 3.3).

The N2 diagnostic is subject to biases caused by the ionization parameter as well as the hardness of the ionization spectrum (Kewley & Dopita 2002), but has been shown to be a useful abundance diagnostic in high excitation regions (Storchi-Bergmann, Calzetti & Kinney 1994; Binette, Wilson & Storchi-Bergmann

1996; Pettini & Pagel 2004; Marino et al. 2013). Furthermore, [N II] λ 6583 and Hα are closely spaced, making their ratio insensitive to variations in reddening corrections. The O3N2 diagnostic is also sensitive to ionization parameter (Kewley & Dopita 2002), but is less sensitive to variations in the hardness of the ionizing

58 spectrum than N2 (Kewley et al. 2013; Brown, Croxall & Pogge 2014; Steidel et al. 2014). N2O2 is insensitive to ionization parameter, but is dependent on the secondary nature of nitrogen (Kewley & Dopita 2002). We will use N2O2 to estimate the eﬀect of ionization parameter variations on the other diagnostics.

With the above considerations in mind, we focus the remainder of our analysis on the N2, O3N2, and N2O2 strong line diagnostics. As discussed above, the distribution of R23 at ﬁxed M⋆ and ∆log(SSFR) is not strongly peaked. Furthermore, the double valued nature of R23 requires that an additional diagnostic sensitive to ionization parameter be used in conjunction with an iterative method to solve for an oxygen abundance. This precludes the empirical nature of our calibrations. Most importantly, a large fraction of our galaxies fall within the “transition zone” of the

R23 diagnostic, where the diagnostic is insensitive to oxygen abundance (Dopita et al. 2013). As a result, we refrain from further consideration of R23.

3.4. Results

In Section 3.2.3 we demonstrated with Figure 3.2 that each M⋆-∆ log(SSFR) stack has characteristic diagnostic line ratios which are representative of the individual galaxies in that stack. Following previous works (e.g., Alloin et al. 1979; Pettini & Pagel 2004; Marino et al. 2013) we combine these diagnostic ratios with direct method oxygen abundances to derive a relationship between the two. Salim et al.

(2014) showed that at ﬁxed M⋆ we expect galaxies with low (high) ∆log(SSFR) to be oﬀset from the star forming main sequence in the sense of high (low) oxygen abundance. Given the strong correlation between our diagnostic ratios and M⋆, we assume the following form for our empirical calibrations:

12 + log(O/H) = f1(X)+ f2(∆log(SSFR)) (3.12)

59 where X is a particular diagnostic value (e.g. N2) and f1 and f2 are functions of the respective variables. For simplicity, we assume f1 and f2 are each linear functions in their respective parameter, except for the case of N2 where we allow f1 to take the form of a second degree polynomial. We use MPFIT (Markwardt 2009), an IDL implementation of the robust non-linear least square ﬁtting routine MINPACK-1, to ﬁt the relationship between log(O/H), X, and ∆log(SSFR).

From Equation 3.9, it is clear that for a galaxy with a known M⋆ and SFR,

∆log(SSFR) then only depends on the average SSFR at that M⋆. In practice, we compute the median SSFR in M⋆ bins 0.1 dex wide. However, a good approximation for log(SSFR) as a function of M is: h iM⋆ ⋆

log(SSFR) ⋆ = 283.728 116.265 log M + h iM − × ⋆ 17.4403 log M 2 1.17146 log M 3 +0.0296526 log M 4 (3.13) × ⋆ − × ⋆ × ⋆

We provide this form rather than the expression from Salim et al. (2007) because the two begin to diverge below log(M /M⊙) 9. ⋆ ∼

3.4.1. N2 Method

Our new calibration of (O/H)Te based on N2 and ∆log(SSFR) is:

12 + log(O/H) =9.12+0.58 log(N2) 0.19 ∆ log(SSFR). (3.14) N2 × − ×

Figure 3.4 shows that the slope of the relationship between (O/H)Te and N2 at ﬁxed ∆log(SSFR) is comparable to the slope of Pettini & Pagel (2004) (red line) and Marino et al. (2013) (magenta line), and agree well for the galaxies with high ∆log(SSFR). This agrees with previous studies (e.g. Brown, Croxall & Pogge 2014) which have shown that those empirical relations accurately predict (O/H)Te for high excitation galaxies. This is not particularly surprising because galaxies with very

60 compact, high star formation rates for a given M⋆ are similar to individual H II regions in terms of excitation conditions.

As one moves from high excitation galaxies toward the star forming main sequence, the population of galaxies tends toward lower excitation conditions than the H II regions used in Pettini & Pagel (2004). The observational consequence is that SDSS galaxies have higher (O/H)Te than predicted by previous calibrations at a given value of N2.

For galaxies above Z⊙, N2 saturates as it becomes the dominant coolant of ∼ the ISM (Baldwin, Phillips & Terlevich 1981; Pettini & Pagel 2004). This explains the pile up of stacks around log(N2) 0.5 in Figure 3.4 for the low ∆log(SSFR) ≈ − stacks. As a result this calibration becomes unreliable when the line ratio reaches this value. The top panel of Figure 3.4 shows the residuals of the ﬁt. It is clear that the quality of the calibration worsens at high metallicities. We include the RMS of the residuals in Table 3.3.

3.4.2. O3N2 Method

Our new calibration of (O/H)Te based on O3N2 and ∆log(SSFR) is:

12 + log(O/H) =8.98 0.32 log(O3N2) 0.18 ∆ log(SSFR). (3.15) O3N2 − × − ×

Figure 3.5 shows that the slope of the relationship between (O/H)Te and O3N2 at ﬁxed ∆log(SSFR) is comparable to the slope of Pettini & Pagel (2004) (thick red line) and Marino et al. (2013) (thick magenta line), and agrees well for the galaxies with high ∆log(SSFR). Again this is in agreement with Brown, Croxall & Pogge (2014), who showed that high excitation galaxies with signiﬁcant populations of young stars are essentially indistinguishable from individual H II regions from

61 the perspective of a diagnostic ratios. We do find a marginally steeper slope than Marino et al. (2013). This could be due to a selection effect because at high (low) metallicities we lack high (low) ∆log(SSFR) bins, which could artificially steepen our calibration. In addition, the steepness of the Pettini & Pagel (2004) calibration may be due to the photoionization models used at high metallicities. The Marino et al. (2013) calibration suffers no such bias, since their measurements are based entirely on individual Hii regions. More data are needed to explore this possibility further.

Closer to the star forming galaxy main sequence, the calibration presented here begins to diverge from the previous calibrations based on H II regions. Again, this is because the galaxies on the star forming main sequence display lower excitation conditions than the H II regions used in the previous calibrations.

The O3N2 diagnostic performs better than the N2 diagnostic at high (O/H)Te . While N2 saturates at high metallicity, the intensity of collisionally excited oxygen lines is still falling with increasing oxygen abundance.

3.4.3. N2O2 Method

Our new calibration of (O/H)Te based on N2O2 and ∆log(SSFR) is:

12 + log(O/H) =9.20+0.54 log(N2O2) 0.36 ∆ log(SSFR). (3.16) N2O2 × − ×

In Figure 3.6 we compare our measurements from the stacks with the N2O2 calibration from Kewley & Dopita (2002). At high metallicities, we ﬁnd excellent agreement between the star forming galaxy main sequence of our stacks and the calibration from Kewley & Dopita (2002). This could be due to the fact that this calibration is insensitive to ionzation parameter. At ﬁxed N2O2, stacks with high

62 ∆log(SSFR) show lower (O/H)Te than stacks with lower ∆log(SSFR), as one would expect in the case of inﬂow driven star formation.

Kewley & Dopita (2002) explicitly state that the N2O2 calibration should only be used above 12 + log(O/H)> 8.6 since this diagnostic derives its utility from the secondary nature of nitrogen at high metallicity. However, in the context of galaxy evolution where inflows and outflows have a strong effect on the oxygen abundance we argue that this selection criteria should instead be based on the value of the N2O2 diagnostic itself. For instance, consider a galaxy which has undergone prolonged star formation and enriched its ISM well above solar metallicity such that the secondary nature of nitrogen is unambiguous. Now, suppose this galaxy were to accrete a substantial amount of gas from the IGM. The ISM would be diluted, the metallicity would decrease, and the SFR would increase. The galaxy would move off the main sequence, increasing ∆log(SSFR). All the while, the N2O2 ratio would remain largely unchanged, since the relative abundance of nitrogen and oxygen is unaffected by inflows of pristine gas (Köppen & Hensler 2005; Masters et al. 2014). The high SFR stacks shown in Figure 14 of Andrews & Martini (2013) are consistent with this picture of inflow driven dilution. Nitrogen can be secondary even at low metallicities, provided the galaxy is sufficiently chemically evolved.

Figure 3 of Kewley & Dopita (2002) shows that the N2O2 diagnostic becomes sensitive to metallicity at log(N2O2) 1.25. Our Figure 3.6 illustrates that ∼ − this happens at the lower range probed by our stacks. The (O/H)Te of our stacks does show a clear dependence on N2O2, even at low metallicities. Unevolved galaxies for which nitrogen is still primary could potentially contaminate the stacks. However, the left panel of Figure 3.2 shows that there are relatively few galaxies with log(N2O2) < 1.25. Thus we are conﬁdent our N2O2 calibrations are valid − even though we apply them at low metallicities.

63 3.4.4. Which Calibration Is Best?

Figure 3.7 summarizes our results in M⋆–∆log(SSFR) space and illustrates several systematic eﬀects correlated with M⋆ and/or ∆ log(SSFR).

The top panel shows the distribution of stacks with measured (O/H)Te in

M⋆-∆log(SSFR) space. The color of each square reflects the metallicity. The second, third, and fourth panels show the residuals for the N2, O3N2, and N2O2 diagnostics, respectively. Red indicates where the strong line diagnostic overestimates the direct method metallicity, while blue indicates the alternative. Column d in Table 3.3 shows the mean residuals for each calibration. On average the calibrations are accurate to within 0.10 dex, although there are typically 2-3 stacks for each diagnostic that have substantially larger residuals. The calibrations perform worse for the highest metallicity stacks. This is evident in residuals shown in the top panels of Figures 3.4, 3.5, and 3.6. The metallicities of the lowest mass stacks are also difficult to accurately predict. This is likely due to the small number ( 5) of galaxies in ∼ these stacks. One or two galaxies with anomoulous line ratios can significantly influence the line ratios of the stack (Andrews & Martini 2013).

In general, no single calibration vastly outperforms the others, though O3N2 does fare slightly better. O3N2 was the preferred diagnostic for 43% (47/110) of the stacks, followed by N2O2 with 30% (33/110), and N2 was ranked last with 27% (30/110). There does not appear to be any systematic trend where one calibration does better than the others, though N2O2 is only marginally worse than O3N2 for many of the stacks and is subject to fewer biases.

The N2O2 calibration has a larger dependence on ∆log(SSFR) (0.36, column d in Table 3.3) than the other calibrations ( 0.2). This likely reﬂects the fact ∼ that N2 and O3N2 are sensitive to ionization parameter, whereas N2O2 is not. At

64 fixed metallicity, a systematically high ionization parameter (correlated with high ∆log(SSFR)) biases the N2 and O3N2 line ratios in the direction of low metallicity. Thus stacks with high ∆log(SSFR) have metal poor line ratios relative to a stack of lower ∆log(SSFR) and identical metallicity. This reduces the inferred dependence of metallicity on ∆log(SSFR). While all three calibrations perform equally well for our sample, these biases may be important considerations for applications to other samples. We emphasize that the rms residuals of the fit to the stacks does not reflect the actual precision of the calibration. As noted in Section 3.2.3, the reliability of the calibrations is primarily determined by the scatter in a given line ratio at fixed M⋆ and ∆log(SSFR), which is assumed to mean fixed O/H. This scatter is ultimately a function of M⋆, SFR, strong-line diagnostic, and sample selection. We include error bars in the lower corners of Figures 3.4, 3.5, and 3.6 to show the typical uncertainty for our different ∆log(SSFR) bins, marginalized over M . The error bars ( 0.2 ⋆ ∼ dex) reflect the uncertainty in inferred O/H due to the scatter in strong-line ratio at

ﬁxed M⋆ and ∆log(SSFR), and typically exceed the widths of the O/H distributions in our bootstrap analysis ( 0.15 dex). ∼

3.5. Discussion

3.5.1. Application of New Calibrations to Local Galaxies

We ﬁrst apply our newly derived strong line calibrations to the sample of individual star forming galaxies that went into our stacks. In Figures 3.8, 3.9, and 3.10 we show the distribution of SDSS galaxies (gray contours) and M⋆–∆ log(SSFR) stacks (colored points) in the M-Z plane. All metallicities are computed using the appropriate strong line calibration. In Figure 3.8 we apply the N2 calibration, in Figure 3.9 we apply the O3N2 calibration, and in Figure 3.10 we apply the new

65 N2O2 calibration. In each panel the solid (dotted) red lines show the appropriate best ﬁt MZR (scatter) from Kewley & Ellison (2008), in which the MZRs were measured by computing the median log(O/H) as a function of mass. The dot-dashed magenta lines show the MZR from Tremonti et al. (2004).

If each M ∆log(SSFR) bin has a known (O/H) e , the uncertainty in the ⋆ − T calibration is dominated by the average scatter in a given diagnostic at ﬁxed (O/H)Te .

The error in any given measurement of (O/H)Te is typically much smaller than this.

We estimate the scatter in a diagnostic at ﬁxed (O/H)Te by averaging the scatter in the diagnostic over all masses at ﬁxed ∆log(SSFR). These uncertainties are shown as error bars in the bottom corner of the plots and are generally comparable to the uncertainties in the calibrations ( 0.10 dex). The error bars on the points ∼ themselves represent the error on the mean. Due to the large number of galaxies in most stacks, the mean is typically measured to high precision.

In the case of N2 and O3N2, we ﬁnd that our direct method strong line calibrations produce MZRs with higher (O/H) normalizations than the Kewley & Ellison (2008) results, as expected from Figures 3.4 and 3.5. In the case of N2O2, the normalization of the MZR is only marginally higher than the results from Kewley & Ellison (2008); this is due to the fact that, without accounting for ∆log(SSFR), our N2O2 calibration is very similar to that presented in Kewley & Dopita (2002). The slopes of all of our MZRs are roughly consistent with the results from Kewley &

Ellison (2008) and also appear to ﬂatten at low masses (log(M⋆) < 8). Each of the ∼ MZRs also agree well with the Tremonti et al. (2004) MZR.

1.5 Figures 3.4 and 3.5 suggest that the ∆log(SSFR)1.0 bins should follow the 1.0 Kewley & Ellison (2008) MZR closest, when in fact it is the ∆log(SSFR)0.5 bins. This is purely a selection eﬀect due to the diﬀerence in binning schemes. Kewley

66 & Ellison (2008) eﬀectively binned in M⋆, whereas we have binned in both M⋆ and

∆log(SSFR). As shown in Figure 3.2 (top left), the M⋆–∆log(SSFR) stacks with high ∆log(SSFR) have lower values of N2 than a corresponding mass stack. This is primarily because at fixed M⋆, higher ∆log(SSFR) implies higher Hα flux, and thus lower N2. The reason we bin in M⋆ and ∆log(SSFR) is to alleviate the dependence of N2 on ∆log(SSFR); the difference between our results and those of Kewley & Ellison (2008) effectively reveal the magnitude of this bias.

We ﬁnd that the N2 MZR (Figure 3.8) asymptotes around solar metallicity and falls slightly below the MZR from Tremonti et al. (2004). This is in agreement with previous studies (Baldwin, Phillips & Terlevich 1981; Pettini & Pagel 2004) and occurs because nitrogen becomes the dominant coolant at high metallicity, so N2 saturates. At high stellar masses (and metallicities), O3N2 continues to decrease as the intensity of [O III] decreases with increasing metallicity. Figures 3.2 and 3.9 show that O3N2 begins to ﬂatten at high M⋆, but this is likely due to the turnover in the MZR.

In the case of the N2O2 MZR (Figure 3.10), we note a marginally higher normalization, and significantly larger scatter at fixed M⋆, than the other calibrations. This is likely the result of a larger dependence on ∆log(SSFR). As previously noted, the ionization parameter is likely correlated with ∆log(SSFR) (see the right panel of Figure 3.3). If this is true, the high ∆log(SSFR) stacks will be biased towards low N2 or high O3N2 (Dopita et al. 2000; Kewley & Dopita 2002; Steidel et al. 2014). Given the slope of the strong line calibrations, this will mask the dependence of log(O/H) and ∆log(SSFR). Being largely insensitive to ionization parameter, N2O2 likely reflects the true relationship between log(O/H) and ∆log(SSFR).

67 For most of the ∆log(SSFR) tracks, the scatter in inferred (O/H) between points is surprisingly small and is much less than that seen in (O/H)Te . This is due to the fact that the inferred (O/H) is merely a reﬂection of how the strong line diagnostics vary as a function of mass. On average, the strong lines exhibit very smooth behavior with mass (Kewley & Ellison 2008). This point was also raised in Steidel et al. (2014) and suggests that another parameter other than gas phase oxygen abundance (likely ionization parameter) is tightly coupled to both mass and the strong line ratios. Thus we are able to measure the average strong line value to exquisite precision, but the uncertainty in gas phase oxygen abundance for any one galaxy is set by the scatter in a particular diagnostic ratio at ﬁxed M⋆ and ∆ log(SSFR).

3.5.2. The M⋆–Z–SFR Relation

Using the masses and newly derived oxygen abundances of galaxies in the local universe, we can investigate the presence of a Fundamental Metallicity Relation (FMR; Mannucci et al. (2010); Lara-L´opez et al. (2010)). The formulation of the FMR from Mannucci et al. (2010) states that (1) galaxies lie along the projection of the local M⋆–Z–SFR relation that minimizes the scatter in metallicity, and (2) the relationship is redshift invariant. In this section we will focus on the ﬁrst of these predictions; we will consider evolution of the M⋆–Z–SFR relation with redshift in Section 3.5.3.

Salim et al. (2014) presented a non-parametric analysis framework for investigating the M⋆–Z–SFR relation in local galaxies. When investigating the nature of the M⋆–Z–SFR relation, non-parametric techniques are preferred since they do not require a ﬁxed SFR dependence at a given M⋆, as is required in the framework of Mannucci et al. (2010) or Lara-L´opez et al. (2010). Following

68 Salim et al. (2014, 2015), we examine the slope of 12 + log(O/H) as a function of

∆log(SSFR) at ﬁxed M⋆. For each M⋆ bin, we assume the form

12 + log(O/H) = β + κ ∆log(SSFR) (3.17) ∗ While this introduces a parametrization, it allows for a direct comparison of the slope κ with previous studies (e.g. Salim et al. 2014, 2015). The dependence of log(O/H) on SFR at fixed M is simply d log(O/H) = d log(O/H) = κ. This differs ⋆ d log(SFR) M⋆ d∆ log(SSFR) from the parameter α that minimizes the scatter about a surface in M⋆–Z–SFR space (e.g., Mannucci et al. 2010; Yates, Kauffmann & Guo 2012; Andrews & Martini 2013). It is straightforward to convert a value of α to an equivalent value of κ if the parametrization of the FMR is known.

Salim et al. (2014) find that the slope κ is a function of M⋆, and becomes flatter at higher masses. They also find that the slope is a function of ∆log(SSFR), and becomes steeper at higher ∆log(SSFR). We apply their framework to the galaxies in our sample. We measure ∆log(SSFR) with Equation 3.9, and apply our new strong line calibrations to derive oxygen abundances.

Each panel of Figure 3.11 shows log(O/H) as a function of ∆log(SSFR) for a given M⋆ denoted in the bottom left corner. We include all galaxies and stacks with masses that fall within the 0.25 dex M window of each panel. The circles show ± ⋆ the direct method abundances of the stacks. The stacks are 0.10 dex wide in M⋆, so there are multiple stacks at ﬁxed ∆log(SSFR) within the M⋆ window of each panel. The gray contours show the SDSS galaxies with oxygen abundances determined with our new calibration.

For each M⋆, we fit log(O/H) as a function of ∆log(SSFR) per Equation 3.17. The dashed red lines show the fits resulting from the SDSS galaxies; the dotted red lines show the fits to the stacks. Note that for higher masses (log(M⋆/M⊙) > 10.0) ∼ 69 there are few to no stacks with direct method abundances. While in some cases the slopes derived from the direct method differ from those derived from the individual galaxies (e.g., log(M⋆/M⊙)=9.5), we typically find agreement within the error bars.

The solid green line in each panel shows the median log(O/H) as a function of ∆log(SSFR). The relationship between log(O/H) and ∆log(SSFR) is non-linear and appears to steepen at high ∆log(SSFR), particularly for the lower mass bins. This is in agreement with Salim et al. (2014) and illustrates the need for a non-parametric approach when investigating the M⋆–Z–SFR relation. Since our detection of auroral lines is biased towards high ∆log(SSFR), we have relatively more direct method measurements at high ∆log(SSFR), which effectively biases the fit to the stacks towards a steeper slope. Accounting for ∆log(SSFR) does lead to a reduction in scatter; the scatter in (O/H) at fixed M⋆ and ∆log(SSFR) is somewhat lower than the scatter at fixed M⋆ alone. In the case of N2, the scatter in O/H at fixed M⋆ is 0.12, while the scatter around the running median is 0.07. ∼

We perform this analysis for the O3N2 and N2O2 diagnostics as well. The results for the O3N2 diagnostic are qualitatively similar to those of the N2 diagnostic. In Figure 3.12 we examine the results of this non-parametric approach with the N2O2 diagnostic. The green line shows the median log(O/H) of the individual galaxies, while the dashed (dotted) red lines show the parametrized ﬁt to the slope of the galaxies (stacks). Interestingly, the N2O2 diagnostic removes much of the nonlinearity of the relationship between log(O/H) and ∆log(SSFR); the green and red lines agree across a wide range of ∆log(SSFR). Furthermore, the slope remains relatively steep, even at high masses, which is not the case for the other diagnostics.

The results of the linear ﬁts for each diagnostic are shown in Figure 3.13. The left panel shows the measured slope (for both the SDSS galaxies and direct

70 method stack abundances). The right panel shows the corresponding intercept for each ﬁt; the small circles show where the stacks fall in the M Z plane. The ⋆ − measured intercepts (right panel) closely track the star forming main sequence, which also follows the Z M 1/3 scaling denoted by the dashed magenta line. ∝ ⋆ This is consistent with momentum driven winds and a mass loading parameter η which scales approximately as η M −1/3 (Murray, Quataert & Thompson 2005; ∝ ⋆ Oppenheimer & Dav´e2006).

The left panel of Figure 3.13 presents clear evidence for evolution of the slope κ as a function of M⋆ for the N2 and O3N2 diagnostics. The slope is steeper at lower masses, in agreement with previous studies (Ellison et al. 2008a; Salim et al. 2014). We measure κ 0.2 to 0.4. Andrews & Martini (2013) measured α = 0.66 and ∼ − − the slope of the FMR to be 0.43 with the direct method. Converting their direct method α to an equivalent value of κ yields κ 0.28, which is in good agreement ∼− with our measurements. Furthermore, the tension between the slope derived from direct method abundances and that derived from strong line inferred abundances is signiﬁcantly reduced from that found in Andrews & Martini (2013). Our values of κ are on average steeper than Salim et al. (2014) found. This is at least in part due to the fact that our new calibrations incorporate ∆log(SSFR) explicitly.

The nonlinear dependence of log(O/H) on ∆log(SSFR) is most prominent in the low mass panels of Figure 3.11. There is a break in slope between log(O/H)N2 and ∆log(SSFR), which appears to denote a boundary between highly star forming galaxies and more moderately star forming galaxies. Salim et al. (2014, 2015) interperet this break and the general ﬂattening of the slope with M⋆ in the context of models from Zahid et al. (2014b). They suggest that the ISM of the more evolved galaxies is saturated and thus the gas phase abundances are largely insensitive to inﬂows of pristine gas and the resulting variations in ∆log(SSFR). In contrast, the

71 more vigorously star forming galaxies have lower gas phase abundances which are more sensitive to inﬂows of pristine gas. However, the ﬂattening in slope could also be due to the N2 diagnostic losing sensitivity at high metallicities. This would not, however, explain the similar behavior seen for the O3N2 diagnostic (see Figure 3.13) which is expected to remain sensitive to oxygen abundance in the high metallicity regime.

The break in slope is not present in Figure 3.12 for N2O2. Furthermore, the slope in Figure 3.12 is relatively steep and constant for all M⋆. Since the N2O2 diagnostic is insensitive to ionization parameter, this may mean that the ionization parameter is more tightly coupled to ∆log(SSFR) in intensely star forming galaxies. For instance, suppose an increase in SFR in a highly star forming galaxy produced a larger increase in ionization parameter than in a more moderately star forming galaxy with the same stellar mass. This would bias the N2 and O3N2 diagnostics in the direction of lower metallicity and cause the slope between inferred log(O/H) and ∆log(SSFR) to steepen. This would explain why the break is present for N2 and O3N2, but not N2O2. We emphasize that Figures 3.11 and 3.12 show how changes in

M⋆ and ∆log(SSFR) aﬀect the diagnostics, from which we only infer a metallicity. While the break in slope may be a real eﬀect resulting from the physical processes governing the M⋆–Z–SFR relation, there remain potential biases associated with strong line calibrations.

3.5.3. Application of New Calibrations to High Redshift Galaxies

Most galaxies found in high redshift surveys are qualitatively similar to gas rich, metal poor, highly star forming galaxies in the local universe (Steidel et al. 2014; Kriek et al. 2014; Shapley et al. 2015; de los Reyes et al. 2015). This is at least in part a selection eﬀect. At high redshift, bright emission line galaxies are easier to

72 detect than quiescent galaxies. However, the average SFR and SSFR of the universe does indeed increase with redshift, peaking near z 2 (e.g., see the compilation by ∼ Hopkins & Beacom 2006b). In this section we investigate how the mean properties of high redshift galaxies compare to those of local star forming galaxies, as well as whether or not the diagnostic tools developed from galaxies in the local universe can yield useful information when applied to high redshift galaxies.

Are the Calibrations Valid at High Redshift?

The calibrations derived in Section 3.4 incorporate M⋆ and ∆log(SSFR) relative to the local star forming main sequence. When applying these calibrations to high redshift galaxies there is an implicit comparison to the local star forming main sequence, rather than the star forming main sequence of the high redshift universe. Since the average star formation rate of the universe evolves with redshift, so does the star forming main sequence. In this sense, the local star forming main sequence is a somewhat arbitrary (albeit convenient) zero point for our calibrations. Utilizing a ∆log(SSFR) deﬁned relative to the high redshift star forming main sequence would require recalibrating the diagnostics using high redshift galaxies. This would merely amount to a zero-point shift (Salim et al. 2015), since in our framework the higher (S)SFRs would be balanced by lower metallicities.

One possible concern is whether or not it is appropriate to apply our calibrations to high redshift galaxies. Steidel et al. (2014) argue that the position of high redshift galaxies in the BPT diagram is largely independent of (O/H), and primarily determined by the ionization parameter Γ, which is highly dependent on Teff , the density of star formation, and geometrical effects. They find that the correlation between (O/H) and the strong line ratios is most likely a result of the correlation between Γ, Teff , and the stellar metallicity which, for young stellar populations,

73 reflects the gas phase metallicity. The average Teff may indeed evolve with redshift due to the compact, gas rich, low metallicity environments that become more common at higher redshifts. These conditions could result in stellar populations with abnormally hard ionizing spectra that drive unusual ionization conditions and abundances (Eldridge & Stanway 2009; Brott et al. 2011; Levesque et al. 2012; Kudritzki & Puls 2000; Kewley et al. 2013). Steidel et al. (2014) show that a factor of 2.5 change in Γ has the same order of magnitude effect on N2 as a factor of five change in Z. Even in the local universe, a factor of 2.5 variation in ionization parameter from one object to another is not unreasonable (Zahid et al. 2012a), although the z 2.3 galaxies would require a systematic increase in ionization ∼ parameter of this order of magnitude. While there is evidence that the ionization conditions of high redshift galaxies are similar to local H II regions (Nakajima et al. 2013), the validity of local strong line calibrations at high redshift is further complicated by the fact that the abundance of nitrogen relative to oxygen may increase with redshift (Steidel et al. 2014; Masters et al. 2014).

While we do not yet have direct method oxygen abundances for a large sample of z 2 galaxies, Brown, Croxall & Pogge (2014) measured the direct method ≥ oxygen abundances and strong line ratios of several Lyman Break Analogs (LBAs; Heckman et al. 2005; Hoopes et al. 2007; Basu-Zych et al. 2007b; Overzier et al. 2008, 2009, 2010; Gon¸calves et al. 2010). LBAs are local (z 0.2) versions of the ∼ Lyman Break Galaxies which dominated the SFR of the universe at z > 2.5 (for a ∼ review of LBGs, see Giavalisco 2002). In the left panel of Figure 3.14 we compare the oxygen abundance determined with our new calibrations with the direct method (O/H) for the four LBAs from Brown, Croxall & Pogge (2014). The circles, triangles, and inverted triangles denote the deviation of the inferred (O/H) from the direct

74 method (O/H) for our N2, O3N2, and N2O2 calibrations respectively. The gray shaded region shows the average uncertainty of the direct method measurements.

The choice of star formation rate indicator is a source of systematic error. Our calibrations are derived using the SFRs from the MPA/JHU pipeline. In order to minimize systematic eﬀects associated with the SFR of LBAs, we adopt the SFRs from the MPA/JHU catalog, which agree with the Hα derived SFRs from Overzier et al. (2009). While the Hα + 24µm SFRs from Overzier et al. (2009) are regarded as the optimal SFR indicator, these values are systematically high compared to the Hα derived SFRs and result in correspondingly low oxygen abundances. Thus we recommend Hα derived SFRs when applying these calibrations.

In general, the oxygen abundances predicted by our new calibrations and the direct method oxygen abundances for these LBAs agree quite well. The biggest difference is the N2O2 based metallicity of the most massive LBA from Brown, Croxall & Pogge (2014), J005527, which is 1σ larger than the direct method metallicity. However, this object displays features consistent with Wolf-Rayet stars, which may drive unusual (N/O) ratios (Pagel, Terlevich & Melnick 1986; Henry, Edmunds & Köppen 2000; Brinchmann, Kunth & Durret 2008; López-Sánchez & Esteban 2010; Berg, Skillman & Marble 2011). We conclude that our new calibrations are suitable for use in LBAs, and that our new calibrations will produce reliable oxygen abundance estimates in the high redshift universe if the ionization conditions of LBAs are representative of their high-z counterparts. Nevertheless, direct method abundance measurements for high redshift galaxies are still needed to determine if local calibrations are suitable for high redshift galaxies.

75 Application to MOSDEF z 2.3 Galaxies ∼

The MOSFIRE Deep Evolution Field (MOSDEF) survey (Kriek et al. 2014) is a spectrocopic survey investigating the rest frame optical emission lines of high redshift star forming galaxies. Sanders et al. (2015) used a sample of MOSDEF galaxies to stack spectra in M⋆ and M⋆–SFR bins in order to measure the rest frame optical emission lines of z 2.3 galaxies with high precision. We use the published M , ∼ ⋆ SFR, and emission line data from Sanders et al. (2015) to calculate ∆log(SSFR) relative to the local star forming main sequence. We apply our new strong line calibrations to the high and low SFR stacks from Sanders et al. (2015) (shown as crosses in Figures 3.8 and 3.9). We determine the uncertainty in oxygen abundances using a Monte Carlo technique similar to that used to determine the uncertainties in our own abundances (see Section 3.3.1). The error bars in the M⋆ direction show the mass range of galaxies in the stack. These galaxies fall well below the local MZR. This is in agreement with Sanders et al. (2015), and other studies which have shown that high redshift, highly star forming galaxies tend to have low gas phase oxygen abundances (e.g. Erb et al. 2006; Maiolino et al. 2008; Maier et al. 2014).

Conceptually, if the gas fueling the star formation has low metallicity, then the ISM of highly star forming galaxies will be relatively metal poor (Ellison et al. 2008a; Mannucci et al. 2010; Lara-López et al. 2010). However, Figures 3.8 and 3.9 also show that high redshift galaxies from Sanders et al. (2015) are metal poor relative to our low-z stacks with similar M⋆ and SFR. The right panel of Figure 3.14 shows a quantitative comparison of where high redshift galaxies fall relative to local galaxies with similar M⋆ and SFR. We find that the high redshift galaxies from Sanders et al. (2015) have metallicities that are on average 0.1 0.2 dex lower than local galaxies ∼ − of the same M⋆ and SFR. There is also evidence that the offset in log(O/H) increases with M⋆, as noted in Salim et al. (2015). This trend holds for both N2 and O3N2.

76 We did not apply our N2O2 calibration as the [O II] λ3727 A˚ line does not fall within the spectral range of the MOSFIRE data reported by Sanders et al. (2015). The oﬀset of the Sanders et al. (2015) galaxies toward lower oxygen abundances than local galaxies with the same M⋆ and SFR appears to contradict the existence of an FMR, and requires some redshift dependence of the M⋆–Z–SFR relation.

Zahid et al. (2014b) use analytic and numerical models to quantify the evolution in their datasets. Their model, which they refer to as the Universal Metallicity Relation (UZR), assumes all galaxies evolve along the star forming main sequence. They model the MZR at any epoch as

γ M⋆ 12 + log(O/H) = ZO + log 1 exp (3.18) − − MO

They ﬁnd that the shape of the MZR is constant (i.e. universal). Only the characteristic turnover mass MO increases with redshift such that at ﬁxed M⋆, O/H decreases with redshift. Above MO, galaxies have essentially the same metallicity

ZO.

Salim et al. (2015) suggest that the high metallicities act as a buffer against inflows diluting the ISM, resulting in the break in κ seen in the top panels of Figure 3.11. With a sufficiently large sample of high redshift galaxies resolving the turnover in the MZR, it may be possible to directly test the evolution of MO with redshift within the framework of Section 3.5.2. If MO increases with redshift as argued by Zahid et al. (2014b), the break in κ should occur at a higher mass than observed for local samples of galaxies. Salim et al. (2015) examine the M⋆–Z–SFR relation with the high redshift galaxies from Steidel et al. (2014), as well as local galaxies with relatively high values of ∆log(SSFR). Their results suggest that κ flattens at high ∆log(SSFR), but current samples of high redshift galaxies are not yet complete enough to reveal a break in κ at lower values of ∆log(SSFR).

77 3.6. Summary

We have recalibrated strong line diagnostics with direct method oxygen abundances of galaxies and applied the new calibrations to investigate the M⋆–Z–SFR relation. We stacked 2 105 spectra of star forming galaxies in the local universe in M ∼ × ⋆ and oﬀset from the star forming main sequence. Our main results are:

We recalibrated the relationship between (O/H) e and the N2, O3N2, N2O2 • T strong line ratios. This included incorporation of ∆log(SSFR) as an additional parameter.

For the N2 and O3N2 diagnostics we ﬁnd a higher (O/H) normalization, • but similar slope, as previous calibrations. We attribute this diﬀerence to

the fact that previous calibrations are based on individual H II regions. No single calibration signiﬁcantly outperforms the others. The O3N2 diagnostic is the most accurate of the three for 43% (47/110) of the stacks, but N2O2 is typically a close second and subject to fewer biases.

We apply our new calibrations to local star forming galaxies. In the context • of galaxy evolution models, our result that the slope of our new calibrations is similar to previous calibrations implies the scaling of galactic outﬂows with stellar mass remains unchanged.

We adopt the non-parametric framework presented in Salim et al. (2014) to • investigate the M⋆–Z–SFR relation in the local universe. When using the N2 and O3N2 diagnostics we ﬁnd variation in the SFR dependence with both

M⋆ and ∆log(SSFR), as noted in previous studies. The N2O2 diagnostic

produces a nearly constant slope, independent of M⋆ and ∆log(SSFR). Below

log(M /M⊙) 10, the slopes measured with strong line diagnostics are in ⋆ ∼ 78 agreement with each other and consistent with the direct method slope to within 10%. At higher masses, the uncertainty in the direct method slope ∼ increases signiﬁcantly, and the N2 and O3N2 inferred slopes ﬂatten compared

to N2O2. We note a modest reduction of scatter in log(O/H) at ﬁxed M⋆ and ∆ log(SSFR).

We also apply our new calibrations to high redshift galaxies presented in • Sanders et al. (2015). We ﬁnd these galaxies to be systematically metal

poor compared to local galaxies of the same M⋆ and SFR, and conclude the

M⋆–Z–SFR relation evolves with redshift.

It is possible that our O/H estimates of high redshift galaxies are biased by • the ionization conditions of the high redshift universe. While direct method measurements of high redshift galaxies are required to deﬁnitively test if this is the case, we apply our new calibrations to the LBAs from Brown, Croxall & Pogge (2014) and ﬁnd consistent results with the direct method measurements of those systems.

There remains some degree of uncertainty as to whether or not these calibrations are valid in the high redshift universe. The ideal path forward would be to recalibrate these empirical relations at z 2.3. While direct method oxygen ∼ abundance determinations at high redshift are challenging, recent progress has been made. There have been several direct method abundance measurements obtained at z 1 (Hoyos et al. 2005; Kakazu, Cowie & Hu 2007; Amor´ın, P´erez-Montero & ∼ V´ılchez 2010; Amor´ın et al. 2012), and Yuan & Kewley (2009) used gravitational lensing to measure [O III] λ4363 at z 1.7. Most recently, Jones, Riess & Scolnic ∼ (2015) showed that α element strong line abundance diagnostics are reliable up to at least z 0.8. Additionally, Steidel et al. (2014) report that direct method ∼ 79 oxygen abundances (in addition the [O II], [O III], Hα,Hβ, [N II], and [S II] optical strong lines) will soon be available for a subset of the KBSS-MOSFIRE targets at z 2.36 2.57. This will improve constraints on the M –Z–SFR relation and ≈ − ⋆ ionization conditions in the early universe.

While we have restricted ourselves to two applications of our newly derived calibrations (the M⋆–Z–SFR relation and the high redshift universe), there are many other potential applications of these calibrations. For example, a set of abundance diagnostics based on direct method abundances of galaxies rather than individual

H II regions is invaluable for any study concerned with gas phase abundances of galaxies, such as transient surveys like ASASSN (Shappee et al. 2014) and ZTF (Bellm 2014). There are also many applications to IFU spectroscopic galaxy surveys (e.g. MaNGA, Bundy et al. 2015), particularly in regions of galaxies where the weak lines are not detected. Lastly, next generation galaxy surveys like DESI (Flaugher & Bebek 2014) will be able to make use of these calibrations to study much larger samples of galaxies.

80 4.0 Hγ Hα [N II] λλ 6543, 84Å [S II] λλ 6713, 31Å λ 3.0 [O III] 4363Å

2.0

1.0

0.0

4250 4300 4350 4400 4450 6550 6600 6650 6700 6750 10.0

8.0

6.0

4.0 [Arbitrary] λ f 2.0

0.0 4000 5000 6000 7000 2.5 λ 2.0 He I 5876Å [Ar III] λ 7135Å [N II] λ 5755Å [O II] λλ 7322, 33Å 1.5

1.0

0.5

0.0 −0.5 5650 5700 5750 5800 5850 7100 7150 7200 7250 7300 Rest Wavelength [Å]

Fig. 3.1.— Illustration of how stacking improves the S/N of the weak lines. The top and bottom sets of plots show diﬀerent regions of the middle spectrum. In each panel, the gray line shows the raw SDSS spectrum (shifted to rest frame wavelength), the blue line shows the stacked spectrum, the red line shows the ﬁt to the stellar continuum, and the thick black line shows the spectrum after stellar continuum subtraction.

81 0.0 3 (a) (b)

1 ] 2 1 ] −0.5 −1 −1 1 0 0

log(N2) −1.0 0 log(O3N2)

−1 log(SSFR) [yr −1 log(SSFR) [yr ∆ −1 ∆ −1.5 8 9 10 11 8 9 10 11 log(M⋆ ) [M ] log(M⋆ ) [M ] ⊙ ⊙ 0.5 (c) (d) 1.0

1 ] 1 ] −1 −1 0.0 0.5 0 0 −0.5 log(R23) log(N2O2) 0.0 −1.0 −1 log(SSFR) [yr −1 log(SSFR) [yr ∆ ∆

−1.5 −0.5 8 9 10 11 8 9 10 11 log(M⋆ ) [M ] log(M⋆ ) [M ] ⊙ ⊙

Fig. 3.2.— Distribution of SDSS galaxies in the various M⋆-diagnostic planes considered here. The individual galaxies are binned in a 2D grid. Color coding denotes the average ∆log(SSFR) of each bin; the underlying gray scale shows the relative density of galaxies in our input catalog. Top left to bottom right, the panels show N2, O3N2, N2O2, and R23 versus M⋆. In the case of N2, O3N2, and N2O2 the scatter in the diagnostic at ﬁxed M⋆ and ∆log(SSFR) is generally small compared to the overall range spanned by the diagnostic. In the case of R23, the distribution of galaxies at ﬁxed M⋆ and ∆log(SSFR) is rather broad compared to the range spanned by the diagnostic, making the R23 line ratios of a given stack less meaningful.

82 1.0 1.0 1.75 1.75 ) 0.5 β 0.8 ] ] −1 −1 0.0 1.25 1.25 0.6 5007/H λ −0.5 0.75 P 0.75 0.4 −1.0 0.25 0.25 log(SSFR) [yr log(SSFR) [yr ∆ ∆ log([O III] −1.5 0.2 −0.25 −0.25 −2.0 0.0 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 log([N II] λ 6583/Hα) log([N II] λ 6583/Hα)

Fig. 3.3.— Left: BPT diagram of the stacks (circles) relative to SDSS star forming galaxies (gray contours) and H II regions from Pilyugin, Grebel & Mattsson (2012) (small black points). Color coding is done according to ∆log(SSFR). The dashed and solid red lines are from Kauﬀmann et al. (2003b) and Kewley et al. (2006) respectively and denote the boundaries between star forming galaxies and AGN. Right: Excitation parameter P R3/R23 versus log(N2). The symbol notation is the same as the left panel. In the≡ high excitation regime, the stacks and SDSS galaxies closely resemble H II regions. At lower excitation (where the majority of SDSS galaxies are located) there are very few H II regions; the two populations are clearly subject to diﬀerent conditions.

83 0.4 0.2 0.0 1.75 −0.2 Residual −0.4

1.25 ] PP04 −1 9.0 M13

Te 0.75

8.5

0.25 log(SSFR) [yr ∆ 12+log(O/H) 8.0 −0.25

−1.8−1.6−1.4−1.2−1.0−0.8−0.6−0.4 log(N2)

Fig. 3.4.— Direct method oxygen abundances of the stacks as a function of N2 and ∆log(SSFR). The circles show the actual measurements; the various lines show our

fit to (O/H)Te as a function of N2 and ∆log(SSFR). The thick red and magenta lines shows the fits from Pettini & Pagel (2004) and Marino et al. (2013), respectively, which are based almost entirely on direct method oxygen abundances of individual H II regions. The top panel shows the residuals of the fit; the dashed lines show the RMS of the residuals.

84 0.4 0.2 0.0 1.75 −0.2 Residual −0.4

1.25 ] PP04 −1 9.0 M13

Te 0.75

8.5

0.25 log(SSFR) [yr ∆ 12+log(O/H) 8.0 −0.25

0.0 0.5 1.0 1.5 2.0 2.5 log(O3N2)

Fig. 3.5.— Same as Figure 3.4 but for the O3N2 diagnostic.

85 0.4 0.2 0.0 1.75 −0.2 Residual −0.4

KD02 1.25 ] −1 9.0

Te 0.75

8.5

0.25 log(SSFR) [yr ∆ 12+log(O/H) 8.0 −0.25

−1.4 −1.2 −1.0 −0.8 −0.6 −0.4 −0.2 log(N2O2)

Fig. 3.6.— Same as Figure 3.4 but for the N2O2 diagnostic. The thick red line shows the ﬁt from Kewley & Dopita (2002).

86 2 9.5 Te 1 9.0 0 8.5

log(SSFR) −1 8.0 ∆ −2 7.5 12+log(O/H)

2 0.2 ⋆⋆⋆ 1 ⊙⊙⊙ 0.1 0 0.0 −0.1

log(SSFR) −1 ∆ −2 −0.2 N2 Residuals

2 0.2 ⋆⋆⋆ 1 ⊙⊙⊙ 0.1 0 0.0 −0.1

log(SSFR) −1 ∆ −0.2

−2 O3N2 Residuals

2 0.2 ⋆⋆⋆ 1 ⊙⊙⊙ 0.1 0 0.0 −0.1

log(SSFR) −1 ∆ −0.2

−2 N2O2 Residuals 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 log(M⋆⋆⋆ ) [M ] ⊙⊙⊙ Fig. 3.7.— Overview of our binning and quality of our strong-line calibrations. The top panel shows the distribution of direct method measurements in M⋆-∆ log(SSFR) space. Each square represents a M⋆-∆log(SSFR) stack. The color coding denotes metallicity. Metallicity generally increases as M⋆ increases and/or ∆log(SSFR) decreases. The second, third, and fourth panels show the residuals for the N2, O3N2, and N2O2 diagnostics respectively. All three diagnostics perform well across most of the parameter space. The O3N2 diagnostic was the most accurate (47/110 bins), followed by N2O2 (33/110 bins) and N2 (30/110 bins).

87 KE08 1.75 Tremonti+04 9.0 Sanders+15 ]

1.25 −1

8.5 0.75

0.25 log(SSFR) [yr 12 + log(O/H) [N2] 8.0 ∆ −0.25

7 8 9 10 11 log(M⋆ ) [M ] ⊙ Fig. 3.8.— The MZR derived with our new N2 calibration. The circles represent our stacks, the crosses represent the high redshift star forming galaxy stacks from Sanders et al. (2015), and the gray contours represent the star forming SDSS galaxies used in our analysis. The thick red line shows the mass binned results from Kewley & Ellison (2008). The dot-dashed magenta line shows the MZR from Tremonti et al. (2004). The smooth behaviour of the stacks is ultimately the result of the average N2 varying so smoothly with M⋆. The galaxies from Sanders et al. (2015) display lower (O/H) than the stacks with comparable M⋆ and ∆log(SSFR).

88 KE08 1.75 Tremonti+04 9.0 Sanders+15 ]

1.25 −1

8.5 0.75

0.25 log(SSFR) [yr ∆

12 + log(O/H) [O3N2] 8.0 −0.25

7 8 9 10 11 log(M⋆ ) [M ] ⊙ Fig. 3.9.— Same as Figure 3.8 but using the O3N2 diagnostic.

89 KE08 1.75 9.5 Tremonti+04 ]

1.25 −1 9.0 0.75 8.5 0.25 log(SSFR) [yr ∆ 12 + log(O/H) [N2O2] 8.0 −0.25

7 8 9 10 11 log(M⋆ ) [M ] ⊙ Fig. 3.10.— Same as Figure 3.8 but for the N2O2 diagnostic. The high redshift star forming galaxy stacks from Sanders et al. (2015) are not included here, as the [O II] λ3727 A˚ line does not fall within the spectral range of the MOSFIRE instrument at z 2.3. Note that the MZR resulting from this calibration has a ∼ higher normalization and larger scatter at ﬁxed M⋆ than the other calibrations.

90 9.5 9.5

9.0 9.0

8.5 8.5 12+log(O/H) [N2] 12+log(O/H) [N2]

log(M⋆ /M ) = 9.5 log(M⋆ /M ) = 10.0 8.0 ⊙ 8.0 ⊙ −2 −1 0 1 2 −2 −1 0 1 2 ∆ log(SSFR) ∆ log(SSFR)

9.5 9.5

9.0 9.0

8.5 8.5 12+log(O/H) [N2] 12+log(O/H) [N2]

log(M⋆ /M ) = 10.5 log(M⋆ /M ) = 11.0 8.0 ⊙ 8.0 ⊙ −2 −1 0 1 2 −2 −1 0 1 2 ∆ log(SSFR) ∆ log(SSFR)

Fig. 3.11.— Oxygen abundance as a function of ∆log(SSFR) for the N2 calibration. Each panel shows galaxies and stacks falling within 0.25 dex of the designated mass. The gray contours show the distribution of SDSS galaxies;± the circles show the stacks falling within the designated mass range (there are often multiple stacks at a given value of ∆log(SSFR)). The color coding denotes ∆log(SSFR). Oxygen abundances of the individual galaxies are derived from our new N2 calibration; oxygen abundances of the stacks are derived from the direct method. In each panel, the solid green line shows the median of the individual galaxies, the dashed red line shows the linear ﬁt to the individual galaxies, and the dotted red line shows the linear ﬁt to the stacks.

91 9.5 9.5

9.0 9.0

8.5 8.5 12+log(O/H) [N2O2] 12+log(O/H) [N2O2]

log(M⋆ /M ) = 9.5 log(M⋆ /M ) = 10.0 8.0 ⊙ 8.0 ⊙ −2 −1 0 1 2 −2 −1 0 1 2 ∆ log(SSFR) ∆ log(SSFR)

9.5 9.5

9.0 9.0

8.5 8.5 12+log(O/H) [N2O2] 12+log(O/H) [N2O2]

log(M⋆ /M ) = 10.5 log(M⋆ /M ) = 11.0 8.0 ⊙ 8.0 ⊙ −2 −1 0 1 2 −2 −1 0 1 2 ∆ log(SSFR) ∆ log(SSFR)

Fig. 3.12.— Same as Figure 3.11 but using the N2O2 diagnostic. The dependence on ∆log(SSFR) is generally steeper than that of the N2 and O3N2 diagnostics, even at high masses. The dependence is also well approximated with the linear parametrization.

92 0.2 N2 9.5 Z ∝ M1/3 O3N2 ⋆ N2O2

0.0 ) β ) Direct Method 9.0 κ −0.2 8.5 Slope (

−0.4 Intercept ( 8.0 −0.6

7 8 9 10 11 7 8 9 10 11 log(M⋆ ) [M ] log(M⋆ ) [M ] ⊙ ⊙

Fig. 3.13.— Slopes and intercepts as a function of M⋆ for our new strong line calibrations (applied to individual galaxies, green, red, and blue points) and direct method measurements (black points). Left: Slope as a function of M⋆. The slopes measured from the strong line calibrations typically agree with those measured from the direct method stacks. The instances of disagreement are likely due to the fact that the direct method abundances are more easily measured at high ∆log(SSFR), where the relation between log(O/H) and ∆log(SSFR) appears to steepen. Right: Intercept as a function of M⋆. The intercept corresponds to the inferred metallicity of the star forming main sequence. The small circles show where the stacks fall in this parameter space. The stacks are colored according to ∆log(SSFR). The measured interepts closely track the star forming main sequence, which roughly follows the dashed magenta line corresponding to Z M 1/3. ∝ ⋆

93 0.2 0.1 Lyman Break Analogs MOSDEF z∼2.3 Stacks e T 0.0 0.1 −0.1 log(SSFR)) ∆ ⋆

− log(O/H) 0.0 −0.2 SL −0.3 −0.1 N2 −0.4 N2 log(O/H) O3N2 O3N2 N2O2 log(O/H | M , −0.2 ∆ −0.5 9.0 9.2 9.4 9.6 9.8 10.0 9.0 9.5 10.0 10.5 11.0 11.5 log(M⋆⋆ ) [M ] log(M⋆ ) [M ] ⊙⊙ ⊙ Fig. 3.14.— Left: Deviation in strong line (SL) inferred (O/H) from the direct method (O/H) for the 4 LBAs (z 0.2) from Brown, Croxall & Pogge (2014). The error bars are generated from the∼ Monte Carlo technique previously described (see Section 3.3.1). The gray band shows the average uncertainty in the direct method oxygen abundances. The oxygen abundances determined with our new strong line calibrations are generally consistent with the measured direct method abundances. Right: Deviation in (O/H) of high redshift galaxies from local galaxies of the same mass and SFR. The MOSDEF z 2.3 points are from the Sanders et al. (2015) stacks. The blue, red, and green denote∼ their high, low, and composite SFR stacks respectively. Both our N2 (circles) and O3N2 (triangles) calibrations are shown. The error bars in the mass direction show the range of M⋆ for each bin and the error bars in ∆ (O/H) are generated from the Monte Carlo technique previously described (see Section 3.3.1). The high redshift galaxies have lower (O/H) than local galaxies of the same M⋆ and SFR regardless of mass, SFR, or strong line diagnostic.

94 Table 3.1: Wavelength Fit and Mask Ranges of Measured Lines. Linea Fit Rangeb Mask Rangec [O ii] λ3727 3700–4300 3710–3744 [Ne iii] λ3868 3800–4100 3863–3873 [S ii] λ4069 3950–4150 ··· Hγ λ4340 4250–4450 4336–4344 [O iii] λ4363 4250–4450 4360–4366 He ii λ4686 4600–4800 4680–4692 [Ar iv] λ4740 3700–7360 ··· Hβ λ4861 3700–7360 4857–4870 [O iii] λ4959 3700–7360 4954–4964 [O iii] λ5007 3700–7360 5001–5013 [N ii] λ5755 5650–5850 5753–5757 [S iii] λ6312 6100–6500 6265–6322 [N ii] λ6548 3700–7360 6528–6608 Hα λ6563 3700–7360 6528–6608 [N ii] λ6583 3700–7360 6528–6608 [S ii] λ6716 3700–7360 6696–6752 [S ii] λ6731 3700–7360 6696–6752 [Ar iii] λ7135 7035–7235 7130–7140 [O ii] λ7320 7160–7360 7318–7322 [O ii] λ7330 7160–7360 7328–7332 aEmission lines. bThe wavelength range of the stellar continuum ﬁt. cThe wavelength range of the stellar continuum ﬁt that was masked out.

95 Table 3.2: Line Fluxes Column Format Description 1 F5.2 Lowerstellarmasslimitofthestack 2 F5.2 Upperstellarmasslimitofthestack 3 F5.2 Lower∆log(SSFR)limitofthestack 4 F5.2 Upper∆log(SSFR)limitofthestack 5 I5 Numberofgalaxiesinthestack 6 F8.3 Oxygenabundanceofthestack 7 F8.3 Erroronoxygenabundance 8 F8.3 [O II] λ3726 line flux 9 F8.3 Erroron[O II] λ3726 line flux 10 F8.3 [O II] λ3729 line flux (This table is published in its entirety in the electronic edition of the journal. The column names are shown here for guidance regarding its form and content.)

96 Table 3.3: Calibration results. Diagnostic a b c d rms Residuals

N2...... 9.25 0.83 0.12 -0.20 0.0965

97 O3N2...... 8.98 -0.32 -0.18 0.0976 ··· N2O2...... 9.20 0.54 -0.36 0.1053 ··· Star Forming Main Sequence

2 3 4 log(SSFR) ⋆ = 283.728 116.265 log M + 17.4403 log M 1.17146 log M +0.0296526 log M h iM − × ⋆ × ⋆ − × ⋆ × ⋆ Chapter 4: Late-time Observations of the Tidal Disruption Event ASASSN-14ae

4.1. Introduction

ASASSN-14ae (Prieto et al. 2014; Holoien et al. 2014) was a nearby (d 200 Mpc, ∼ z = 0.0436) TDE discovered by the All-Sky Automated Survey for SuperNovae (ASAS-SN; Shappee et al. 2014) on 2014-01-25.51. An immediate follow-up campaign (Holoien et al. 2014) observed ASASSN-14ae for 150 days. We found the ∼ evolution of ASASSN-14ae to be consistent with that of a blackbody with constant temperature and exponentially declining luminosity. Although the relative strength of the He II λ4686 and Balmer lines appears to vary with time, we also found that the spectral characteristics of ASASSN-14ae fell near the middle of the H-to-He dominated continuum proposed by Arcavi et al. (2014).

In this paper we present late-time observations of ASASSN-14ae that follow the transition from a ﬂare dominated state to a host galaxy dominated state. We present an improved ASAS-SN pre-discovery upper limit, as well as extensive follow-up data consisting of optical spectra taken with the Multi-Object Double Spectrograph 1 (MODS1) on the 8.4 m Large Binocular Telescope (LBT), and UVOT/X-ray observations from the Swift space telescope, which provide an

This chapter is adapted from “Hello Darkness My Old Friend: The Fading of the Nearby TDE ASASSN-14ae”, Brown et al., MNRAS, 462, 3993, (2016).

98 exceptional opportunity for characterizing the late-time evolution of a TDE. Our limits on the previously strong Hα and UV emission are the most stringent limits to date on late-time emission from a TDE. In Section 4.2 we describe our observations, in Section 4.3 we present our measurements of the late-time evolution, and ﬁnally in Section 4.4 we provide a summary of our results and discuss the implications for future studies.

4.2. Observations

4.2.1. Spectroscopic Observations

Follow-up spectroscopy of ASASSN-14ae was obtained with MODS1 (Pogge et al. 2010) on the LBT between February 2014 and February 2016. Observations were performed in longslit mode with a 1′′.0 slit, with the exception of the latest epoch, which used a 1′′.2 slit. MODS1 uses a dichroic that splits the light into separately optimized red and blue channels at 5650 A.˚ The blue CCD covers a wavelength ∼ range of 3200 – 5650 A,˚ with a spectral resolution of 2.4 A,˚ while the red CCD ∼ covers a wavelength range of 5650 – 10000 A,˚ with a spectral resolution of 3.4 A.˚ ∼

Our first spectrum was taken on 2014-02-24 (t = 29.7 days after discovery; Prieto et al. 2014), and consisted of three 300s exposures. The following two observations (t = 93.8, 131.7 days) consisted of three 1050s exposures. These spectra were presented in Figure 5 of Holoien et al. (2014) but the detailed analysis of the evolution of Hα was restricted to the first 70 days. We obtained two additional ∼ observations unique to this paper, on 2014-11-22 (6 1200s) and 2016-02-08 × (3 600s) corresponding to 301.0 and 743.5 days after discovery, respectively. The × position angle of the slit approximated the parallactic angle at the midpoint of the observations in order to minimize slit losses due to differential atmospheric refraction. We obtained bias frames and Hg(Ar), Ne, Xe, and Kr calibration lamp

99 images for wavelength calibration. If the arc lamp or flat field data were not available on the night of the observation, we used calibration data obtained within 1-2 days of our observations. Given the stability of MODS1 over the course of an observing run, this is sufficient to provide accurate calibrations. Night sky lines were used to correct for the small ( 1 A)˚ residual flexure. Standard stars were observed with ∼ a 5 60′′ spectrophotometric slit mask and used to calibrate the response curve. × The standard stars are from the HST Primary Calibrator list, which is composed of well observed northern-hemisphere standards from the lists of Oke (1990) and Bohlin, Colina & Finley (1995). We list the information regarding our observational configuration in Table 4.1.

We used the modsCCDRed1 suite of python programs to bias subtract, flat field, and illumination correct the raw data frames. We removed cosmic rays with L.A. Cosmic (van Dokkum 2001). The sky subtraction and one-dimensional extraction were performed with the modsIDL pipeline2. We correct residual sky features with reduced spectra of standard stars observed on the same night under similar conditions and the iraf task telluric. Finally, the individual spectra from each night were combined, yielding a total of five high S/N spectra corresponding to the five observation epochs.

Our spectra were taken under variable conditions with a relatively narrow (1′′) slit. In order to facilitate comparison of spectra across multiple observing epochs, we calibrated the ﬂux of each spectra with the contemporaneous r′-band MODS acquisition images. We performed aperture photometry on the ASASSN-14ae host and bright stars in the ﬁeld with the iraf package apphot. We scaled the magnitudes of the stars to match their SDSS r′-band magnitudes, and applied the same scale

1http://www.astronomy.ohio-state.edu/MODS/Software/modsCCDRed/ 2http://www.astronomy.ohio-state.edu/MODS/Software/modsIDL/

100 factor to the host of ASASSN-14ae. Finally, following Shappee et al. (2013), we scale each spectrum of ASASSN-14ae such that its synthetic r′-band photometry matched the corresponding r′-band aperture photometry. The spectral evolution of ASASSN-14ae is presented in Section 4.3.1.

4.2.2. Swift Observations

After the publication of Holoien et al. (2014), we also obtained additional Swift observations of ASASSN-14ae. The UVOT (Poole et al. 2008) observations were obtained in six ﬁlters: V (5468 A),˚ B (4392 A),˚ U (3465 A),˚ UVW 1 (2600 A),˚ UVM2 (2246 A),˚ and UVW 2 (1928 A).˚ We used the UVOT software task uvotsource to extract the source counts from a 5.0′′radius region and a sky region with a radius of 40′′. The UVOT count rates were converted into magnitudes and ﬂuxes based on ∼ the most recent UVOT calibration (Poole et al. 2008; Breeveld et al. 2010). For the most recent observations, we coadded several exposure taken over a 2 week period ∼ in order to obtain a high S/N determination of the host magnitudes.

We also obtained X-ray observations with the Swift X-ray Telescope (XRT; Burrows et al. 2005). The XRT was operating in Photon Counting mode (Hill et al. 2004) during all Swift observations. We reduced and combined all 30 epochs of observations using the software tasks xrtpipeline and xrtselect to produce an image in the 0.3 10 keV range with a total exposure time of 58000 s. We − ∼ extracted source counts and background counts using a region with a radius of 20 pixels (47′′.1) centered on the position of ASASSN-14ae and a source-free region with radius of 70 pixels (165′′.0), respectively. The results of our X-ray and UVOT photometric analysis are presented in Section 4.3.2.

101 4.2.3. ASAS-SN Pre-Discovery Upper Limit

To further constrain the early-time light curve of ASASSN-14ae we re-evaluate the pre-discovery ASAS-SN non-detection first reported by Prieto et al. (2014). The last ASAS-SN epoch before discovery was observed on 2014-01-01.53 under favorable conditions by the quadruple 14-cm “Brutus” telescope in Haleakala, Hawaii. This ASAS-SN field was run through the standard ASAS-SN pipeline (Shappee et al. in prep.) using the isis image subtraction package (Alard & Lupton 1998; Alard 2000), except we did not allow images acquired between 2013-11-03 and 2015-12-13 to be used in the construction of the reference image to avoid light from ASASSN-14ae contaminating the reference. We then performed aperture photometry at the location of ASASSN-14ae on the subtracted images using the IRAF apphot package and calibrated the results using the AAVSO Photometric All-Sky Survey (APASS; Henden et al. 2016). There was no excess flux detected at the location of ASASSN-14ae over the reference image on 2014-01-01.53 (t = 23.98 days), and we − place a 5-sigma limit of V > 18.21 mag on ASASSN-14ae at this epoch.

4.3. Evolution of the Late-Time Emission

4.3.1. Spectral Analysis

In Holoien et al. (2014) we showed that the evolution of ASASSN-14ae is consistent with a constant temperature blackbody and exponentially decreasing luminosity. We also analyzed the spectral characteristics up to 70 days after discovery and showed that both the blue continuum and the strength of prominent emission lines (Hα,

Hβ, and He II λ4686) decreased with time, while the strength of He II λ4686 relative to the Balmer lines increased. The Hα proﬁle was analyzed up to 70 days after ∼ discovery and was shown to evolve from what was initially a very broad (FWHM 20000 km s−1) symmetric proﬁle to a slightly narrower (FWHM 10000 km s−1) ∼ ∼

102 asymmetric profile, and then to narrower still (FWHM 8000 km s−1) symmetric ∼ profile. The Hα emission also showed a consistent red offset (∆v 2000–4000 km ∼ s−1) from the systemic velocity.

The additional observations presented here provide further constraints on the evolution of the TDE ﬂare. Figure 4.1 shows the evolution of the optical emission beginning 30 days after discovery (red) and ending 750 days after discovery ∼ ∼ (dark blue). The black spectrum shows the archival SDSS DR7 (Abazajian et al. 2009) spectrum of the host galaxy taken on 2008-02-17 for a total exposure time of 2220.50s. The top panel shows the full optical spectrum, while the bottom panels show expanded views of the He II λ4686 (left) and Hα (right) regions. Prominent spectral features are labeled, while the shaded bands denote regions prone to systematic errors related to telluric correction. In particular, the B-band telluric feature is in close proximity to Hα at the redshift of ASASSN-14ae.

In order to measure the Hα emission from the TDE, we must first subtract the underlying host galaxy. All signatures of the flare have vanished by 750 ∼ days, which allows us to precisely subtract the host spectrum without introducing uncertainties associated with modeling the underlying population (e.g. Gezari et al. 2015). Furthermore, using the host spectrum obtained with MODS, rather than the archival SDSS spectrum, increases our signal to noise in the subtracted spectrum and eliminates systematic errors caused by differences in the spatial coverage of the two instruments, which are likely to be significant. After subtracting the host spectrum, we fit the Hα profile with a Gaussian superimposed on a low-order continuum. We subtract the continuum and measure the line flux by directly integrating the observed Hα profile within 3σ of the line center. While the observed Hα profiles ± are typically asymmetric and more strongly peaked than a Gaussian, this method

103 appears to be accurate to 10%, which is suﬃcient for our purposes. We list our ∼ measurements of the Hα line proﬁle in Table 4.2.

Our initial spectrum taken 30 days after discovery (red) shows broad (FWHM 13000 km s−1) emission lines superimposed on a strong blue continuum. The lines ∼ are redshifted with respect to the host galaxy (∆v 2000 km s−1). The optical ∼ emission from the ﬂare gradually decays with time and by 90 days (green), the ∼ continuum emission has weakened substantially along with the Hα and Hβ emission lines. The strength of the He II λ4686 line has grown to be comparable to that of Hβ, as noted in previous studies (Holoien et al. 2014; Arcavi et al. 2014). Approximately 130 days after discovery (cyan), there is very little continuum emission remaining, while the Hα,Hβ, and He II λ4686 emission features are still rather prominent. The width of the Hα feature ( 5000 km s−1) has decreased by a factor of 2 since ∼ ∼ our observation 30 days after discovery, and maintains a modest red oﬀset from ∼ the systemic velocity (∆v 400 km s−1). Our deepest spectrum (blue), taken at ∼ 300 days, shows only marginal evidence for any optical emission whatsoever, and ∼ looks nearly identical to both the spectrum taken at 750 days (dark blue) and the ∼ pre-outburst SDSS spectrum (black).

Figure 4.2 shows the results of our host subtraction after 300 days. The top ∼ panel shows the observed spectrum (black) and the estimate of the host spectrum (red), both binned to the approximate spectral resolution ( 4A).˚ The bottom panel ∼ shows the residuals of our host subtraction. The gray bands show the regions of the spectrum prone to systematic effects associated with the telluric correction, and the red band shows the 3500 km s−1 region where we expect to see residual Hα ± emission from the TDE. We find excess emission relative to the host spectrum; the green curve shows our best fit to the residual Hα emission assuming the feature is roughly Gaussian.

104 We find no evidence for excess Hα emission in our latest spectrum relative to the archival SDSS spectrum of the host. The lower left panel of Figure 4.1 appears to show evidence for excess blue emission relative to the SDSS spectrum. However, the fact that all wavelengths blueward of the MODS1 dichroic show uniform excess flux relative to the SDSS spectrum suggests that this is likely a systematic effect associated with our flux calibration rather than excess emission due to the TDE. Additionally, we find that the equivalent widths of strong absorption lines (e.g. Hβ) are consistent between the archival SDSS spectrum and our latest spectrum.

While our non-detection of residual emission precludes the determination of an upper limit on the Hα equivalent width, we are able to place an upper limit on the Hα luminosity. We measure the RMS of the residuals between the MODS spectrum from 750 days and the archival SDSS spectrum, and assuming a FWHM of the ∼ Hα feature of 2000 km s−1 and a spectral resolution of 4A˚ yields a 1-σ upper ∼ ∼ limit on the Hα luminosity of 1.3 1039 ergs s−1. ×

We quantify the evolution of the Hα profile in Figure 4.3. We show the luminosity (blue points, left axis) and equivalent width (red points, right axis) of the Hα line as a function of time. The triangle denotes our upper limits on the Hα emission. We also show various curves that describe the luminosity evolution of ASASSN-14ae. The thick solid line shows our fit to the Hα luminosity evolution assuming an exponential decline. Interestingly, the Hα luminosity evolves on a significantly longer timescale than implied by the bolometric luminosity evolution from Holoien et al. (2014) (dashed line). In contrast, both exponential profiles decline much faster than typical power-law models (Holoien et al. 2014), though we lack the crucial early time data needed for constraining the power-law models. Assuming the Hα emission is driven primarily by photoionization and recombination, we expect the Hα emission to track the shortest wavelength UVW2 evolution more than any

105 other UVOT band. The dotted line shows our best ﬁt to the Hα luminosity assuming L (t t )−5/3 (Evans & Kochanek 1989; Phinney 1989), where t = 18.0 days Hα ∝ − 0 0 − is based on a ﬁt to the UVW2 early time photometry. While the power law appears to describe the photometry reasonably well (see Figure 4.4), this model over-predicts the observed Hα luminosity by a factor of > 2 at late times, even with the most ∼ accommodating value of t permitted by the ASAS-SN data (t = 23.98 days). 0 0 −

While the Hα luminosity decreases with time, the Hα equivalent width increases slightly during the 300 day period following the ﬂare. The measurement of equivalent width is sensitive to seeing variations as well as slit positioning, but our observations are largely consistent with the Hα emission decreasing more slowly than the bolometric luminosity from Holoien et al. (2014). If the Hα emission is driven primarily by photoionization and recombination, this implies that the ﬂux in the far-UV decreases more slowly than the near-UV/optical continuum. Similarly, the increasing strength of He II λ4686 relative to Hβ supports the hardening of the UV spectrum at late times. This is consistent with some models (e.g. Lodato & Rossi 2011; Metzger & Stone 2016), which predict that at later times the reprocessing envelope dissipates and allows higher energy photons to escape, ultimately giving rise to a harder observed spectrum. However, in contrast with this picture, we detect no signs of X-ray emission (see Section 4.3.2). Furthermore, as the luminosity decreases and radiation escapes from regions closer to the black hole, the observed line widths could be expected to increase, similar to what is seen for AGN (McGill et al. 2008; Denney et al. 2009). Interestingly, this is the opposite of what we observe in ASASSN-14ae as well as other TDEs (Holoien et al. 2016a,b), in which the line widths appear to decrease with decreasing luminosity. The decreasing line width may suggest that the line emission arises from predominantly larger radii at later times (e.g. Guillochon, Manukian & Ramirez-Ruiz 2014).

106 Our analysis is not without systematic uncertainties. Figures 4.1 and 4.2 show that at a redshift of z = 0.0436, the Hα line is in close proximity to the B-band telluric feature. While we have corrected for telluric effects with observations of standard stars, this nonetheless introduces a source of systematic error. Similarly, the subtraction of the host continuum also introduces a source of systematic error. However, following Gezari et al. (2015), we minimize this source of uncertainty by performing our host subtraction with a late-time observation of the host with a similar observational setup as was used to observe the TDE flare. Our overall flux normalization is also a source of systematic error, but the typical uncertainty in our photometry is < 0.02 mag. More importantly, variations in the seeing and slit ∼ configuration directly affect the spatial regions probed by our observations. These effects are minimized by the fact that our slit alignment is largely consistent between epochs, and are likely to be insignificant relative to the overall evolution of the Hα luminosity, which spans more than two orders of magnitude. Finally, as noted in

Gezari et al. (2015), the He II line (n = 6 4) at 6560A˚ likely introduces some → bias to our measurement of Hα. This is particularly true 130 days after discovery, ∼ when the He II λ4686 line is comparable in strength to Hα. However, the He II line at 6560A˚ is an order of magnitude weaker than He II λ4686 in photoionized gas

(Osterbrock 1989), so even when the relative strength of He II is at its highest, there is likely to be only marginal contamination of Hα.

4.3.2. Photometry

In Figure 4.4 we show the UVOT photometric evolution of ASASSN-14ae. The small open circles show data previously presented in Holoien et al. (2014); the filled circles show the data presented in this work. The solid lines show power-law fits to the early data points. We assume a simple model for the host subtracted flux f (t t )−5/3 (Phinney 1989; Evans & Kochanek 1989). We allow t to vary λ ∝ − 0 0

107 within the 24 day window constrained by our pre-discovery ASAS-SN non-detection. The horizontal dashed lines show the host magnitudes measured from the late-time observations, which agree well with the host magnitudes estimated from the SED modeling in Holoien et al. (2014).

The agreement between our late-time photometric points and the host magnitude estimates based on optical and near-IR archival photometry from Holoien et al. (2014) provides further evidence that the emission from the TDE has faded completely by 750 days. Our observations between 400 and 500 days are consistent ∼ with host magnitudes, but these observations are less constraining because they only include only three of the six UVOT filters, and are not as deep as those taken at later times. Given the simplicity of the model, the power-law fits agree reasonably well with the early observations. We note that, as we showed in Figure 4.3, the power-law models tend to over-predict the observed brightness after 100 days. In ∼ Holoien et al. (2014), we showed that these observations can be described with a more rapidly declining exponential model. Our non-detection of excess flux at 400 ∼ days provides additional support for an evolution timescale that is faster than the canonical t−5/3 value. We note that, particularly at late-times, the accretion flow is likely to be highly sub-Eddington. In general, the photometric evolution agrees well with our detection of low level Hα emission at 300 days and the lack of optical emission in excess of the host at 750 days. ∼

We do not detect X-ray emission from the TDE to a 3-sigma upper limit of

4.1 10−4 counts s−1. Assuming a power law spectrum with Γ = 2 and Galactic H I × column density (Kalberla et al. 2005), as was done in Holoien et al. (2014), yields an upper limit on the X-ray ﬂux of f 1.5 10−14 ergs cm2 s−1. This corresponds X ≤ × 40 −1 7 to a limit of L 6.7 10 ergs s (1.7 10 L⊙) on the average X-ray luminosity X ≤ × ×

108 at the distance of ASASSN-14ae, which is a slightly tighter constraint than was presented in Holoien et al. (2014).

4.4. Conclusions

We have presented late-time optical follow-up spectra of ASASSN-14ae with LBT/MODS1 alongside a pre-discovery ASAS-SN non-detection and late-time UVOT and XRT observations from Swift. Our observations span from 20 days ∼ before to 750 days after discovery, and is the first study to follow the evolution ∼ of a TDE from a flare dominated state to a host dominated state and place such stringent limits on the late-time emission. If ASASSN-14ae is representative of TDEs in general, our findings suggest that optical emission can vanish on a timescale as short as 1 yr. This is in agreement with previous studies of some TDE candidates ∼ (e.g. Cenko et al. 2012; Vinkóet al. 2015; Holoien et al. 2016a), but is not ubiquitous among TDEs (Brown et al. 2016, in preparation).

It is interesting to consider how our results for ASASSN-14ae compare to the larger population of optical TDE candidates. In particular, our new stringent limit on the Hα emission of ASASSN-14ae may provide insight into what drives TDE emission at late times. For instance, Roth et al. (2016) show that the continuum emission and line strengths are likely to be highly dependent on the physical conditions of the reprocessing envelope. Our observations require that any physical model for ASASSN-14ae satisfy our observational constraints on the luminosity and equivalent width evolution of the Hα emission, as well as our non-detection limits for late-time optical emission.

However, ASASSN-14ae is only one in a diverse assortment of TDE candidates (van Velzen et al. 2011; Gezari et al. 2012; Cenko et al. 2012; Chornock et al. 2014; Arcavi et al. 2014; Vink´oet al. 2015; Holoien et al. 2016a). In Figure 4.5 we

109 show how our limit on Hα emission from ASASSN-14ae compares to approximate limits for other optical TDE candidates. Many of the transients in Figure 4.5 lack formal upper limit estimates of the Hα emission and simply assume that their late-time spectra are host dominated. For these cases (TDE1; van Velzen et al. 2011, the five TDE candidates from Arcavi et al. 2014, Dougie; Vinkóet al. 2015, and ASASSN-15oi; Holoien et al. 2016a) we assume an upper limit on the Hα equivalent width of 2A˚ and compute a limit on the Hα luminosity based on an estimate of the host continuum. The assumption of 2A˚ is relatively generous, given that, for a line width of 3000 km s−1,a2A˚ equivalent width corresponds to a flux excess of only ∼ a few percent relative to the continuum. This measurement can be challenging for higher redshift objects, especially if they are lacking archival spectra. For TDE2 (van Velzen et al. 2011), PS1-11af (Chornock et al. 2014), and PTF10iya (Cenko et al. 2012), we adopt the authors’ measurements of Hα emission as fiducial upper limits on the Hα emission arising from the TDE. We emphasize that these limits are unlikely to be accurate to better than a factor of a few. However, they demonstrate how the proximity of ASASSN-14ae coupled with our dedicated follow-up effort, allows us to place an unusually stringent limit on late-time Hα luminosity with a relatively modest allocation of telescope resources. As the number of TDEs with extensive optical follow-up grows, characterizing the distribution of flare lifetimes will be crucial for understanding TDE demographics (Kochanek 2016b).

The characterization of host galaxies is also critical for understanding the physical conditions that produce TDEs. The host of ASASSN-14ae, like the hosts of several other TDE candidates, shows the strong Balmer absorption features associated with a relatively recent ( 2 Gyr) burst of star formation. In fact, ∼ Balmer-strong galaxies are signiﬁcantly overrepresented in samples of TDE host galaxies (Arcavi et al. 2014; French, Arcavi & Zabludoﬀ 2016b). Coupled with

110 the TDE rate estimate in E+A galaxies from French, Arcavi & Zabludoﬀ (2016b) ( 10−3 yr−1 galaxy−1), our results suggest that on the order of one out of every ∼ 1000 E+A galaxies should show evidence for emission from a recent TDE. A cursory search of previously studied E+A galaxies that show time variable Hα and/or

He II λ4686 emission features could yield several new TDE candidates. Signiﬁcant changes in the equivalent width or relative strength of these lines would be consistent with accretion events observed in AGN (e.g. Peterson & Ferland 1986), and in the absence of previous nuclear activity, would be strongly indicative of a recent TDE.

Similarly, E+A galaxies are rare and make up only 1% of SDSS galaxies ∼ (Quintero et al. 2004; French, Arcavi & Zabludoﬀ 2016b; Kochanek 2016b). However, a spectroscopic survey of many thousands of galaxies will likely include some number of E+A galaxies. For instance, MaNGA (Bundy et al. 2015) will eventually obtain spatially resolved spectroscopy of 104 galaxies, approximately 100 of which will resemble the Balmer-strong galaxies from French, Arcavi & Zabludoﬀ (2016b). Most observations of MaNGA galaxies will rarely span more than one night (Bundy et al. 2015), but they will all have prior SDSS spectra. Thus E+A galaxies with peculiar nuclear Hα and/or He II λ4686 emission features could potentially be explained with a recent TDE. While a more complete understanding of the relationship between host galaxy properties and TDE rates is necessary, TDE signatures in excess of 1 out of every 1000 E+A galaxies would provide strong evidence for further peculiarity of TDE hosts, such as complex debris streams, sharply peaked TDE rates, or SMBH binaries (e.g. Wegg & Bode 2011; Li et al. 2015; Ricarte et al. 2016). Spectroscopic monitoring of TDEs during the years following discovery will continue to be crucial for constraining the nuclear properties of TDEs as well as their hosts.

111 Fig. 4.1.— Rest frame absolute-flux-calibrated spectra of ASASSN-14ae. Color denotes days since discovery. The top panel shows the full optical spectrum, while the bottom panel shows zoomed portions of the regions in the immediate vicinity of He II λ4686 (left) and Hα (right). The shaded regions show the location of telluric features where systematic errors may be significant. The spectra show clear temporal evolution in the sense of decreasing continuum and emission line features with increasing time. We find no evidence for TDE emission in the spectrum taken at 750 days, and adopt this as a nominal host spectrum. ∼

112 Fig. 4.2.— Top: late-time spectra of ASASSN-14ae, showing the spectrum taken at 300 days (black) and the host spectrum taken at 750 days (red). Bottom: residuals∼ after host subtraction. The red shaded band shows∼ the 150A˚ wide region − ∼ ( 3500 km s 1) of the spectrum we searched for Hα emission, while the gray shaded bands± shows the regions of the spectrum prone to systematic errors associated with telluric features. The green curve shows our best ﬁt model for the emission we ﬁnd in the vicinity of Hα.

113 Fig. 4.3.— Luminosity and equivalent width evolution of the Hα emission line feature up to 750 days after discovery. The left (right) axis shows the measured luminosity ∼ (equivalent width) of the Hα emission. Circles show our detections, and triangles denote upper limits. The solid line shows our ﬁt to the Hα luminosity evolution assuming an exponential decay, while the dashed and dotted lines show the expected evolution if the Hα luminosity followed the bolometric evolution from Holoien et al. (2014) and a power-law ﬁt to the UVW2 emission, respectively.

114 Fig. 4.4.— Non-host-subtracted Swift UVOT photometry of ASASSN-14ae. The open circles denote data previously published in Holoien et al. (2014); the ﬁlled circles show the data presented in this work. The solid curves show power-law ﬁts to the previously published data. The horizontal dashed lines show the host magnitudes measured from the late-time observations, and the vertical dashed line denotes the date of the ASAS-SN pre-discovery non-detection of ASASSN-14ae 24.0 days before discovery. The vertical marks along the x-axis show the dates of our spectroscopic observations.

115 Fig. 4.5.— Estimated limits on late-time Hα emission from optical TDE candidates. The late-time spectra of most of these objects are simply assumed to be host dominated and lack upper limit estimates. For these objects, we assume an upper limit of 2A˚ for the Hα emission, and compute the luminosity based on the approximate continuum and distances to the hosts available for each TDE. Even with the optimistic limits for the higher redshift TDEs, the proximity of ASASSN-14ae allows us to place an unprecedented limit on the late-time Hα emission. The dotted lines show lines of constant energy.

116 Table 4.1: Observations. P.A.b Par. P.A.c Fluxd Seeing Exposure r′e UT Date Daya [deg] [deg] Airmassc Standard [arcsec] [s] n [mag] × 2014Feb24.20 29.69 90.0 76 to 77 1.33–1.39 Feige34 1.1 300.0 3 16.78 0.03 − − × ± 2014Apr29.29 93.78 90.0 80to77 1.20–1.33 HZ44 1.1 1050.0 3 16.84 0.01 × ± 2014 Jun 06.18 131.67 90.0 82to78 1.18–1.30 GD153 0.75 1050.0 3 16.90 0.02 × ±

117 2014 Nov 22.49 300.98 105.0 73 to 83 1.15–1.60 Feige34 0.9 1200.0 6 16.94 0.02 − − × ± 2016 Feb 08.33 743.48 95.0 90 to 114 1.04–1.00 G191-B2B 1.1 600.0 3 16.94 0.02 − − × ± a Days since discovery (tdisc = 56682.51; Prieto et al. 2014). b Position angle of the spectrograph slit. c Par. P.A. and airmass give the range of parallactic angles and airmasses for each observation, respectively. d Standard stars were observed on the same night as science observations. e r′ magnitude is derived from the acquisition images. Table 4.2: Measurements of Hα Proﬁle Properties ∆va FWHMb Hα Flux Hα Equivalent Width Hα Luminosity UT Date 103 km s−1 103 km s−1 [10−14 ergs s−1 cm−2] [A]˚ [1040 ergs s−1] 2014Feb24.20 1.81 13.34 5.78 0.07 662.5 5.2 25.76 0.31 ± ± ±

118 2014Apr29.29 1.15 7.79 2.52 0.02 596.3 3.0 11.23 0.17 ± ± ± 2014Jun6.18 0.37 4.86 1.30 0.03 707.4 13.0 5.80 0.12 ± ± ± 2014 Nov 22.49 0.20 2.46 0.09 0.01 725.7 16.1 0.41 0.03 − ± ± ± 2016Feb08.33 ...... < 0.03 ... < 0.13 a Relative to systemic velocity of the host at z =0.0436. b Estimated from model ﬁt to Hα proﬁle. Chapter 5: The Late-time Evolution of the Tidal Disruption Event ASASSN-14li

5.1. Introduction

Near the centers of galaxies, stars can make close approaches to supermassive black holes (SMBHs). Roughly speaking, if the pericenter of a star’s orbit is outside the SMBH horizon but inside the Roche limit, the star will be disrupted. When a main sequence star is disrupted, approximately half of the stellar debris will remain on bound orbits and asymptotically return to pericenter at a rate proportional to t−5/3 (Rees 1988; Evans & Kochanek 1989; Phinney 1989). The observational consequences of these tidal disruption events (TDEs) are varied and depend on the physical properties of the disrupted star (e.g. MacLeod, Guillochon & Ramirez-Ruiz 2012; Kochanek 2016a), the post-disruption evolution of the accretion stream (e.g. Kochanek 1994; Strubbe & Quataert 2009; Guillochon & Ramirez-Ruiz 2013; Hayasaki, Stone & Loeb 2013, 2016; Piran et al. 2015; Shiokawa et al. 2015), and complex radiative transfer eﬀects (e.g. Gaskell & Rojas Lobos 2014; Strubbe & Murray 2015; Roth et al. 2016).

This chapter is adapted from “The Long Term Evolution of ASASSN-14li”, Brown et al.,

MNRAS, 466, 4904 (2017).

119 A large sample of well studied TDEs is crucial for understanding the observational characteristics and physical processes governing these exotic objects. While the number of well studied TDE candidates is growing (e.g. van Velzen et al. 2011; Cenko et al. 2012; Gezari et al. 2012; Arcavi et al. 2014; Chornock et al. 2014; Holoien et al. 2014; Gezari et al. 2015; Vink´oet al. 2015; Holoien et al. 2016a,b; Brown et al. 2016a), the diversity of the observational signatures is surprising given that observed TDEs should be heavily dominated by stars and SMHBs spanning a narrow parameter range (Kochanek 2016b). Perhaps most notably, the majority of optically discovered TDEs show little evidence of X-ray emission, while the energetics of other TDE candidates may be dominated by their X-ray emission (e.g. Grupe, Thomas & Leighly 1999; Komossa & Bade 1999; Komossa & Greiner 1999).

ASASSN-14li (Jose et al. 2014; Holoien et al. 2016b) was a nearby (d 90 ∼ Mpc, z =0.0206) TDE discovered by the All-Sky Automated Survey for SuperNovae (ASAS-SN; Shappee et al. 2014) on 2014-11-22.6 (MJD = 56983.6). An immediate follow-up campaign (Holoien et al. 2016b) observed ASASSN-14li for 200 days. We ∼ gathered data from a wide variety of both ground and space based observatories and found that the spectral characteristics of ASASSN-14li resembled the “intermediate H+He” TDEs from Arcavi et al. (2014), while the optical/NUV evolution was consistent with that of a blackbody and a roughly exponentially declining luminosity.

We also found signiﬁcant spectral evolution: at early times the He II λ4686 feature is dominant, while at later times it is merely comparable in strength to the Balmer lines. This is in contrast with ASASSN-14ae, in which the He II λ4686 line became stronger relative to the Balmer lines as the event progressed (Brown et al. 2016a). Unlike the two other ASASSN TDEs, ASASSN-14li showed strong X-ray emission, and, due to it’s proximity, was the target of several ground-based (Alexander et al. 2016; van Velzen et al. 2016; Romero-Ca˜nizales et al. 2016), space-based (Miller

120 et al. 2015; Cenko et al. 2016; Peng, Tang & Wang 2016; Jiang et al. 2016), and theoretical eﬀorts (Krolik et al. 2016; Kochanek 2016a).

In this paper we follow the evolution of ASASSN-14li to 600 days after ∼ discovery. We present improved ASAS-SN pre-discovery upper limits, late-time optical spectra taken with the Multi-Object Double Spectrograph 1 (MODS1) on the 8.4 m Large Binocular Telescope (LBT), and extensive UVOT and XRT observations from the Swift space telescope, which provide unprecedented insight into this rare class of objects. In Section 5.2 we describe our observations, in Section 5.3 we present our measurements of the late-time evolution, and ﬁnally in Section 5.4 we provide a summary of our results and discuss the implications for future studies.

5.2. Observations

In this section we summarize the optical, UV, and X-ray observations taken during our 600 day follow-up campaign of ASASSN-14li. ∼

5.2.1. Spectroscopic Observations

Follow-up spectroscopy of ASASSN-14li was obtained with MODS1 (Pogge et al. 2010) on the LBT between January 2015 and April 2016. The observations were performed in longslit mode with a 1′′.2 slit. MODS1 uses a dichroic that splits the light into separately optimized red and blue channels at 5650 A.˚ The blue CCD ∼ covers a wavelength range of 3200 – 5650 A,˚ with a spectral resolution of 2.4 A,˚ ∼ while the red CCD covers a wavelength range of 5650 – 10000 A,˚ with a spectral ∼ resolution of 3.4 A.˚

Our ﬁrst spectrum was taken on 2015-01-20 (t = 58.9 days after discovery; Jose et al. 2014), and consisted of three 600s exposures. The observations on 2015-02-16

121 (t = 85.8 days) consisted of four 900s exposures. The following three observations (t = 177.7, 381.9, and 442.8 days) consisted of three 1200s exposures. Our most recent, and deepest, observation (t = 498.6 days) consisted of six 1200s exposures. The position angle of the slit was chosen to match the parallactic angle at the midpoint of the observations in order to minimize slit losses due to diﬀerential atmospheric refraction (Filippenko 1982).

We obtained bias frames and Hg(Ar), Ne, Xe, and Kr calibration lamp images for wavelength calibration. If the arc lamp or flat field data were not available on the night of the observation, we used calibration data obtained within 1-2 days of our observations. This is standard practice with MODS given the stability of the instrument, and is sufficient to provide accurate calibrations. Night sky lines were used to correct for the small ( 1 A)˚ residual flexure. Standard stars were ∼ observed nightly with a 5 60′′ spectrophotometric slit mask and used to calibrate × the response curve. The standard stars are from the HST Primary Calibrator list, which is composed of well observed northern-hemisphere standards from the lists of Oke (1990) and Bohlin, Colina & Finley (1995). We list the information regarding our observational dates and configurations in Table 5.1.

The modsCCDRed 1 python package was used to bias subtract, ﬂat ﬁeld, and illumination correct the raw data frames. We removed cosmic rays with L.A.Cosmic (van Dokkum 2001). The sky subtraction and one-dimensional extraction were performed with the modsIDL pipeline2. We correct residual sky features with reduced spectra of standard stars observed on the same night under similar conditions using the iraf task telluric. Finally, we combined the individual exposures from

1http://www.astronomy.ohio-state.edu/MODS/Software/modsCCDRed/ 2http://www.astronomy.ohio-state.edu/MODS/Software/modsIDL/

122 each epoch, yielding a total of six high quality spectra (continuum S/N > 100) ∼ corresponding to the six observation epochs.

In order to facilitate comparison of spectra across multiple observing epochs, we flux-calibrated each spectra with the contemporaneous r′-band MODS acquisition images. Following Shappee et al. (2013) and Brown et al. (2016a), We performed aperture photometry on the ASASSN-14li host and bright stars in the field with the iraf package apphot. We determined the r′ magnitude scale factor for stars in the field and used this to both calibrate the broadband flux of ASASSN-14li in the acquisition image and the new spectra. The typical uncertainty in the aperture photometry is 0.01 magnitudes. The spectral evolution of ASASSN-14li ∼ is presented in Section 5.3.1.

5.2.2. Swift Observations

After the publication of Holoien et al. (2016b), we also obtained additional Swift observations of ASASSN-14li. The UVOT (Roming et al. 2005) observations were obtained in six ﬁlters: V (5468 A),˚ B (4392 A),˚ U (3465 A),˚ UVW 1 (2600 A),˚ UVM2 (2246 A),˚ and UVW 2 (1928 A).˚ We used the UVOT software task uvotsource to extract the source counts from a 5′′.0 radius region and a sky region with a radius of 40′′. The UVOT count rates were converted into magnitudes and ﬂuxes based ∼ on the most recent UVOT calibration (Poole et al. 2008; Breeveld et al. 2010). The uncorrected UVOT magnitudes are presented in Table 5.4.

123 observations following the Swift XRT data reduction guide3 and reprocessed the level one XRT data using the Swift xrtpipeline version 0.13.2 script, producing cleaned event ﬁles and exposure maps for each observation.

To extract the number of background subtracted source counts in the 0.3–10.0 keV energy band from each individual observation, we used a source region centered on the position of ASASSN-14li with a radius of 47′′ and a source free background region centered at (α,δ) = (12h48m39s, +17◦46′54′′) with a radius of 236′′. The count rates are presented in Table 5.4 and have not been corrected for Galactic absorption.

To increase the S/N of our observations, we also combined individual observations using XSELECT version 2.4c. We ﬁrst combined the observations into 8 time bins spanning our campaign. Additionally, in order to determine the evolution in the X-ray emission between early and late times, we combined the individual observations into early (ﬁrst 200 days) and late (remaining 360 days) ∼ time bins, yielding high S/N spectra we can compare directly.

For the merged observations we used the task xrtproducts version 0.4.2 to extract both source and background spectra using the same regions used to extract our count rates. The task xrtproducts task takes advantage of XSELECT ’s ability to extract spectra, while using the task xrtmkarf and the exposure maps produced during by the xrtpipeline to create ancillary response files (ARF) for each spectra. To produce the ARF for the merged event files, we first had to merge their individual exposure maps using XIMAGE version 4.5.1 before running xrtmkarf. The response matrix files (RMFs) are ready-made files which we were obtained from the most

3http://swift.gsfc.nasa.gov/analysis/xrt_swguide_v1_2.pdf

124 recent calibration database. None of our observations suﬀer from signiﬁcant pileup issues.

To analyse the spectral data, we used the X-ray spectral fitting package (XSPEC) version 12.9.0d and chi-squared statistics. Each individual spectrum was grouped with a minimum of 10 counts per energy bin using the FTOOLS command grppha, while the spectra obtained from the merged observations were grouped with a minimum of 20 counts per energy bin. The X-ray observations favor a thermal spectrum over the power-law model used in Holoien et al. (2016b). We fit the spectra from 0.3–1.0 keV using an absorbed blackbody spectrum emitted at the redshift of the TDE and integrate the flux in the observed frame 0.3–10.0 keV band. Due to the softness of the spectrum, the flux above 1 keV is < 1% of the total X-ray flux. ∼ We assumed the Wilms, Allen & McCray (2000) abundance model and initially let

NH , the temperature of the blackbody (kT) and its normalization be free. For a number of the individual observations, especially the later observations, the S/N is insuﬃcient to constrain N , and thus we ﬁx it to 1.64 1020 cm−2 which is the H × I Gal Galactic H column density (NH ) in the direction of ASASSN-14li (Kalberla et al. 2005).

5.2.3. ASAS-SN Pre-Discovery Upper Limits

To further constrain the early-time light curve of ASASSN-14li we re-evaluated the pre-discovery ASAS-SN non-detection discussed in Holoien et al. (2016b). The last ASAS-SN epoch before discovery was observed on 2014-07-13.25 under moderate conditions by the quadruple 14-cm “Brutus” telescope in Haleakala, Hawaii. This ASAS-SN ﬁeld was processed by the standard ASAS-SN pipeline (Shappee et al. in prep.) using the isis image subtraction package (Alard & Lupton 1998; Alard 2000), except we did not allow images with ﬂux from ASASSN-14li to be used in

125 the construction of the reference image. We then performed aperture photometry at the location of ASASSN-14li on the subtracted images using the iraf apphot package and calibrated the results using the AAVSO Photometric All-Sky Survey (APASS; Henden et al. 2016). There was no excess ﬂux detected at the location of ASASSN-14li over the reference image on 2014-07-13.25 (t = 132.35 days), and we − place a 3-sigma limit of V > 17.37 mag on ASASSN-14li at this epoch. Additionally, we stack the previous 4 epochs taken under favorable conditions (2014-06-18.30 through 2014-06-27.28 or t = 148.32 through 157.30 days) to place a deeper limit − − V > 19.00 mag during this time.

5.3. Evolution of the Late-Time Emission

In this section we discuss the optical, UV, and X-ray evolution of ASASSN-14li. We interpret our observations in the context of physically motivated models to gain insight into how the physical conditions evolve over time.

5.3.1. Evolution of the Optical Spectra

In Holoien et al. (2016b) we obtained spectra spanning 145 days between UT 2014 December 02 and 2015 April 14. The optical spectra of ASASSN-14li qualitatively resembled that of ASASSN-14ae and the “intermediate H+He events” from Arcavi et al. (2014). The spectroscopic evolution mirrored that of ASASS-14ae, in the sense that both showed a weakening blue continuum accompanied by weaker and narrower emission lines with time. However, the emission features of ASASSN-14li were not identical to those of ASASSN-14ae. Speciﬁcally, ASASSN-14li showed strong

He II λ4686 emission even at early epochs. The emission line proﬁles in ASASSN-14li were also narrower and evolved more slowly than in ASASSN-14ae. While part of

126 these differences may be attributed to differences in the ages of the TDEs, there are likely to be additional factors responsible for the observed differences between the two objects.

Figure 5.1 shows the evolution of the optical spectra beginning 60 days after ∼ discovery (pink) and ending 500 days after discovery (dark blue). The black ∼ spectrum shows the archival SDSS DR7 (Abazajian et al. 2009) spectrum of the host galaxy taken on 2008-02-15. The top panel shows the full optical spectrum, while the bottom panels show expanded, host-subtracted views of the He II λ4686 (left) and Hα (right) regions. Prominent spectral features are labeled, while the shaded bands denote regions prone to systematic errors related to telluric correction.

We focus on the evolution of the Hα profile, since it shows the clearest detection at late times and is less prone to systematic errors associated with flux calibration (since we scale the flux to match the r′-band photometry). In order to measure the Hα emission from the TDE, we must first subtract the underlying host galaxy. Previous late-time studies of TDEs simply obtained a late-time spectrum of the host after all signatures of the TDE had faded (e.g. Gezari et al. 2015; Brown et al. 2016a). However, in the case of ASASSN-14li, we still find evidence for residual emission from the TDE even after 500 days, so we must instead subtract the archival SDSS spectrum.

Our initial spectrum taken 60 days after discovery (pink) shows moderately broad (FWHM 2000 km s−1) He II λ4686, Hβ, and Hα emission lines superimposed ∼ on a blue continuum. The lines are slightly redshifted with respect to the host galaxy (∆v 100 km s−1). The relative weakness of the blue continuum in this ∼ spectrum appears to be due to slit losses caused by a combination of variable seeing and slit positioning. If this variability in the continuum were real then it would

127 be evident in the UVOT photometry (see Section 5.3.2), but we ﬁnd no evidence for such a correlation. The next spectrum, taken 85 days after discovery shows ∼ slightly weaker, but still prominent He II λ4686, Hβ, and Hα emission features. Our subsequent spectra taken at 180, 380, 440, and 500 days show a progression in ∼ the sense of weakening emission line strength with increased time after discovery. In general, the blue continuum associated with the TDE is weaker at later time. It is not clear if the late-time variability in the blue continuum (Figure 5.1, bottom left panel) is real, but it would be consistent with the apparent 0.1 mag variability ∼ seen in the UVOT photometry at later times (see Section 5.3.2).

While the He II λ4686 and Hβ detections are fairly marginal at later times, there is still an unambiguous detection of Hα 500 days after discovery. This suggests that while some TDEs are short lived (Vinkóet al. 2015; Holoien et al. 2016a; Brown et al. 2016a), others may persist long after the time of disruption, even at optical wavelengths. The residual emission lines are unlikely to be attributable to systematics associated with differences in the spatial sampling of the two instruments. The primary evidence for this is that the line profile is broad ( 1000 ∼ km s−1) and shows a redward offset relative to the location of Hα in the rest frame of the host galaxy, similar to previous epochs. As an additional check, we performed multiple slit extractions and found no evidence that the Hα emission is a host-subtraction artifact. Finally, the presence of residual Hα emission is fully consistent with our late-time UVOT photometry (see Section 5.3.2).

We do however measure a slight excess of [O III] λ5007 in our host subtracted spectra, suggesting that the late time MODS spectra include nebular emission not associated with the TDE. Similarly, we ﬁnd evidence for excess Hα emission corresponding to the narrow nebular Hα feature in the archival spectrum. This is not particularly surprising given the complex morphology of the nebular emission

128 in this galaxy (Prieto et al. 2016), and the diﬀerences in the spatial sampling of the MODS1 longslit and the SDSS ﬁber. We estimate the magnitude of this contamination by modeling the excess Hα emission with two components: a broad component corresponding to the emission associated with the TDE, and a narrow

( 100 km s−1) component scaled from the [O III] λ5007 residual feature. We find ∼ that even in the latest epoch when the Hα flux is weakest, the flux in the narrow component is < 20% that of the broad component, and thus does not substantially ∼ affect our results.

5.3.2. Evolution of the UVOT Photometry

In Figure 5.2 we show the photometric evolution of ASASSN-14li in the UVOT bands (left axis) as well as in the XRT 0.3–10.0 keV energy range (right axis). In Holoien et al. (2014) we presented the first 175 days; here we extend our ∼ observations to 600 days after discovery. The horizontal dashed lines show the ∼ UVOT host magnitudes synthesized from the SED fit to the GALEX (NUV), SDSS (u′, g′, r′, i′, and z′), and 2MASS (J, H, K) archival data, as well as the upper limit on the X-ray count rate estimated from the archival flux limit of 7.5 10−14 ergs s−1 × cm−2 (see Holoien et al. 2016b). The vertical marks along the time-axis show the dates corresponding to our spectroscopic observations. The extensive archival data (most importantly the GALEX NUV) allows us to constrain the host SED well. We estimate the accuracy of our synthetic host magnitudes with a bootstrapping scheme in which we perturb the input fluxes according to their 1-σ errors and fit the resulting SED. We perform 1000 realizations and find that the resulting magnitude estimates are accurate to within 0.1 mag. ∼

The most striking aspect of Figure 5.2 is that ASASSN-14li is still bright relative to the host galaxy in the UV and X-ray bands, even after 600 days. ∼ 129 The excess emission above that of the host decreases toward redder ﬁlters, and the photometry in the optical bands becomes consistent with the host 200 days after ∼ discovery.

In order to characterize the excess emission, we correct all fluxes for Galactic extinction assuming RV =3.1 and AV =0.07 (O’Donnell 1994; Schlafly & Finkbeiner 2011). We then subtract the host flux and model the SED of the flare as a blackbody using MCMC methods (Foreman-Mackey et al. 2013). We fit the W2, M2, W1, and U band fluxes, and exclude the B and V photometry due to the negligible excess flux in those bands. At later epochs, the excess flux in the U band also becomes relatively weak, but the measurements are consistent with the models given the observational uncertainties. Figure 5.3 shows example fits to the UV+U band photometry for the dates closest to our spectroscopic observations. The colors denote the observation epoch and correspond to those in Figure 5.1. The circles show the host subtracted fluxes in the W2, M2, W1, and U bands, and the triangles denote lower limits required to produce the observed Hα flux. While a marginal deviation from our model is expected due to instrumental effects (e.g., red leaks in the UVOT filters Brown et al. 2016b), we find that the observed UVOT fluxes are indeed well described by a blackbody. Such a model also produces enough ionizing flux to power the Hα emission at all epochs.

As we found in Holoien et al. (2016b), the UVOT photometry suggests ASASSN-14li evolves at a roughly constant temperature ( 3.5 104 K), while the ∼ × photospheric radius decreases by a factor of a few over the course of our observations. This inference is driven in part by the fact that we lack the wavelength coverage needed to place a strong constraint on the temperature. We estimate the bolometric luminosity by integrating the fits to the SED of the flare for each of our SWIFT epochs, and derive confidence intervals based on the values containing 68% of the

130 MCMC distribution for each epoch. We show the evolution of the bolometric luminosity as gray circles in Figure 5.4, along with the evolution of the 0.3–10.0 keV X-ray luminosity (cyan crosses), and a scaled version of the Hα luminosity (red squares).

Figures 5.4 shows that there is a marked change in the luminosity evolution of the flare 200 days after discovery. In Holoien et al. (2016b) we showed that ∼ the initial decline in luminosity is well described by an exponential decay with an e-folding time of 60 days (solid black line). However, after 200 days, the luminosity ∼ evolution becomes significantly shallower and only declines by a factor of a few over the next 400 days, causing the exponential to under-predict the luminosity at later times. The dashed black line shows a fit to the UV/optical data assuming L (t t )−5/3. We find a best-fit value for t = 29 days, which is consistent with ∝ − 0 0 − our ASAS-SN pre-discovery upper limits.

We perform a similar exercise for the Hα emission (red squares). The solid red line shows a scaled version the exponential fit from Holoien et al. (2016b), and the dashed line shows a power-law fit to the Hα luminosity. While an exponential can provide an adequate fit to the early-time data, it significantly under-predicts the luminosity at later times. Additionally, as we found in Brown et al. (2016a), the Hα luminosity decays on a longer timescale than the bolometric luminosity. The power-law fit to the Hα luminosity prefers a slightly larger value of t = 56 0 − days, which is consistent with our ASAS-SN pre-discovery upper limits. While a Γ = 5/3 power-law fit is an improvement over an exponential for the late-time − bolometric and Hα luminosity, ASASSN-14li remains significantly brighter than these power-law models predict. Furthermore, a wide variety of power-law models can provide adequate fits to the data, given our weak pre-discovery constraints.

131 Based on Eddington arguments and the assumption that the X-ray emitting material be located outside the innermost stable circular orbit, Miller et al. (2015)

6 inferred that M 2 10 M⊙. Well-established SMBH–host galaxy scaling BH ∼ × relations (e.g. Kormendy & Ho 2013; McConnell & Ma 2013) suggest that this may be an underestimate. Based on the host bulge mass Mendel et al. (2014), one would

6.7 infer M 10 M⊙. However, there is significant intrinsic scatter in these scaling BH ∼ relations (Gültekin et al. 2009). Given that the host galaxy may have recently undergone a merger, an episode of significant star formation, and may potentially host a binary SMBH system (Prieto et al. 2016; Romero-Cañizales et al. 2016), it is not inconceivable for the SMBH responsible for the TDE to be undermassive

6 relative to the stellar mass of the host galaxy. Interestingly, even for MBH = 10 M⊙, the luminosity of ASASSN-14li remains below Eddington throughout our observing campaign. With these considerations in mind, we adopt a ﬁducial mass for the

6 SMBH MBH = 10 M⊙.

Given that the luminosity decreases with time and the temperature is roughly constant (but only weakly constrained by the UVOT data), the radius must also decrease with time. Figure 5.5 shows the radial evolution of various emission

2 components relative to the gravitational radius, where rg = GMBH/c , and we have

6 adopted a fiducial mass MBH = 10 M⊙. Gray circles show the radii inferred from our blackbody fits to the host subtracted UVOT fluxes, the cyan crosses show the characteristic X-ray radius from our blackbody fits to the binned XRT spectra, and red squares show the radii inferred from the Hα line width. The dashed line shows the radial evolution of a parabolic orbit with closest approach equal to the tidal radius. Overall, the photospheric radius (gray circles) decreases, but only by a factor of 2, and less dramatically than the other ASASSN TDEs (Holoien et al. 2016a). ∼ The characteristic radius inferred from the UV/optical is on the order of 10 AU. ∼

132 This corresponds to several tens of tidal radii, but that depends directly on the assumed MBH.

We infer a characteristic radius of the line emitting gas (red squares) under the assumption that the width of the Hα feature reﬂects the characteristic velocity at a given radius, and that v c(2r /r)1/2. The Hα emission arises from much larger ≈ g radii than both the UV continuum and X-ray emission (cyan crosses). Additionally, the Hα emitting material appears to be expanding at a rate comparable to that of a parabolic orbit. Given a suﬃciently uniform and high cadence dataset, the radial distribution of the emission components could be testable by reverberation mapping to measure the correlations between variability in the X-rays, UVOT passbands, and optical emission lines. Unfortunately, our dataset does not meet the criteria necessary for such an analysis, but reverberation studies in TDEs have recently been attempted (e.g. Jiang et al. 2016; Kara et al. 2016).

5.3.3. Evolution of the X-ray Emission

Compared to other optically discovered TDEs (e.g. Gezari et al. 2012; Holoien et al. 2014; Arcavi et al. 2014; Holoien et al. 2016a), ASASSN-14li is X-ray bright. Over the first 200 days, the average background subtracted count rate was 0.25 s−1, ∼ ∼ similar to that derived by Holoien et al. (2016b). At later times, the count rate is a factor of 5 lower ( 0.05 s−1). However, even though the emission has decreased ∼ significantly by late times, Figure 5.2 shows that, even 600 days after discovery, the X-ray flux remains an order of magnitude above the ROSAT archival upper limit.

We show the X-ray luminosity evolution as cyan crosses in Figure 5.4. Due to the low S/N of the individual epochs, we divide our observations into 8 equally spaced time bins and combine the observations in each bin. While there is short

133 timescale variability, this produces 8 spectra for which we can obtain a robust blackbody fit. Overall, we find that the X-ray luminosity remains comparable to the UV/optical luminosity throughout the 600 day follow-up campaign. The X-ray luminosity at 150 days presented here is a factor two 2 lower than that ∼ ∼ originally found in Holoien et al. (2016b). This is mainly due to the fact that we model the data as an absorbed blackbody, which provides a significantly better fit to the observations than the power-law used in Holoien et al. (2016b).

In Figure 5.5 we also show the characteristic radius of the X-ray emission (cyan crosses) assuming blackbody emission and a spherical geometry. Viewed as a blackbody, the X-ray emitting surface is on the order of a few gravitational radii, and shows only moderate temporal evolution. We can characterize the overall evolution of the X-ray spectrum by dividing the observations into two sets representing early and late times. The early-time observations corresponds to the ﬁrst 200 days of ∼ X-rays observations that were analysed by Holoien et al. (2016b), while the late time observations correspond to the observations over the remaining 360 days. The ∼ merged early and late time observations have a total exposure times of 131 and 63 ks, respectively.

In Figure 5.6 we show the merged X-ray spectrum obtained for both the early (black) and late (red) time emission. We ﬁnd that the best ﬁt blackbody model has a temperature of kT =0.068 0.001 keV and kT =0.056 0.002 keV, and a early ± late ± column density of N early = (4.5 0.05) 1020 cm−2 and N late = (2.1 0.1) 1020 H ± × H ± × cm−2 respectively. The total column densities along the line of sight are a factor of

Gal 2–3 larger than NH (Kalberla et al. 2005), and comparable to the values from Miller 2 et al. (2015). However, the reduced chi-squared χr values for these fits are relatively large ( 3 and 1.7, respectively), suggesting that there are higher order effects ∼ ∼ not captured by our simple absorbed blackbody model. We also fit the early-time

134 X-ray spectra with two Gaussians superimposed on a blackbody. We find that this significantly improves our fits to the observations. The energies of the Gaussian emission features are centered on 0.376 and 0.406 keV, which are near strong C and N lines at 0.3675 and 0.4307 keV, respectively. If that is indeed the origin of these ∼ features, it would be consistent with the presence of strong, highly ionized C and N emission lines in the UV (Cenko et al. 2016). Interestingly, Miller et al. (2015) also suggest several highly ionized emission features are present in their high resolution spectra, particularly near the O K-edge.

Irrespective of the origin of the emission features, the X-ray emission from ASASSN-14li is reasonably well described by a blackbody. The temperature of the X-ray emission shows only a moderate decrease with time, from 8 105 K down ∼ × to 4.5 105 K. We also ﬁnd that between the early and late-time observations, the × mean column density decreases by a factor of 2, becoming comparable to N Gal ∼ H at later times. This could indicate that at early times the material surrounding the TDE was dense, not highly ionized, and obscured the lower energy X-rays, while at late times the material surrounding the event has been nearly completely ionized and thus transparent to the lower energy X-ray photons. We note that the amount of material required to produce this absorbing column is small relative to the overall mass budget, even in the contrived scenario where all of the absorbing material is

2 spherically distributed at the Hα emitting radius: M 0.01fr N M⊙, where abs ∼ 17 20 f is the covering fraction, r17 is the characteristic radius of the absorbing material

17 20 −2 in units of 10 cm, and N20 is the hydrogen column density in units of 10 cm . Furthermore, our modeling suggests there may be a factor of a few variability in the column density between the individual epochs. Unfortunately the spectra for the individual epochs do not reach the S/N required for a precise determination of the column density. We also note similar variability and overall decrease in the

135 absorbing column in the 8 temporally binned spectra. The moderately decreasing temperature and variability in the column density are similar to the ﬁndings from Miller et al. (2015), but we have increased the temporal baseline by a factor of 3. ∼

Finally, we note that the SWIFT XRT detector lacks the energy coverage to discriminate between a bremsstrahlung and blackbody spectrum. While we have assumed the X-ray emission to be well described as a blackbody, there is only marginal evidence that the X-ray spectrum turns over at lower energies. It is plausible that the X-ray emission arises from tidal debris shocking the ambient medium in the vicinity of the SMBH. For ionized gas in the strong shock limit, the temperature is roughly T 1.4 107v2 K, where v is the shock velocity ∼ × 3 3 relative to 103 km s−1 (Draine 2011). The characteristic shock velocities needed to produce the observed X-ray temperature are at most a few hundreds of km s−1. The bremsstrahlung emissivity is roughly ǫ 1.7 10−18T 1/2n2 ergs s−1 cm−3, ff ∼ × 6 3 6 where T6 is the temperature relative to 10 K and n3 is the density relative to 103 cm−3 (Rybicki & Lightman 1979). If the X-rays were to originate only from bremsstrahlung emission, it would require an emitting volume with a characteristic − − radius of r 1020T 1/6n 2/3 cm. Thus the X-ray emission most likely originates s ∼ 6 3 from a blackbody-like source powered by accretion onto the SMBH, rather than shocks in the ambient medium.

5.4. Conclusions

We have presented late-time optical follow-up spectra taken with LBT/MODS1, extensive UVOT and XRT observations from Swift, and improved ASAS-SN pre-discovery non-detections of the nearby TDE ASASSN-14li. Our observations span from the epoch of detection to 600 days after discovery. In contrast to the late ∼ time evolution of ASASSN-14ae (Brown et al. 2016a), observations of ASASSN-14li

136 show that TDEs can remain luminous, particularly in the UV and X-ray, for many hundreds of days. We find that the energy radiated in the X-rays is comparable to that of the UV/optical. Integrating over the duration of our campaign, we find that the total radiated energy is E 7 1050 ergs. The entire event can be powered by ≈ × −3 −1 the accretion of a small faction of the overall mass budget (∆M 4 10 η M⊙), ∼ × 0.1 where η0.1 is the radiative efficiency relative to 0.1.

While the late-time emission is broadly consistent with the accretion of material onto an SMBH, ASASSN-14li diﬀers from typical AGN. For example, as we have observed in other TDEs (Holoien et al. 2014, 2016b,a and Brown et al. 2016a), the optical emission lines narrow as the luminosity decreases, which is the reverse of the behavior observed in AGN (McGill et al. 2008; Denney et al. 2009).

In Figure 5.7 we show our late time measurements of the Hα luminosity from ASASSN-14li. Unlike ASASSN-14ae, the Hα luminosity in ASASSN-14li remains signiﬁcant for at least 500 days after disruption. We emphasize that the late-time brightness of ASASSN-14li is not simply due to its proximity; it is indeed more luminous at later times than other TDE candidates. Similarly, the evolution of the Hα line width in ASASSN-14li spans a much smaller dynamic range than that of ASASSN-14ae. While the evolution of the Hα line width and luminosity likely encodes information about the evolution of the tidal debris, a larger sample of objects with follow-up spectra is required in order to draw any ﬁrm conclusions.

The modest decrease in the X-ray temperature is one of the strongest observational constraints to come out of this work. Most TDE theory predicts that the observed spectrum will become harder at later times (e.g. Lodato & Rossi 2011; Strubbe & Quataert 2011; Metzger & Stone 2016), but these claims are typically made in the context of a super-Eddington outﬂow that obscures the

137 6 X-rays at early times. For the assumed black hole mass of 10 M⊙, the X-ray (and optical/UV) luminosity remains below the Eddington limit even at early times, immediately bringing into question the applicability of these theoretical predictions to ASASSN-14li. Given the variable nature of the X-ray spectra from one epoch to the next as well as the early-time results from Miller et al. (2015), it is likely that the column density and ionization state of the absorbing material along the line of sight are variable, further complicating the evolution of the observed spectrum. This is supported by the fact that X-ray emission comparable to the optical/UV emission is not ubiquitous among optically selected TDE candidates (e.g. Holoien et al. 2014; Arcavi et al. 2014; Holoien et al. 2016a; Brown et al. 2016a). Thus, it is not particularly surprising that theoretical predictions fail to match the observations in this instance. We remain agnostic with regard to the adoption of any speciﬁc model characterizing the luminosity evolution. While the rate of material returning to pericenter is frequently invoked to explain the luminosity evolution of TDEs, given the complexity of the physical processes involved (Kochanek 1994; Guillochon & Ramirez-Ruiz 2013; Guillochon, Manukian & Ramirez-Ruiz 2014; Metzger & Stone 2016; Krolik et al. 2016), it is likely that the rate of material returning to pericenter has limited bearing on the overall luminosity evolution.

The extended lifetime of ASASSN-14li has important implications for future TDE studies. Our results demonstrate that, even after 500 days, spectra of TDE host galaxies may be contaminated by residual emission from the ﬂare, particularly near strong recombination lines. While this complicates the characterization of TDE host galaxies, it extends the baseline over which residual TDE emission can potentially be discovered in spectroscopic surveys like MaNGA (Bundy et al. 2015). Unfortunately, even under the assumption that TDE rates are sharply peaked in E+A galaxies (French, Arcavi & Zabludoﬀ 2016b), the chances of trivially discovering residual

138 TDE emission in a MaNGA-like survey may be hampered by the rarity of these galaxies (see the discussion in Brown et al. 2016a).

Alternatively, the Hα emission in TDEs is driven by the ionizing UV continuum, and the strong residual UV emission results in unusually blue UV optical colors. In − order to assess the peculiarity of the late time colors, we examine the UV optical − colors of a sample of E+A galaxies selected from the SDSS. The original selection criteria is described in Goto (2004, 2007). In short, the selection criteria require that EW(Hδ) > 5.0A,˚ EW([O II]) > 2.5A,˚ EW(Hα)> 3.0A,˚ and S/N(r) > 10. − − We adopt an updated catalog4 based on the SDSS Data Release 7 (Abazajian et al. 2009), yielding an initial sample of 837 E+A galaxies. We then select a subsample of E+A galaxies that also have a GALEX NUV detection within 5′′.0 of the SDSS position, yielding 683 galaxies with both SDSS optical and GALEX NUV observations. In the absence of late-time GALEX observations of ASASSN-14li, we estimate the late-time GALEX NUV magnitude based on the late-time SED and ﬁnd that NUV W 2 0.14. We ﬁnd that, relative to other E+A galaxies, the ≈ − late-time NUV optical colors of ASASSN-14li are indeed substantially bluer than − the majority of E+A galaxies.

Given the peculiarity of the ASASSN-14li late-time colors, we also attempt to identify galaxies with similarly peculiar NUV optical colors. We model each E+A − galaxy with the public SED fitting code FAST (Kriek et al. 2009) based on the SDSS u,g,r,i, and z photometry. We then estimate synthetic GALEX NUV magnitudes from the best fit SED for each galaxy, and compute the difference between the observed GALEX NUV magnitudes and the synthetic NUV magnitudes based on the optical SED. The distribution of the observed and synthetic magnitude difference

4 http://www.phys.nthu.edu.tw/~tomo/cv/index.html

139 is shown as the histogram in Figure 5.8. The vertical red line shows the late-time NUV excess for ASASSN-14li, which we know is due to residual TDE emission. We note that the early-time NUV excess for ASASSN-14li (as well as ASASSN-14ae and ASASSN-15oi) is several magnitudes bluer, well outside the range shown here.

We can estimate the upper limit of the TDE rate in E+A galaxies by examining the UV excess observed in our sample and making a few basic assumptions. The first assumption we make is that UV excesses larger than that of ASASSN-14li are due to residual emission from a TDE. We also assume that the residual emission is strictly blueward of the optical bandpasses and does not affect the SED modeling of the host galaxy, which is justifiable given the short duration of excess optical TDE continuum emission seen in ASASSN-14li and other TDEs (e.g. Holoien et al. 2014, 2016a). Additionally, our modeling of the SED is clearly imperfect, as there are a number of galaxies that appear significantly dimmer in the UV than the optical colors would suggest. Thus some of the apparent UV excesses are likely due to systematic errors in the modeling. We estimate the magnitude of this contamination by counting the number of galaxies with UV deficits that are greater in magnitude (relative to 0) than the UV excess of ASASSN-14li, and subtract this number (9) from the population of galaxies with UV excesses greater than that of ASASSN-14li (41). This leaves 32 out 683 E+A galaxies showing excess UV emission characteristic of residual TDE emission. If we make the additional assumption that the residual UV emission remains for, on average 2 years, this yields an upper limit on the rate of 2 10−2 yr−1 per galaxy, which is approximately an order of magnitude larger ∼ × than the rate estimate from French, Arcavi & Zabludoff (2016b). Alternatively, if no instances of UV excess are associated with residual TDE emission, then the upper limit on the TDE rate in E+A galaxies becomes 7 10−4. We note that this is ∼ × simply an illustrative exercise and is subject to many systematic effects, including

140 the true late-time ﬂux of ASASSN-14li in the GALEX NUV band, the robustness of the SED modeling, potential source confusion in the NUV, and contamination by other sources of UV excess (O’Connell 1999; Brown 2004). A similar exercise with a large sample of early type galaxies yields an even broader distribution in NUV NUV , suggesting that the E+A galaxies with blue excess may indeed obs− synth be due to modeling systematics. Nonetheless, the substantial UV excess in some of the galaxies may be due to residual emission from a TDE. Identiﬁcation of residual TDE emission in spectroscopic surveys like MaNGA is reliant upon archival spectra of the host, whereas the approach illustrated here has yielded a relatively small sample of galaxies well suited for targeted follow-up observations without the need for archival spectroscopy. Spectroscopic signatures that are sensitive to TDE emission on a longer temporal baseline (e.g. coronal line emission Komossa et al. 2008; Wang et al. 2011; Yang et al. 2013) could prove useful in determining if the UV excess in these galaxies is due to residual TDE emission and, ultimately, improving our understanding of TDE host galaxies.

141 Fig. 5.1.— Rest frame ﬂux-calibrated spectra of ASASSN-14li. Color denotes days since discovery. The top panel shows the full optical spectrum, while the bottom panels show host-subtracted regions in the immediate vicinity of He II λ4686 (left) and Hα (right). The shaded regions show the location of telluric features where systematic errors may be signiﬁcant. The spectra show clear temporal evolution in the sense of decreasing continuum and emission line features with increasing time. Even the latest spectra show excess broad emission relative to the host spectrum.

142 Fig. 5.2.— Evolution of ASASSN-14li in the SWIFT UVOT bands from discovery to 600 days after discovery. Circles show the observed non-host-subtracted ∼ magnitudes. All UV and optical magnitudes are shown in the Vega system (left scale), and X-ray count rates are shown as counts s−1 in the 0.3–10.0 keV energy range (right scale). Horizontal dashed lines correspond to the brightness of the host. Vertical marks along the time-axis show the dates of our spectroscopic observations.

143 Fig. 5.3.— Example blackbody fits to the host-subtracted W2, M2, W1, and U band fluxes. The UVOT epochs were selected to match the dates of our spectroscopic observations; each epoch is assigned a color corresponding to the spectra in Figure 5.1. The solid lines show blackbody fits to the host-subtracted fluxes. The triangles show the lower limits required to produce the observed Hα emission.

144 Fig. 5.4.— Luminosity evolution of ASASSN-14li. Gray circles show the bolometric luminosity inferred from our blackbody fits to the host subtracted UVOT fluxes, cyan crosses show the X-ray luminosity in the 0.3–10.0 keV band, and red squares show the measured Hα luminosity scaled upward by a factor of 100 for visibility. The solid black line shows the exponential fit from Holoien et al. (2016b), and the solid red line shows the same fit renormalized to the earliest Hα observation. The black and red dashed lines show power-law fits (Γ = 5/3) to the UV/optical and Hα luminosity, − respectively.

145 Fig. 5.5.— Radius evolution of ASASSN-14li. Gray circles show the radii inferred from our blackbody fits to the host subtracted UVOT fluxes, the cyan crosses show the characteristic X-ray radius from our blackbody fits to the binned XRT spectra, and red squares show the radii inferred from the Hα line width. All quantities are 6 shown relative to the gravitational radius of the SMBH assuming MBH = 10 M⊙. The dashed line shows the evolution of a parabolic orbit with a closest approach equal to the tidal radius.

146 Fig. 5.6.— Merged X-ray spectra of ASASSN-14li seen at early times (first 200 days, black crosses) and later times (after 200 days, red crosses). Each spectrum is binned with a minimum of 20 counts per energy bin. The early-time spectrum is best fit with with two Gaussian emission features superimposed on a blackbody (black solid line), while the late-time spectrum is consistent with a purely blackbody model (red solid line). The residuals from the fits are shown in the bottom panel.

147 Fig. 5.7.— Measurements and limits on late-time Hα emission from optical TDE candidates. The late-time spectra of most of these objects are simply assumed to be host dominated and lack formal upper limit estimates. For these objects, we assume an upper limit of 2A˚ for the Hα equivalent width, and compute the luminosity based on the approximate continuum and distances to the hosts available for each TDE. The dotted lines show lines of constant emitted energy.

148 Fig. 5.8.— Histogram showing the diﬀerence between observed GALEX NUV magnitudes and the expected NUV magnitudes based on models of the optical SED for a sample of E+A galaxies from the SDSS. The vertical dashed line shows the diﬀerence between the ASASSN-14li late-time NUV and the archival GALEX NUV magnitudes of the host. We estimate the late-time NUV magnitude based on the SWIFT UVW2 observations.

149 Table 5.1: LBT/MODS1 observations. Pos.Angle Flux Seeing Exposure r′ UTDate Day [deg] Airmass Standard [arcsec] [s] N [mag] × 2015 Jan 20.53 58.9 62.0 1.04–1.05 Feige34 1.2 600.0 3 15.48 0.01 − × ± 150 2015 Feb 16.36 85.7 55.0 1.06–1.13 Feige34 1.4 900.0 4 15.48 0.01 − × ± 2015 May 19.30 177.7 125.0 1.22–1.38 BD+33d2642 1.3 1200.0 3 15.53 0.01 − × ± 2015Dec09.50 381.9 119.0 1.30–1.51 Feige67 0.8 1200.0 3 15.53 0.01 × ± 2016Feb08.37 442.8 105.0 1.11–1.20 G191-B2B 1.0 1200.0 3 15.53 0.01 × ± 2016Apr04.17 498.6 125.0 1.09–1.41 Feige67 1.0 1200.0 6 15.53 0.01 × ± The Day column is in days since discovery (tdisc = 56983.6). Table 5.2: Measurements of Hα Properties ∆v FWHM Hα Flux Hα Luminosity UT Date [103 km s−1] [103 km s−1] [10−14 ergs s−1 cm−2] [1040 ergs s−1]

151 2015 Jan 20.53 0.10 1.82 3.533 0.008 3.447 0.008 − ± ± 2015 Feb 16.40 0.11 1.68 2.499 0.007 2.438 0.007 − ± ± 2015 May 19.31 0.25 1.42 0.901 0.004 0.879 0.004 − ± ± 2015 Dec 09.51 0.25 1.32 0.530 0.005 0.518 0.005 − ± ± 2016 Feb 08.40 0.22 1.27 0.420 0.005 0.410 0.005 − ± ± 2016 Apr 04.25 0.24 1.08 0.371 0.005 0.362 0.005 − ± ± Table 5.3: ASASSN-14li X-ray Properties

Mean kT Radius Luminosity

MJD [keV] [1013 cm] [1042 ergs s−1]

57024.81 0.070 0.001 0.49 0.04 24.49 0.29 ± ± ± 57089.83 0.064 0.002 0.41 0.10 14.93 0.39 ± ± ± 57136.02 0.064 0.001 0.37 0.03 7.46 0.12 ± ± ± 57187.54 0.058 0.003 0.41 0.21 6.00 0.17 ± ± ± 57236.79 0.056 0.005 0.45 0.23 4.31 0.15 ± ± ± 57364.53 0.050 0.004 0.67 0.32 3.65 0.11 ± ± ± 57425.53 0.049 0.003 0.56 0.15 2.56 0.17 ± ± ± 57538.48 0.043 0.003 0.65 0.22 1.18 0.13 ± ± ±

152 Table 5.4: Swift Observations. MJD XRT counts s−1 W2 M2 W1 U B V 56991 0.316 0.011 14.15 0.04 14.39 0.03 14.66 0.05 15.14 0.04 15.97 0.04 15.55 0.06 ± ± ± ± ± ± ± 56994 0.408 0.013 14.59 0.04 14.84 0.03 14.91 0.05 15.26 0.04 16.03 0.04 15.65 0.06 ± ± ± ± ± ± ±

153 56995 0.318 0.011 14.20 0.03 14.47 0.03 14.75 0.04 15.22 0.04 15.93 0.04 15.56 0.05 ± ± ± ± ± ± ± Table published in its entirety in Brown et al. (2017). Magnitudes and uncertainties are presented in the Vega system. X-ray count rates anduncertainties are given in units of counts per second in the energy range 0.3 10 keV. Uncertainties are given next to − each measurement. Data are not corrected for Galactic absorption. Chapter 6: The Ultraviolet Evolution of the Tidal Disruption Event iPTF16fnl

6.1. Introduction

TDEs are a highly inhomogenous class of objects. The optical spectra and X-ray properties in particular are highly diversified (e.g Gezari et al. 2012; Holoien et al. 2014; Arcavi et al. 2014; Vinkóet al. 2015; Holoien et al. 2016b,a; Auchettl, Guillochon & Ramirez-Ruiz 2016). Furthermore, the evolutionary timescales, peak luminosities, and spectral energy distributions of optical TDEs vary considerably from one TDE to the next (e.g., Gezari et al. 2015; Brown et al. 2016a, 2017; Holoien et al. 2016a). Despite their non-uniform characteristics, all optically discovered TDEs are associated with a hot (tens of thousands of Kelvin) and luminous (L > 1040 ∼ ergs s−1) flare from an otherwise non-active galactic nuclei. While TDEs are now most frequently discovered in optical transient surveys, energetically speaking, they are predominantly ultraviolet (UV) phenomena. While many TDEs have been monitored with broadband UV filters, UV spectra can reveal much more about the kinematics and ionization structure of the debris. Cenko et al. (2016) obtained HST/STIS spectra of what was, at the time, the closest TDE ever discovered

This chapter is adapted from “The Ultraviolet Spectroscopic Evolution of the Low-Luminosity

Tidal Disruption Event iPTF16fnl”, Brown et al., MNRAS, 473, 1130 (2018).

154 (ASASSN-14li; Holoien et al. 2016b). Their observations revealed the presence of highly ionized, broad C, N, and Si emission, in addition to ionized H and He that had been previously observed in the optical. The lack of Mg II emission, a feature universally seen in AGN/quasar spectra, was also particularly interesting.

The transient iPTF16fnl was discovered on 2016-08-26 and was promptly classiﬁed as a TDE on 2016-08-31 (Gezari et al. 2016). The position of the transient (J2000 RA/Dec = 00:29:57.04 +32:53:37.5) is consistent with the center of the galaxy Mrk 0950 at a redshift of z =0.0163, corresponding to a luminosity distance

−1 −1 of d = 67.8 Mpc (H0 = 73 km s Mpc , ΩM = 0.27, ΩΛ = 0.73). In the discovery paper, Blagorodnova et al. (2017) analyzed the photometric evolution and optical spectroscopy and demonstrated that iPTF16fnl is indeed a rapidly evolving, low luminosity TDE. Our analysis was carried out independently, and is broadly consistent with the results of that paper, though there are some important diﬀerences. After Gezari et al. (2016) classiﬁed the transient as a TDE, we inspected the reported location in ASAS-SN data and found a transient near our sensitivity limit. Since the transient exceeded our triggering criteria, was very nearby, and was apparently brightening, we triggered our HST ToO program and obtained 3 HST/STIS UV spectra of the TDE over the course of the following six weeks. We also obtained Swift observations, ground-based photometric monitoring, and optical spectra probing the early and late phases of the event.

In this paper, we present the results of this observing campaign. In Section 6.2 we present UV spectra taken with HST/STIS alongside broadband X-ray, UV, and optical photometry. In Section 6.3 we use our observational data to model the physical nature of the transient, and also place a stringent upper limit on the X-ray emission from the TDE. In Section 6.4 we and summarize our results and discuss the most important implications of our ﬁndings.

155 6.2. Observations

Once the transient iPTF16fnl was classiﬁed as a TDE, we initiated a follow-up campaign in order to study in detail the nearest TDE yet discovered. In this Section we summarize the observational data used in our analysis.

6.2.1. Archival Host Data

In order to constrain the properties of the host galaxy, we performed a search of archival databases for observations of Mrk 0950. We retrieved archival ugriz images of Mrk 0950 from the Twelfth Data Release of the Sloan Digital Sky Survey (SDSS;

Alam et al. 2015). We also retrieved near-IR JHKs Two-Micron All Sky Survey (2MASS; Skrutskie et al. 2006) images of the host, as well as UV imaging from the Galaxy Evolution Explorer (GALEX ;Martin et al. 2005). The AllWISE color of W 1 W 2=0.01 0.05 (Cutri & et al. 2014) indicates that Mrk 0950 lacks a strong − ± AGN component (Stern et al. 2012; Assef et al. 2013). We examine images from the ROSAT All-Sky Survey (RASS; Voges et al. 1999) and derive an upper limit on the count rate in the 0.3–10 keV band of < 1.9 10−2 counts s−1. This corresponds to a × −13 −1 −2 41 −1 limit on the unabsorbed ﬂux of 2 10 ergs s cm (LX < 1.1 10 ergs s ), ∼ × ∼ × which provides further evidence that Mrk 0950 lacks a strong AGN. We performed aperture photometry on the GALEX, SDSS, and 2MASS images and measured the ﬂux enclosed in a 5′′.0 aperture. We present the host magnitudes derived from the archival data in Table 6.1.

There are no archival Spitzer, Herschel, HST, Chandra, or X-ray Multi-Mirror Mission (XMM-Newton) observations of Mrk 0950, and there are no radio sources listed at this position in the FIRST (Becker, White & Helfand 1995) or NVSS (Condon et al. 1998) catalogs.

156 We modeled the host galaxy SED with the Fitting and Assessment of Synthetic Templates (FAST; Kriek et al. 2009), using the ﬂuxes derived from the GALEX, SDSS, and 2MASS archival images. We assumed a Cardelli, Clayton & Mathis

(1989) extinction law with RV = 3.1 and Galactic extinction of AV = 0.22 (Schlaﬂy & Finkbeiner 2011), an exponentially declining star-formation history, a Salpeter IMF, and the Bruzual & Charlot (2003) stellar population models. We

2 obtained a reasonable ﬁt (χν = 0.98) which yielded the following parameters: +0.61 9 +0.33 M∗ = (2.34 ) 10 M⊙, age= 1.29 Gyr, and a 1-σ upper limit on the star −0.05 × −0.03 −1 formation rate of SFR< 0.007 M⊙ yr . In Table 6.2 we show the magnitudes inferred from the ﬁt to the archival data.

There are no black hole mass measurements for this galaxy in the literature. In order to obtain an estimate of the black hole mass, we adopt an upper limit on the bulge mass using the stellar mass derived from the photometry in the central 5′′ of the galaxy. This a reasonable approximation given the properties of the light proﬁle measured from the SDSS imaging (i.e. half light radius 3′′.5). We then adopt the ∼ Mbulge–MBH scaling relation from McConnell & Ma (2013) and estimate the mass of

6 the black hole to be MBH < 5.5 10 M⊙. Thus the black hole is not so massive that ∼ × a main sequence star would simply be absorbed by the SMBH before being tidally disrupted. Given the lack of archival spectra, we will address the spectroscopic nature of the host in Section 6.3.

6.2.2. ASAS-SN Detection

After the discovery of the transient was announced (Gezari et al. 2016), we examined the location of the object in ASAS-SN data. The last ASAS-SN epoch before discovery was observed on UT 2016-08-26.51 under moderate conditions by the quadruple 14-cm “Brutus” telescope in Haleakala, Hawaii. This ASAS-SN ﬁeld was

157 processed by the standard ASAS-SN pipeline (Shappee et al. 2014) using the isis image subtraction package (Alard & Lupton 1998; Alard 2000), except we took extra care to exclude images with ﬂux from iPTF16fnl from the construction of the reference image. We performed aperture photometry at the location of iPTF16fnl on the subtracted images using the iraf apphot package and calibrated the results using the AAVSO Photometric All-Sky Survey (APASS; Henden et al. 2016). We have detections of the transient on UT 2016-08-26.51 (V = 17.96 0.24), and on ± UT 2016-08-30.52 (V = 17.49 0.18). We do not detect the object in images taken ± before UT 2016-08-26.51, but our limits preceeding the discovery of the transient are relatively shallow (V > 17), so this is not to say the transient is not present at ∼ earlier epochs.

6.2.3. HST/STIS ToO Observations

We observed iPTF16fnl using STIS and the FUV/NUV MAMA detectors. We used the 52′′.0 0′′.2 slit and the G140L (1425A,˚ FUV-MAMA) and G230L (2736A,˚ × NUV-MAMA) gratings. The visits were obtained over 1, 2 and 4 orbits, respectively, as the target faded. The integration times were 792 seconds (FUV and NUV) in four equal exposures (each setting) for the ﬁrst visit, 1854 (FUV) and 2466 (NUV) seconds in six exposures for the second visit, and 4785 (FUV) and 5500 (NUV) seconds in ten roughly equal exposures for the third visit. A cosmic ray CR-SPLIT image pair was obtained at each dither position and the telescope was dithered along the slit by 16 pixels. Since the trace of iPTF16fnl was clearly present in the two-dimensional frames and spatially unresolved, we use the one-dimentional spectra output by the HST pipeline. For each epoch, we perform inverse-variance-weighted combinations of the one-dimensional spectra and merge the FUV and NUV channels.

158 We correct for Galactic reddening assuming AV = 0.22 and RV = 3.1 (O’Donnell 1994; Schlaﬂy & Finkbeiner 2011). The merged spectra are shown in Figure 6.1.

6.2.4. Swift Observations

We also obtained Swift observations of iPTF16fnl. The UVOT (Roming et al. 2005) observations were obtained in six ﬁlters: V (5468 A),˚ B (4392 A),˚ U (3465 A),˚ UVW 1 (2600 A),˚ UVM2 (2246 A),˚ and UVW 2 (1928 A).˚ We used the UVOT software task uvotsource to extract the source counts from a 5′′.0 radius region and a sky region with a radius of 40′′. The UVOT count rates were converted ∼ into magnitudes and ﬂuxes based on the most recent UVOT calibration (Poole et al. 2008; Breeveld et al. 2010). The observed UVOT magnitudes are shown in Figure 6.5 and are tabulated in Table 6.3. In Table 6.4 we present the host subtracted and Galactic reddening corrected UVOT magnitudes.

We simultaneously obtained Swift X-ray Telescope (XRT; Burrows et al. 2005) observations of the source. The XRT was run in photon-counting (PC) mode (Hill et al. 2004) which is the standard imaging mode of the XRT. We reduced all observations following the Swift XRT data reduction guide1 and reprocessed the level one XRT data using the Swift xrtpipeline version 0.13.2 script, producing cleaned event ﬁles and exposure maps for each observation.

To extract the number of background subtracted source counts in the 0.3–10.0 keV energy band from each individual observation, we used a source region centered on the position of iPTF16fnl with a radius of 50′′ and a source free background region centered at (α,δ) = (00h29m25.5s, +32◦51′15.6′′) with a

1http://swift.gsfc.nasa.gov/analysis/xrt_swguide_v1_2.pdf

159 radius of 200′′. We correct for Galactic absorption assuming a column density of 5.6 1020 cm−2 (Kalberla et al. 2005). ×

6.2.5. Ground-Based Monitoring

In addition to space-based observations, we also obtained ground based photometric and spectroscopic monitoring of iPTF16fnl for approximately 4 months following discovery. The photometric monitoring consisted of BgV ri imaging, which we obtained from several telescopes including 1-m telescopes on the Las Cumbres Observatory telescope network Brown et al. (2013), the 20-in DEMONEXT telescope (Villanueva et al. 2016), and the 24-in telescope at Post Observatory. We measured aperture photometry with the same 5′′.0 aperture radius used for both the Swift and archival host photometry. Photometric zero-points were determined using nearby stars with SDSS and/or APASS magnitudes.

We also obtained several early (t < 14 days) optical spectra of iPTF16fnl, ∼ as well as late-time spectra taken after the transient had faded considerably. The early time spectra were obtained with the FAST Spectrograph (FAST; Fabricant et al. 1998) on the Fred L. Whipple Observatory Tillinghast 1.5-m telescope, the Wide Field Reimaging CCD Camera (WFCCD) mounted on the Las Campanas Observatory du Pont 2.5-m telescope, and the Goodman Spectrograph on the Southern Astrophysical Research (SOAR) 4.1-m telescope. The late-time spectra were obtained with the Multi-Object Double Spectrographs (MODS; Pogge et al. 2010) mounted on the dual 8.4-m Large Binocular Telescope (LBT) on Mt. Graham. The MODS data were reduced with a combination of the modsccdred2 python package and the modsidl pipeline3. The other spectroscopic data were reduced using

2http://www.astronomy.ohio-state.edu/MODS/Software/modsCCDRed/ 3http://www.astronomy.ohio-state.edu/MODS/Software/modsIDL/

160 standard techniques in iraf. While there are slight diﬀerence in the wavelength coverage and resolution of the spectrographs, the spectra cover the majority of the optical bandpass ( 3000A˚ to > 7000A)˚ and have a resolution of 5A.˚ Finally, ∼ ∼ ∼ in order to facilitate comparison of spectra across multiple observing epochs and instruments, we ﬂux-calibrated each spectra with contemporaneous r-band imaging.

6.3. Analysis

In this section we present the evolution of iPTF16fnl from 1200A˚ up to 8000A.˚ ∼ ∼ This is the ﬁrst time the temporal evolution of a TDE has been spectroscopically observed in the the UV, and provides key constraints for theories attempting to explain the observed properties of TDEs.

6.3.1. Spectroscopic Analysis

The spectroscopic evolution of iPTF16fnl in the UV is shown in Figure 6.1. Each spectrum is shown in a color corresponding to the observation date. The squares show the contemporaneous Swift observations, which, for purposes of comparison, we have used to set the overall normalization of the HST/STIS spectra. The gray line shows the best fit SED based on the archival host data, while the dashed curves show our blackbody fits to the host-subtracted UVOT fluxes (see Section 6.3.2). Prominent atomic transitions are labeled, and the portion of the spectrum affected by geocoronal airglow is marked with the telluric symbol.

We emphasize that the HST/STIS and Swift observations sample diﬀerent regions of the galaxy and thus have diﬀerent levels of host contamination. The spectrum is dominated by the blue emission of the TDE at the very center of the galaxy, while the modeling of the host is based on the central 5′′ of the galaxy. Thus

161 a direct comparison between the two is not possible since the contribution of the host in the HST spectra is not precisely known. However, a relative comparison between the observed Swift fluxes, the archival host SED, and our blackbody fits is fair and demostrates the relative contribution of the host and TDE to the observed broadband flux at each epoch.

Our first spectrum of iPTF16fnl bears a strong resemblance to that of ASASSN-14li from Cenko et al. (2016). Both objects are well approximated by a combination of blackbody continuum emission with a temperature of a few 104 K, coupled with broad emission and narrow absorption associated with highly ionized atomic transitions. Our blackbody fits agree well with the shape of the UV spectra, and the best agreement is seen at earlier times when the flux from the TDE dominates the observed UV emission and the contribution from the underlying host is negligible. At later times, as the transient fades, the observed (host+TDE) spectrum begins to diverge from our blackbody fits because the host contribution (which we subtract before modeling the excess emission) becomes more significant.

The line proﬁles are complex; absorption and emission features of multiple lines are blended together and also frequently coincide with Galactic absorption features. In the earlier spectra, the emission features are systematically redshifted relative to the line center. For instance, the peak of the N V feature is redshifted by

2000 2500 km s−1, as is that of C IV. Some lower ionization features (e.g. N III]) ∼ − show no apparent redshift at all. The He II profile is particularly interesting. While the emission peaks near the transition wavelength at 1640A,˚ there is a significant component of the line profile that extends to redder wavelengths. This suggests that the distribution of the highly ionized metals may differ from that of the gas producing the bulk of the lower ionization features. However, given the complex nature of the line blending, it is difficult to differentiate between this scenario and

162 one in which the high ionization lines are systematically broader and/or happen to coincide with more absorption features at shorter wavelengths. In fact, the Si IV and C IV show clear blueshifted absorption troughs (∆v FWHM 6000 km s−1) ∼ ∼ that may signify an outflow, and also likely contribute to the apparent redshift of the emission line profiles. Additionally, there is a non-negligible amount of Galactic extinction along the line of sight (AV = 0.22), and nearly all identified line profiles in Figures 6.1 and 6.3 have relatively strong Galactic absorption features located blueward of the transition wavelength in the rest frame of the TDE, as was also observed by Cenko et al. (2016) for ASASSN-14li.

The shapes of the line proﬁles vary with time. This includes the apparent width of the lines, as well as their peak wavelengths. The systematic redshift observed in N V, Si IV, and C IV at early times is less dramatic in the last HST/STIS spectrum, and the broad absorption features are also less apparent at late times.

There is an apparent decrease in flux in the region between Lyα and N V λ1240A.˚ While this region is affected by geocoronal afterglow, the latest spectrum shows a substantial drop in flux in this region relative to the previous two. We also note the sudden appearance of the N IV] λ1486A˚ line, which was relatively weak in the initial

HST/STIS spectrum but quite prominent in the last spectrum. Similarly, the He II line becomes much stronger at later times relative to the apparent continuum, and by 50 days the proﬁle is strongly peaked at the transition wavelength. The evolution ∼ of the spectra can be explained in large part by the narrowing of the emission lines as the ﬂare fades. This is opposite the behavior seen in actively accreting SMBHs (McGill et al. 2008; Denney et al. 2009), but appears to be typical of TDEs (e.g., Holoien et al. 2014, 2016b,a; Brown et al. 2016a, 2017). The increasing equivalent width of the He II feature indicates that it is not fading as fast as the other lines.

163 This may also suggest that the bulk of the He II emission is produced by gas that evolves on a longer timescale than the gas producing the highly ionized metal lines.

In Figure 6.2 we show zoomed in views of the most prominent line features, this time plotted in velocity space. The vertical dashed lines show the location of transitions in the rest frame of the host galaxy. The vertical gray bands show regions aﬀected by other line features. In order to facilitate comparison across multiple epochs, we have normalized the spectra relative to the largely featureless continuum in the 2400A˚ – 2600A˚ region and smoothed the spectra with a 3 pixel boxcar. The narrow absorption features (Lyα,N V, Si IV, and C IV) show no clear wavelength evolution. In contrast, the broad absorption features (e.g., blueward of

Si IV and C IV) appear to evolve toward smaller velocities, which could indicate that the material responsible for the narrow absorption features is located at larger distances and varies on longer timescales than the material responsible for the broad features. We note that the narrow absorption features could be associated with the bound stellar debris. In the case of ASASSN-14li, Cenko et al. (2016) argued that the narrow absorption features in the UV spectra are most likely associated with the low velocity outﬂow inferred from the X-ray spectra (Miller et al. 2015). Contemporaneous X-ray and UV spectroscopy of a bright TDE will be invaluable for characterizing the nature and temporal evolution of the absorbing material.

Figure 6.3 shows the blue portion of the iPTF16fnl HST/STIS spectrum compared to that of ASASSN-14li (black) from Cenko et al. (2016). The spectra have been scaled by a constant factor for ease of comparison. The phase of the ASASSN-14li spectrum most closely matches that of our last HST spectrum, though the phases of the two are not necessarily comparable given the uncertainty on the rise times. The spectra are shown in the rest frame of the respective TDEs. Due to the diﬀerent redshifts of the two objects, Galactic absorption features in the

164 ASASSN-14li spectrum are located at systematically shorter wavelengths than their counterparts in the iPTF16fnl spectrum. This includes the geocoronal afterglow which strongly affects the Lyα portion of the iPTF16fnl spectrum, but has a subtler effect on the ASASSN-14li spectrum. Nonetheless, both spectra show the same set of prominent emission features. The line profiles of ASASSN-14li most closely resemble those in the latest iPTF16fnl spectrum, which is not necessarily surprising given the timing of the observations. Specifically, both the ASASSN-14li spectrum and our latest spectrum of iPTF16fnl show little evidence of the strongly redshifted emission profiles that are so apparent in the early time iPTF16fnl spectrum.

Interestingly, neither ASASSN-14li nor iPTF16fnl show the Mg II emission typically associated with accreting SMBHs. The Mg II emission comes from the relatively large partially ionized regions in AGN (e.g. Peterson 1993; Richards et al.

2002). The absence of Mg II emission in TDEs could be a symptom of the shape of the radiation ﬁeld, or it could indicate that the nebula is matter bounded and the

Mg is predominantly in higher ionization states. The ionization energy of Mg II is low enough (Eion = 15.03 eV) for this to be plausible. Like Mg II, He I emission is typically quite strong in the spectrum of quasars, but is relatively weak in the spectra of TDEs. In the SDSS quasar composite spectrum from Vanden Berk et al. (2001), the He I λ5877A˚ ﬂux is a factor of a few larger than the He II λ4686A˚ ﬂux. However,

ASASSN-14li and iPTF16fnl show evidence for only weak He I emission, which has a slightly higher ionization energy than Mg II (Eion = 24.59 eV). We also note that there is no C III] emission in any of the TDE spectra. This line is generally used to constrain the density of the broad line region in AGN to n < 109 cm−3 (Ferland et al. ∼ 1992; Peterson 1997), since at higher densities the line is suppressed by collisional deexcitation. The absence of this feature from the TDE spectra may be due to the

165 high density of the emitting material, which would have direct implications for the modeling of TDEs.

Despite these diﬀerences between the QSO and TDE spectra, the N-rich QSO spectrum from Batra & Baldwin (2014) bears some striking similarities to the UV spectra of TDEs. While this has been previously noted for the UV spectrum of ASASSN-14li (Kochanek 2016a; Cenko et al. 2016), the strong N features are also present in the spectra of iPTF16fnl. The prevalence of the N lines in the spectra of TDEs further suggests a link between the population of N-rich QSOs and TDEs (Kochanek 2016a).

The optical spectra of iPTF16fnl taken at t = 9, 10, 13, 65, and 81 days are shown in Figure 6.4. The spectra are qualitatively similar to observations of other TDEs (e.g. Arcavi et al. 2014; Holoien et al. 2014; Brown et al. 2016a), which show a strong blue continuum and broad emission features associated with H and He recombination. Blagorodnova et al. (2017) also present optical spectra of iPTF16fnl that show these same features typically associated with TDEs. The emission line proﬁles in iPTF16fnl are relatively broad, the host galaxy is bright, and the TDE itself is faint, causing the optical lines to appear relatively weak. In the spectrum taken at t = 13 days the He II λ4686A˚ feature is quite prominent. This change may in part be due to a narrowing of the line proﬁle, but it is most easily explained by varying levels of host contamination between the observations and across multiple instruments.

While it is challenging to cleanly separate the TDE emission features in our optical spectra, the He II feature is broad and has a slight blueward asymmetry. This is most evident in the spectrum taken 13 days after discovery, and is also ∼ quite evident in several spectra from Blagorodnova et al. (2017). They were able to

166 measure the shape of the He II profile and found it to be slightly blueshifted, and also more broad (> 104 km s−1) than the Hα profile. ∼ Other TDEs have shown He II profiles with blueward asymmetries. The most striking example of this is seen in the spectra of ASASSN-14li (Holoien et al. 2016b).

The spectra have two strongly peaked line proﬁles near He II, at approximately 4686A˚ and 4640A.˚ In fact, in the earliest spectra of ASASSN-14li, the feature at 4640A˚ is signiﬁcantly stronger than the the feature at 4686A.˚ After 60 days, ∼ ∼ ∼ the anomalous blue feature fades rapidly, and the component at 4686A˚ remains the stronger of the two for several hundred days (Brown et al. 2017). Similarly, the

H-poor TDE PS1-10jh (Gezari et al. 2012, 2015) also had a He IIHeii proﬁle with a signiﬁcant blue wing. There is some evidence for this second emission feature in iPTF16fnl as well as in other TDEs (e.g. ASASSN-14ae, PTF09ge), but its presence is more ambiguous than in ASASSN-14li.

The origin of these peculiarities in the shape of the He II profile is not immediately clear. The most straightforward interpretation is that both features arise from He II, with one component blueshifted by > 3000 km s−1 relative to a ∼ component centered on the wavelength of the transition at 4686A.˚ The structure of the stellar debris in TDEs is not well understood, and the kinematics inferred from the line profiles could be useful for constraining the distribution of of the emitting material. For instance, Arcavi et al. (2014) was able to fit the asymetric double peaked Hα profile of the TDE PTF09djl using a Keplerian disk model from Strateva et al. (2003). However, it is unlikely that such a model can explain the peculiarity of the He II profile, because the emission lines in general do not show similar structure.

Given the new information aﬀorded by the HST/STIS UV spectra, it seems plausible that the anomolous feature blueward of He II 4686A˚ may in fact be due

167 to highly ionized metal lines associated with C III,N III, and possibly N V as well.

Gezari et al. (2015) suggested that the blue wing in the He II proﬁle of PS1-10jh could be due to blue shifted C III/N III Wolf-Rayet blends (Niemela, Ruiz & Phillips

1985; Massey & Johnson 1998; Leonard et al. 2000). These lines (including N V) are also prominent in the spectra of the ﬂash ionized material surrounding core collapse supernovae (Shivvers et al. 2015; Gal-Yam et al. 2014; Khazov et al. 2016; Yaron et al. 2017). The complexity of the He II proﬁles of most optically discovered TDEs suggests that these C III and N III features are actually quite common, and could exacerbate the apparent He/H ratios observed in many TDEs. These features may serve as useful probes of the UV emission when space-based UV observations are not possible, but rapid spectroscopic follow-up of TDEs in both the UV and optical is needed to precisely characterize if and how they relate to the emission features in the UV.

It is now clear that TDEs frequently have emission features associated with highly ionized metals. In AGN, the highly ionized lines (e.g. C IV) typically have blueshifted line profiles (e.g. Vanden Berk et al. 2001; Richards et al. 2002), and this is clearly seen in the composite quasar spectrum in Figure 6.3. The apparent blue shift is thought to arise from a relative absence of red flux due to the geometry of AGN and resulting opacity effects. This systematic blueshift is not observed in iPTF16fnl; the highly ionized metal lines are redshifted relative to the systemic velocity. In fact, the emission line profiles in TDEs show a variety of velocity offsets that evolve on a relatively short timescale (e.g. Brown et al. 2016a, 2017). Additionally, ASASSN-15oi appeared to show varying Doppler shifts between different ionic species (Holoien et al. 2016a). Thus the varying Doppler shifts of the lines are likely to be partially associated with the geometry of the event and the resulting kinematics of the emitting material, rather than being driven only

168 by opacity eﬀects. Such rapid kinematic evolution is not surprising. For example,

15 6 material at r = 10 r15 cm from a SMBH with mass MBH = 10 MBH6 M⊙ has − a characteristic velocity of v = (GM/r)1/2 3000M 1/2 r 1/2 km s−1, and the ∼ BH6 15 timescale for gravitational accelerations to signiﬁcantly change the velocity is of − order t 33r3/2M 1/2 days. ∼ 15 BH6

When the late-time MODS spectra were taken the TDE had largly vanished in the optical, and the resulting spectra show no clear signs of TDE emission. The spectra closely resemble that of a post-starburst galaxy (e.g., Dressler & Gunn 1983; Zabludoff et al. 1996). The Hδ absorption is quite strong (EW 5A),˚ and there Hδ ∼− are no signatures of significant ongoing star formation. This is fully consistent with the SED modeling, and places this galaxy firmly in the E+A classification. Thus, iPTF16fnl serves as an additional piece of evidence that TDEs are preferentially found in post-starburst galaxies (French, Arcavi & Zabludoff 2016b,a).

The spatial resolution of our optical spectra is limited to 1′′.2 due to a ∼ combination modest observing conditions and slit widths. However, the configuration of the most recent LBT/MODS observation on 2016-11-18 allowed us to align the slit with the major axis of the host galaxy and perform multiple extractions along the slit out to 6′′ (corresponding to a physical scale of 2 kpc). In the spectra ± ∼ extracted near the galaxy center (Figure 6.4), there is relatively weak [O III] λ5007A˚ emission line. The strength of this nebular feature relative to the stellar continuum increases with distance from the center of the galaxy. Beyond 2 kpc, the S/N ∼ of both the stellar continuum and nebular emission decrease rapidly. While the stellar absorption features show clear velocity structure due to the rotation of the disk, there is very little evidence of any kinematic signature in the emission profiles associated with the nebular gas. The LBT/MODS spectrum from 2016-11-02, despite being misaligned with the major axis of the galaxy by 45 degrees, also shows ∼ 169 spatially extended nebular emission. While the S/N is relatively low, it appears that the nebular emission probed by this slit orientation does in fact show kinematic structure. It is not unprecedented for the kinematic signatures of the gas to differ from that of a galaxy’s stellar population (e.g. Sarzi et al. 2006; Davis et al. 2011; Jin et al. 2016). Similarly, Prieto et al. (2016) showed the host of ASASSN-14li to have spatially extended, filamentary nebular emission well outside the optical extent of the galaxy. In the case of ASASSN-14li, the origin and structure of the nebular gas is most likely related to a merger event (Prieto et al. 2016; Romero-Cañizales et al. 2016), which may explain why TDEs are preferentially found in post-starburst galaxies (French, Arcavi & Zabludoff 2016b,a). Future integral field observations of TDE hosts are necessary to characterize the prevalence of disturbed nebular gas around these unusual galaxies.

6.3.2. Photometric Analysis

With a combination of Swift and ground-based telescopes, we monitored iPTF16fnl continuously for the 120 days following discovery in the near-UV through optical ∼ bandpasses. In Figure 6.5 we show the photometric evolution of iPTF16fnl in the UVOT bands as well as the ground-based observations from Post Observatory. The horizontal dashed lines show the UVOT host magnitudes synthesized from the SED

′ ′ ′ ′ ′ fit to the GALEX (NUV), SDSS (u , g , r , i , and z ), and 2MASS (J, H, Ks) archival data. The vertical marks along the time-axis show the dates corresponding to our spectroscopic observations. The extensive archival data (in particular the GALEX observations) allows us to constrain the host SED quite well. We estimate the accuracy of our synthetic host magnitudes with a bootstrapping scheme in which we perturb the input fluxes by their 1-σ errors and fit the resulting SED. We perform 1000 realizations and find that the resulting magnitude estimates are accurate to

170 within 0.1 mag, which is much smaller than the UV excess in the bluest UVOT ∼ bands at later times. The ﬂux in excess of that the host galaxy decreases as one moves toward redder ﬁlters, and the photometry in the optical bands is consistent with the host magnitudes only 20 days after discovery. ∼

In order to characterize the excess emission, we correct all fluxes for Galactic extinction assuming RV =3.1 and AV =0.22 (O’Donnell 1994; Schlafly & Finkbeiner 2011). We then subtract the host flux and model the SED of the flare as a blackbody using MCMC methods (Foreman-Mackey et al. 2013). We fit the W2, M2, W1, and U band fluxes, and exclude the B and V photometry due to the negligible contribution of the TDE in those bands. In the later epochs, we only use the W2, M2, and W1 measurements if excess flux in the U band is not significantly detected.

In Figure 6.6 we show the temperature evolution of iPTF16fnl inferred from the UV/optical photometry (black circles) relative to ASASSN-14ae, ASASSN-14li, and ASASSN-15oi (open blue circles, filled red squares, and open green squares, respectively). There is marginal evidence for temperature modulation during the first 30 days, but in general the UV/optical continuum is 3 4 104 K throughout ∼ − × our follow-up campaign. This inference is driven in part by the fact that we lack the wavelength coverage needed to place a strong constraint on the temperature, and so we impose a prior on our fits of log(T/K)=4.5 0.1. The temperature ± evolution is most similar to that of ASASSN-14li, which remained roughly constant, whereas ASASSN-15oi showed signs of increasing temperature in the weeks following discovery. While the temperature could in principle be higher than our inferred value, the measurements are largely inconsistent with a lower value.

Figure 6.7 shows the radial evolution of iPTF16fnl relative to ASAS-SN TDEs. The dashed line shows the radial evolution of a parabolic orbit with closest approach

171 2 equal to the tidal radius, where rg = GMBH/c , and we have adopted a ﬁducial mass

7 MBH = 10 M⊙. Overall, the evolution of the photospheric radius in iPTF16fnl is not unlike that of ASASSN-14ae and ASASSN-15oi. The characteristic emitting radius of these three objects decreases by a factor of 5 10 within the ﬁrst 100 ∼ − ∼ days, whereas the radius of ASASSN-14li, which remained luminous for much longer than the other ASAS-SN TDEs, decreases only by a factor of 2. The absolute ∼ size of the apparent photospheric radius in iPTF16fnl is in stark contrast with the more luminous ASAS-SN TDEs. The radius peaks at only a few thousand R⊙ and rapidly declines after 10 days. While we have used the term “radius” here, it is ∼ unlikely the TDE debris is actually spherically distributed. In any case, it is clear that the emitting surface of iPTF16fnl is smaller and decreases more rapidly than other optically discovered TDEs.

We estimate the bolometric luminosity by integrating the fits to the SED of the flare for each of our Swift epochs, and derive confidence intervals based on the values containing 68% of the MCMC distribution for each epoch. We show the evolution of the bolometric luminosity as black circles in Figure 6.8. At the earliest phases, iPTF16fnl is a factor of few fainter than the ASAS-SN TDEs and decreases in luminosity by a factor of 20 30 over the course of the following weeks. ∼ − Approximately 50 days after discovery, the decline rate slows, and the emission fades by an additional factor of 2 between 50 and 100 days after discovery. The ∼ combination of a low peak luminosity and rapid decline results in iPTF16fnl being a factor of 10 less luminous than the ASAS-SN TDEs after 100 days. ∼

We do not detect X-ray emission in any epoch, and the proximity of iPTF16fnl allows us to place relatively strong constraints on the X-ray emission. In order to derive upper limits on the X-ray ﬂux, we adopt a characteristic X-ray temperature of 5 105 K, as we found for ASASSN-14li (Brown et al. 2017). We correct for × 172 Galactic absorption assuming a column density of 5.6 1020 cm−2 (Kalberla et al. × 2005). The downward arrows in Figure 6.8 denote the upper limits on the X-ray emission from iPTF16fnl. We perform a similar exercise assuming a Γ = 2 power-law spectrum rather than a blackbody. This provides upper limits which are a factor of 2 smaller. Given the lack of constraints on the true X-ray spectrum, we adopt ∼ the relatively conservative limits derived assuming a blackbody emission spectrum, which are still a factor of 5 more stringent than those obtained for ASASSN-14ae ∼ and ASASSN-15oi. At early times, our limits require that the X-ray luminosity be < 1% of the UV/optical luminosity. This is in stark contrast with ASASSN-14li, in which the X-ray luminosity remained comparable to the UV/optical luminosity for several hundred days (Holoien et al. 2016b; van Velzen et al. 2016; Brown et al. 2017).

In Figure 6.9 we show the SED of iPTF16fnl at the same three epochs shown in Figure 6.1, and the color scheme is the same as that used in earlier plots to denote the observation dates. The colored squares show the host-subtracted Swift fluxes corrected for Galactic extinction, and the solid lines show our blackbody fits to data. The dashed lines show similar blackbody models but with the temperature fixed at T = 2 104 K and an increased normalization. In general, the Swift fluxes are × better described with a relatively hot blackbody rather than the cooler models.

Figure 6.9 also shows constraints on the luminosity at short wavelengths derived from the X-ray limits and the He II optical line flux. In order to improve the constraints on the X-ray flux beyond the single epoch limits shown in Figure 6.8, we stack the individual exposures. We obtain a flux limit of 1.1 10−13 ergs s−1 cm2 ∼ × 7 corresponding to a luminosity of L 1.3 10 L⊙, which we show as the downward ∼ × pointing triangle. Following Holoien et al. (2014) we use the flux of the He II λ4686A˚ line to infer a lower limit on the He II ionizing luminosity, which we show in

173 Figure 6.9 as the upward pointing triangle. However, this assumes that the material is optically thin to the He II emission, and that the He II emission arises from a balance of photoionization and recombination. Roth et al. (2016) argue that for reasonable physical conditions, the optical depth of the TDE debris in the Hα line can be be signiﬁcant. Furthermore, given the presence of the collisionally excited resonance lines in the UV, collisional ionization of H may be signiﬁcant. Thus these assumptions are unlikely to be true for H, but should be more appropriate for He II.

The He II line flux is highly uncertain, but we can still infer an approximate lower limit. Over the course of the observations we measure a He II flux corresponding to a luminosity > 1040 ergs s−1 in the early epochs and < 1039 ergs s−1 in the later epochs. ∼ ∼ We adopt a conservative lower limit of 1039 ergs s−1 for the He II λ4686A˚ luminosity, and note that decreasing the lower limit by an additional order of magnitude would have no impact on our conclusions. The limits on the X-ray luminosity are quite strong and rule out the presence of a soft (T 5 105 K) X-ray source down to ∼ × 7 10 L⊙. On the other hand, the He II λ4686A˚ flux requires a non-negligible amout ∼ of flux near 200A.˚ Our 3 104 K blackbody models produce enough ionizing flux ∼ × to power the He II line, while the cooler blackbody models (dashed lines) do not produce enough ionizing flux on their own. However, the X-ray limits are not so stringent as to rule out the presence of a soft X-ray component with enough ionizing

ﬂux to power the He II λ4686A˚ line. In fact, the optical line ﬂuxes of other TDEs appear to require an additional source of ionization beyond a simple UV/optical blackbody (Holoien et al. 2014; Roth et al. 2016; Holoien et al. 2016a).

There is some tension between the results presented here and those presented in Blagorodnova et al. (2017). First, we systematically favor a higher blackbody temperature (> 3 104 K instead of 2 104 K). This appears to be driven by the ∼ × × assumption in Blagorodnova et al. (2017) that the late time ﬂux is dominated by

174 the host galaxy. We find that there is still a significant contribtion to the UV flux from the TDE at late times, as shown in Figure 6.5. This is corroborated by the fact that the late-time Swift M2 flux is 0.5 mag brighter than the comparable ∼ archival GALEX NUV flux. Overestimating the UV flux of the host will naturally drive the temperature estimate downward. We also adopt a slightly higher Galactic extinction (AV = 0.22 instead of AV = 0.19), but this is a secondary effect. The second difference is that Blagorodnova et al. (2017) claim an X-ray detection. In our analysis, the Swift counts associated with the source are consistent with a background fluctuation, assuming Poisson statistics. Given the low X-ray flux of the detection reported by Blagorodnova et al. (2017), this has no practical impact on our conclusion that the X-rays are not an energetically important component of the observed fluxes.

6.4. Conclusions

We presented for the first time the UV spectroscopic evolution of a TDE using data from HST/STIS. We have shown that the shape and velocity offset of the broad UV emission and absorption features evolve with time. While the UV spectra closely resemble that of ASASSN-14li (Cenko et al. 2016), there is little qualitative resemblance to the UV spectra of typical quasars. However, there are some similarities between the of the UV spectra of iPTF16fnl, ASASSN-14li, and N-rich quasars (Batra & Baldwin 2014), which further suggests that there may be a link between N-rich quasars and TDEs (Kochanek 2016a). While the UV line profiles are significantly blended, future higher signal-to-noise observations of brighter TDEs will permit a more quantitative assessment of the line evolution.

The optical spectra of iPTF16fnl resemble those of several other optically discovered TDEs. Given the emission features in the UV, it seems likely that the

175 anomolous emission features just blueward of He II λ4686A˚ that have been observed in many TDEs are in fact due to N III and C III Wolf-Rayet blends. These features may contaminate He II λ4686A,˚ which would make them partly responsible for the large He/H ratios inferred in some TDEs. However, they could also serve as indirect probes of the UV emission when space based observations are not possible. Prompt, high signal-to-noise UV and optical spectra of TDEs are needed before a robust connection between the two can be established.

We monitored the TDE for over 100 days using the Swift space telescope and used the XRT and UVOT observations to characterize the broadband SED of the TDE. We showed that the characteristic temperature of the UV/optical emission was > 3 104 K and remained relatively constant over the course of our 100 day ∼ × observing campaign. Interestingly, the TDE remained dim and faded rapidly relative to other optically discovered TDEs. This is presumably due to an unusually small emitting surface compared to other TDEs. Integrating the UV/optical luminosity over the course of our observing campaign, the total energy radiated by iPTF16fnl is 5 1049 ergs, which is approximately an order of magnitude less than the ASAS-SN ∼ × TDEs found to date. This corresponds to a small fraction of a solar mass of accreted

−4 −1 matter: ∆M 3 10 η M⊙, where η is the radiative eﬃciency relative to 0.1. ∼ × 0.1 0.1 Despite the low luminosity of the TDE, we obtain strong limits on the X-ray emission and constrain the 0.3–10 keV X-ray luminosity to be < 1% that of the UV/optical ∼ luminosity. The disparate X-ray properties of iPTF16fnl and ASASSN-14li are somewhat surprising given the similarities in their UV spectroscopic properties.

Given the low luminosity of iPTF16fnl it is likely that there are many TDEs of similar (or lesser) luminosity that are simply undetected by current transient surveys. Kochanek (2016b) argue that if the luminosity function of TDEs scales roughly with the black hole mass function then there should be a large number of

176 relatively low luminosity TDEs around relatively low mass SMBHs that are generally missed by current transient surveys. Given the proximity and low luminosity of iPTF16fnl, it appears that this may indeed be the case. As the current generation of transient surveys matures and the detection eﬃciencies are better characterized, it should be possible to constrain the approximate luminosity function of TDEs and improve the estimate of the volumetric rate. Accurately characterizing the properties of low luminosity events like iPTF16fnl are a key aspect of determinining the volume corrected statistical properties of TDEs.

177 Fig. 6.1.— The UV evolution of iPTF16fnl as revealed by HST/STIS spectra and Swift photometry. The spectra have been smoothed with a 5 pixel boxcar and scaled by a constant factor to best match the Swift photometry for ease of comparison. The dashed lines show our blackbody ﬁts to the host subtracted Swift ﬂuxes. Prominent atomic transitions are marked with vertical dotted lines. The thin gray line shows our estimate of the UV spectrum of the host based on the SED model.

178 Fig. 6.2.— Evolution of the strongest line profiles in the HST/STIS spectra of iPTF16fnl. The spectra have been normalized to the continuum in the 2400A˚ – 2600A˚ region and smoothed with a 3 pixel boxcar. The color scheme is the same as that in Figure 6.1. Each panel is centered on a particular feature, and the vertical dashed lines mark the location of the respective features in the rest frame of the host galaxy. The vertical gray bands correspond to wavelengths affected by other identified transitions.

179 Fig. 6.3.— Comparison of the HST/STIS spectral evolution of iPTF16fnl (colored lines) with the HST/STIS spectrum of ASASSN-14li from Cenko et al. (2016) (black), a nitrogen rich quasar (Batra & Baldwin 2014), and the composite quasar spectrum of Vanden Berk et al. (2001). Spectra have been oﬀset by a constant factor for clarity. Prominent features associated with atomic transitions are labeled. Each spectrum is shown in the rest frame of the respective object. The Galactic absorption features appearing in both iPTF16fnl and ASASSN-14li spectra appear at bluer wavelengths in the spectrum of ASASSN-14li due to the diﬀerent redshifts of the objects.

180 Fig. 6.4.— Optical spectral evolution of iPTF16fnl. Color denotes days since discovery. Prominent atomic transitions are labeled, and the shaded regions show the location of telluric features where systematic errors may be signiﬁcant. The strength of the blue continuum and emission line features decrease with time. The latest spectrum taken with MODS/LBT closely resembles that of a post-starburst galaxy; there is little evidence for residual TDE emission.

181 Fig. 6.5.— Photometric evolution of iPTF16fnl from discovery to 130 days after discovery. Circles show the observed non-host-subtracted magnitudes.∼ All UV and optical magnitudes are shown in the Vega system. Horizontal dashed lines show the host magnitudes synthesized from the best fit SED. Like other TDEs, iPTF16fnl remains bright in the UV for significantly longer than in the optical bands, with the bluest bands showing the largest residual flux.

182 7 iPTF16fnl ASASSN-14li ASASSN-14ae ASASSN-15oi 6

K 4 4

/ 10 3 BB T

0 0 20 40 60 80 100

MJD - MJD0

Fig. 6.6.— Temperature evolution of iPTF16fnl. Black circles show the temperature of the UV/optical continuum of iPTF16fnl inferred from our blackbody fits to the host subtracted UVOT fluxes. The open blue circles, filled red squares, and open green squares show the temperature evolution of ASASSN-14ae, ASASSN-14li, and ASASSN-15oi, respectively.

183 5.5 iPTF16fnl ASASSN-14li ASASSN-14ae ASASSN-15oi 5.0 1/2 r /r) v ≈c(2 g r(t) for 4.5 ) ⊙ / R

phot 4.0 (R 10

log 3.5

3.0

2.5 0 20 40 60 80 100

MJD - MJD0

Fig. 6.7.— Radius evolution of iPTF16fnl. Black circles show the bolometric luminosity of iPTF16fnl inferred from our blackbody fits to the host subtracted UVOT fluxes; the open blue circles, filled red squares, and open green squares show the radius evolution of ASASSN-14ae, ASASSN-14li, and ASASSN-15oi, respectively. The dashed line shows the evolution of a parabolic orbit with a closest approach 7 equal to the tidal radius for a 10 M⊙ SMBH. The optical photosphere of iPTF16fnl is significantly smaller than those of the three ASAS-SN TDEs.

184 iPTF16fnl ASASSN-14li 11.0 ASASSN-14ae ASASSN-15oi

10.5

10.0 ) ⊙ 9.5 / L BB

(L 9.0 10

log 8.5

8.0

7.5

7.0 0 20 40 60 80 100

MJD - MJD0

Fig. 6.8.— Luminosity evolution of iPTF16fnl. Black circles show the bolometric luminosity of iPTF16fnl inferred from our blackbody fits to the host subtracted UVOT fluxes; the open blue circles, filled red squares, and open green squares show the temperature evolution of ASASSN-14ae, ASASSN-14li, and ASASSN-15oi, respectively. The downward pointing arrows denote the single-epoch upper limits on the X-ray emission for iPTF16fnl. The bolometric luminosity of iPTF16fnl is significantly lower than that of the ASAS-SN TDEs.

185 Fig. 6.9.— Spectral energy distribution of iPTF16fnl. The colored squares show the host-subtracted Swift fluxes corrected for Galactic extinction. The solid lines show our blackbody fits to the TDE flux; the dashed lines show similar blackbody models but with the temperature fixed at T =2 104 K. The downward and upward arrows show the flux limits inferred from our X-ray× and optical spectroscopic observations, respectively.

186 Table 6.1: Archival Photometry of Mrk 0950 Filter Magnitude Magnitude Uncertainty FUV 21.10 0.27 NUV 19.87 0.08 u 17.62 0.01 g 16.08 0.01 r 15.49 0.01 i 15.18 0.01 z 14.92 0.01 J 14.69 0.05 H 14.47 0.05

Ks 14.68 0.05 These are 5′′.0 radius aperture magnitudes from GALEX, SDSS, and 2MASS. Magnitudes are in the AB system.

Table 6.2: Inferred Magnitudes of Mrk 0950 Filter Magnitude Swift Filters UVOT W 2 20.24 UVOT M2 20.02 UVOT W 1 19.26 UVOT U 17.68 UVOT B 16.31 UVOT V 15.70 Ground-based Filters B 16.29 g 16.01 V 15.66 r 15.43 i 15.16 These are AB magnitudes synthesized from the FAST ﬁt to the archival magnitudes from Table 6.1.

187 Table 6.3: Swift Observations. MJDXRTLimits W2 M2 W1 U B V 57631 < 3.85 14.95 0.04 15.25 0.04 15.34 0.05 15.42 0.04 15.97 0.03 15.43 0.05 ± ± ± ± ± ±

188 57635 < 3.01 15.20 0.04 15.42 0.03 15.47 0.05 15.62 0.05 16.02 0.04 15.54 0.05 ± ± ± ± ± ± 57637 < 3.55 15.23 0.04 15.48 0.03 15.56 0.05 15.60 0.05 16.12 0.04 15.63 0.05 ± ± ± ± ± ± Table published in its entirety in Brown et al. (2018). Magnitudes and uncertainties are presented in the Vega system. X-ray count rate limits are given in units of 10−3 counts per second in the energy range 0.3 10 keV. Data are not corrected for Galactic absorption. − Table 6.4: Host and Reddening Corrected Swift Observations. MJDW2 M2 W1 U B V 57631 16.03 0.04 16.31 0.04 16.52 0.05 16.51 0.07 16.66 0.20 16.83 0.42 ± ± ± ± ± ± 57635 16.29 0.04 16.50 0.03 16.66 0.06 16.81 0.10 16.82 0.24 17.41 0.70

189 ± ± ± ± ± ± 57637 16.32 0.04 16.56 0.04 16.77 0.06 16.77 0.09 17.14 0.31 ... ± ± ± ± ± Table published in its entirety in Brown et al. (2018). Host subtracted and Galactic reddening corrected Swift photometry of iPTF16fnl. Magnitudes and uncertainties are presented in the AB system for comparison with Tables 6.1 and 6.2. Epochs for which the transient was not detected above the host ﬂux are omitted. Chapter 7: The Speciﬁc Type Ia Supernova Rate from Three Years of ASAS-SN

7.1. Introduction

The SN Ia dependence on stellar population age has motivated several studies geared towards understanding the relationship between SNe Ia and their host galaxies. In particular, the Sloan Digital Sky Survey–II Supernova Survey (Frieman et al. 2008), the Lick Observatory Supernova Seach (LOSS; Li et al. 2000), the Palomar Transient Facility (Law et al. 2009, PTF;), and the SuperNova Legacy Survey (SNLS; Astier et al. 2006; Guy et al. 2010) identiﬁed several trends between SNe Ia properties and their host galaxies (Neill et al. 2009; Sullivan et al. 2010; Lampeitl et al. 2010; Pan et al. 2014, e.g.,), as well as the relative SN Ia rate as a function of host galaxy properties (Neill et al. 2006; Sullivan et al. 2006; Quimby et al. 2012; Smith et al. 2012; Gao & Pritchet 2013; Li et al. 2011a; Graur & Maoz 2013; Graur, Bianco & Modjaz 2015; Graur et al. 2017; Heringer et al. 2017). A more contentious issue is whether these trends extend to local environments within the host galaxies. Several studies have suggested this is indeed the case (Rigault et al. 2013, 2015; Moreno-Raya et al. 2016; Roman et al. 2017), while Jones, Riess & Scolnic (2015) argue that there is no dependence on local star formation when a suﬃciently large sample is used and a more rigorous analysis is performed. Similarly, Anderson et al. (2015) used an independent sample of SNe and recovered the dependence of SN Ia properties on host galaxy parameters, but found no dependence of SN Ia properties

190 on the local environment. Characterizing the relationship between SNe Ia and their hosts is immensely important, since the residuals of ﬁts to the dependence of distance on redshift (i.e., Hubble residuals) are correlated with host galaxy properties (e.g., Lampeitl et al. 2010; Sullivan et al. 2010; Kelly et al. 2010; Gupta et al. 2011; Johansson et al. 2013; Pan et al. 2014; Wolf et al. 2016; Uddin et al. 2017), and of course the general galaxy population evolves with redshift (Madau et al. 1996; Hopkins & Beacom 2006a).

In this paper we perform a census of SN Ia host galaxies using data from the first 3 years of ASAS-SN operation, in order to better understand the connection ∼ between SNe Ia and their host galaxies. In Section 7.2 we describe the SN Ia sample and the archival data used to analyze the host galaxies. In Section 7.3 we analyze the mass distribution of the SN Ia host galaxies and derive the specific SN Ia rate for an unprecedentedly wide range of stellar masses. In Section 7.4 we summarize our findings and discuss future directions.

7.2. Data

7.2.1. The SN Ia Sample

The SN Ia sample is constructed from the ASAS-SN Bright Supernova Catalogs (Holoien et al. 2017a,b,c). These catalogs contain 476 SNe Ia in total. ASAS-SN discovered 325 of these SNe Ia, and out of the 151 not discovered by ASAS-SN, 84 were recovered in ASAS-SN data. In order to build our unbaised sample of SNe Ia, we selected SN Ia hosts for which the transient was either discovered by ASAS-SN or recovered after discovery in ASAS-SN data. We exclude the 67 SNe Ia that were not discovered by ASAS-SN. Additionally, we exclude 6 SNe Ia that were classiﬁed as

191 either peculiar (e.g., Ia-pec or Ia-CSM) or Ia-02cx (Li et al. 2003) events. We retain the Ia-91bg, Ia-91T, Ia-06bt, Ia-07if, and Ia-09dc subtypes in our analysis, since they constitute the tails of the distribution of “normal” SNe Ia. The breakdown of SN Ia subtypes included in our analysis is shown in Figure 7.4.

The resulting sample represents a nearly complete and unbiased census of SNe Ia in the nearby universe (Holoien et al. 2017b). However, the sample is not entirely complete. A fraction of SNe are either undiscovered or excluded from the sample due to quasi-random effects (e.g., the position of the Sun, high Galactic extinction, or bright foreground sources). These sources of incompleteness are physically unassociated with the SNe, and thus do not bias our sample in any significant way. There is also likely a population of SN Ia that are missed due to extinction in the host galaxy. However, out of all SN types, SNe Ia are the most weakly associated with star forming regions (Anderson et al. 2015), so the immediate local environment of SNe Ia is unlikely to be a significant source of systematic incompleteness. There are populations of dusty galaxies in which SNe would be obscured in a significant volume of the host (e.g., ultraluminous infrared galaxies or ULIRGS Lonsdale, Farrah & Smith 2006), but at low redshift these galaxies are relatively rare. Goto et al. (2011) found that LIRGS and ULIRGS are responsible for < 10% and < 0.5% ∼ ∼ of the total infrared luminosity in the local universe, respectively, which means that these heavily dust obscured galaxies are not representative of the underlying stellar mass distribution in the universe. Furthermore, the SNe in these dusty galaxies are not necessarily missed by modern optical surveys: SN 2014J was discovered in the optical despite the fact that the host galaxy M82 is relatively dusty by low redshift standards. With these considerations in mind, the ASAS-SN sample is the closest realization of a statistically complete and unbiased supernova survey of the nearby universe to date.

192 The supernova sample constructed here is by design a magnitude limited sample. All else being equal, the relatively luminous SNe Ia (and their host galaxies)

3/2 will be over represented, since the effective survey volume scales roughly as LSN . The situation is more complex, however, because while massive host galaxies host fainter, faster SNe Ia, the intrinsic luminosities of SNe Ia of a given color and stretch (i.e. after correction) are higher in more massive galaxies. Furthermore, many of the SNe in our sample are found deep within their host galaxies, where extinction may be non-negligible. If one knew a priori the intrinsic brightness of the individual SNe, the host galaxies could be weighted accordingly and this bias could be mitigated. However, without stretch and color information, the intrinsic brightnesses are unknown. To minimize the dependence on completeness corrections, we also construct a volume limited sample (z < 0.02; DL < 90 Mpc), which should ∼ not be significantly affected by the correlation between SN Ia brightness and host galaxy mass. Similarly, if the correlation between SN Ia brightness and host galaxy mass is not particularly strong, then any resulting bias should be relatively weak.

In Figure 7.1 we show the distribution of SN Ia absolute magnitudes. We have applied a correction for Galactic reddening (Cardelli, Clayton & Mathis 1989; O’Donnell 1994; Schlaﬂy & Finkbeiner 2011) and a K correction (Kim, Goobar & Perlmutter 1996; Hogg et al. 2002). The K corrections are computed with SNooPy (Burns et al. 2011), which uses the SN Ia templates from Hsiao et al. (2007). The magnitudes have not been corrected for the local reddening from the host galaxy. Thus the absolute magnitudes are simply

M = m A µ(z) K(z) (7.1) V V − V,Gal − − We show these absolute magnitudes versus luminosity distance with the redshift shown on the top axis. The black points denote SNe either discovered or recovered by ASAS-SN, while the red points denote SNe that were not recovered by ASAS-SN

193 and are excluded from our analysis. The squares represent SN Ia subtypes, and the small circles represent the peculiar SNe Ia that are excluded from our analysis. The gray dashed curve shows the detection threshold for a magnitude limited survey with a limiting magnitude mV = 17.0. The vertical gray dashed line shows the distance limit for our volume limited sample. Within this volume, we expect to recover all SN

Ia with absolute magnitudes MV < 18, which is > 80% of SNe Ia (Li et al. 2011b). ∼ − ∼ For SNe Ia with absolute magnitudes MV > 18, even our volume limited sample is ∼ − incomplete, but this is a relatively small fraction of of SNe.

If Figure 7.2 we show the relative completeness of our sample as a function of peak apparent magnitude. The black histogram shows the observed cumulative distribution; the dashed gray line shows the expected distribution in a Euclidean universe, normalized to the number of SNe discovered at mV < 16.0. In order to gain

5 a better estimate of the expected distribution in mV , we simulate 10 SNe uniformly distributed in comoving volume, with distances up to 500 Mpc. For each SN, we randomly generate an absolute magnitude drawn from a Gaussian distribution with mean M = 18.5 mag and σ = 1.0 mag, which is a reasonable approximation of V − the SN Ia luminosity function (Li et al. 2011b). We weight each SN by a factor of (1+ z)−1 to account for time dilation (i.e., smaller time intervals are probed at progressively higher redshifts). The resulting distribution is shown in Figure 7.2 by the green histogram. The simulated distribution diﬀers little from the expectation for a Euclidean universe. At m 17, our sample is roughly 70% complete, V ∼ ∼ consistent with the results from Holoien et al. (2017b). We use the diﬀerential form of this distribution in order to compute a completeness correction as a function of apparent magnitude for SNe fainter than m 16. We apply no completeness V ∼ correction to the bright end of the distribution, since the SNe that populate this

194 portion of the distribution are generally nearby, where the assumption of an isotropic and homogenous universe is not necessarily valid.

Once we have the completeness corrections, we estimate the relative luminosity function of SNe Ia, which we show in Figure 7.3. In the left panel we show the observed distribution of absolute magnitudes. The black histogram shows the full sample, and the red histogram shows the volume limited sample. The volume limited sample has a higher fraction of low luminosity SNe Ia than the full magnitude limited sample. We convert these distributions into estimates of the true luminosity function using the V/Vmax method (Schmidt 1968; Huchra & Sargent 1973; Felten

1976). For each SN, we compute the maximum volume (Vm) in which that particular

SN could be recovered by a survey with a limiting magnitude mV = 16.8. This choice of limiting magnitude produces a median value of V/Vmax that is reasonably close to 0.5, which is to be expected if sources uniformly populate the survey volume. We compute the relative luminosity function for each bin in absolute magnitude centered on M as N 1 Φ(M)= w (1 + z ) (7.2) V × i × i Xi=1 M,i where the sum is over all the SNe within the bin. The weights wi correct for the incompleteness given the apparent magnitude of each SN, and the factor of (1+ z) accounts for time dilation. The results are shown in the right panel of Figure 7.3. The black circles show the relative luminosity function computed from the full sample, and the red squares show the results for the volume limited sample. The luminosity functions have been normalized to the bin at M = 19; the absolute V − luminosity function will be addressed in a future paper. The shape of the relative luminosity function is consistent with the volume limited luminosity function presented in Li et al. (2011b), but our sample spans a substantially larger range in absolute magnitude. We ﬁt a Schechter (1976) function to the relative luminosity

195 function of both the full sample and volume limited sample, which has the form

φ∗ L α L φ(L)dL = exp dL. (7.3) L∗ L∗ −L∗ where φ∗ is the normalization (which is arbitrary in this case), α faint-end slope, and L∗ (alternatively M ∗ in magnitude space) determines the “knee” of luminosity function. Our ﬁts are shown in Figure 7.3 as dashed lines. We ﬁnd (φ∗, α, M ∗) corresponding to (2.5 0.6 107, 1.3 0.2, 18.07 0.03) and ± × ± − ± (1.06 0.4 107, 1.9 0.3, 17.73 0.12) for the full sample and the volume limited ± × ± − ± sample, respectively.

7.2.2. Archival Host Data

We ﬁrst assemble the archival host data from the ASAS-SN Bright Supernova Catalogs (Holoien et al. 2017a,b,c, Tables 2 and 4;). These tables contain archival data from the near-ultraviolet (NUV) magnitudes from the Galaxy Evolution Explorer (GALEX ;Morrissey et al. 2007) All Sky Imaging Survey, optical ugriz model magnitudes from the Sloan Digital Sky Survey Data Release 13 (SDSS DR13;

Albareti et al. 2017), near-infrared (NIR) JHKS magnitudes from the Two-Micron All Sky Survey (2MASS Skrutskie et al. 2006), and IR W 1 and W 2 magnitudes from the Wide-ﬁeld Infrared Survey Explorer (WISE;Wright et al. 2010) AllWISE source catalog.

In order to supplement the optical coverage of host galaxies in our sample, we also retrieve grizy data from the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS; Chambers et al. 2016; Flewelling et al. 2016), which expands the sample of SN Ia host galaxies with optical coverage to include all galaxies with

◦ declinations δ > 30 and apparent magnitudes mg < 23. In order to assemble a − ∼ sample of Pan-STARRS magnitudes, we use the Pan-STARRS stack images and

196 the Pan-STARRS Mean Object Catalog to identify the sources and their unique object IDs. We use these objIDs to cross match with the StackObjectThin and StackObjectAttributes tables, and then extract the stacked Kron magnitudes and radii corresponding to the primary detection for each host galaxy. We also retrieve the detection flags, but in most cases we find that a by-eye inspection of the galaxy spectral energy distribution (SED) provides a more robust discriminator of the reliability of the photometry. For the host galaxies with SEDs that fail our by-eye inspection (e.g., due to vastly different Kron radii amongst the filters), or if the host was too faint or diffuse to be detected by the Pan-STARRS pipeline, we perform aperture photometry on the stack images with a circular aperture and a fixed radius. The aperture is chosen by eye to capture as much of the galaxy flux as possible; circular apertures are also used to mask contaminating sources such as foreground stars. As a test, we compared our “by hand” magnitudes with reliable stack Kron magnitudes and find good agreement.

7.3. Analysis

The 2MASS and WISE magnitudes form the starting point for the host galaxy SED modeling. The WISE catalog, in particular, is relatively deep, and nearly all host galaxies are detected in both W1 and W2. These bands are primarily sensitive to the stellar mass. Similarly, we also include the GALEX NUV magnitudes in the model by default, since the NUV coverage provides constraints on the stellar age and mass-to-light ratio. However, there is no uniform all-sky optical survey, so we have a choice as to which dataset to include in the SED ﬁtting. When possible, we adopt the masses derived from the SDSS data. In a small number of instances, the SDSS magnitudes are unreliable and we adopt the mass derived from the Pan-STARRS data instead. For a small number of cases, the host galaxy spans several arcminutes

197 on the sky, and the catalogued photometry for most surveys does not reﬂect the true photometry of the host galaxy. In these instances, we adopt the JHKS magnitudes from the 2MASS Large Galaxy Atlas (2MASS LGA; Jarrett et al. 2003) and model the galaxy using only these magnitudes. The breakdown of source of the host photometry is shown in Figure 7.4.

We model the host galaxy SEDs with the publicly available Fitting and Assessment of Synthetic Templates (fastKriek et al. 2009). We assume a Cardelli,

Clayton & Mathis (1989) extinction law with RV =3.1 and the Galactic extinction taken from Schlafly & Finkbeiner (2011) for the coordinates of the host galaxy. We also assume an exponentially declining star-formation history, a Salpeter initial mass function, and the Bruzual & Charlot (2003) stellar population models. Given the heterogenous mix of photometry for these galaxies, the statistical uncertainties are generally much smaller than the systematic uncertainties. Even in the case of Pan-STARRS photometry alone, the statistical uncertainties of a given measurement may be a few hundredths of a magnitude or smaller, while the systematic uncertainties (e.g., due to variations in aperture size or background subtraction between filters) are generally at the tens of percent level. Artificially small uncertainties in a single survey or measurement will drive the fit to match that particular survey at the expense of fitting the archival data from other archival surveys. In order to minimize this effect, we assign a minimum uncertainty of 0.1 mag to the photometry when modeling the host galaxy SED.

For each galaxy we inspect the various fits to the archival data and adopt a preferred mass given the considerations outlined above. As a check, we compare the masses derived with our fast fits to those from the MPA-JHU Galspec pipeline (Kauffmann et al. 2003c) where available, and we find the results are generally consistent. The comparisons between the masses and SFRs are shown in Figure 7.5.

198 Our SFR estimates are less well constrained than the Galspec data, but this is to be expected given that we are utilizing photometric data only. Additionally, while our SFR estimates agree reasonably well with the Galspec values, there is some indication that for high SFR galaxies, our SFRs are systematically lower than the Galspec values.

We also see an indication of discrepant SFR estimates when we view the distribution of SDSS galaxies compared to the distribution of our host galaxies in the M SFR plane. This is shown in Figure 7.6. The gray shaded contours ⋆ − represent the SDSS galaxies, while the colored circles show host galaxies from our sample. The green dashed line corresponding to a sSFR = 11 represents our − nominal separation between high and low star forming galaxies. For host galaxies with nominal SFR< 10−4, we adopt the SFR upper limit from the fast results, which are shown with downward arrows. The host galaxies from our sample follow the overall distribution of SDSS galaxies, but at the high SFR end, we appear to have a deﬁcit of SN Ia hosts. However, given the generally weak constraints on our SFR estimates and the potential for signiﬁcant systematics between our models and the Galspec results, we refrain from making any strong claims about the origin of this trend. Future work addressing the SFR as well as chemical distributions of SN Ia host galaxies will require additional observational constraints (namely spectroscopic follow-up) in order to 1) improve the constraints on these parameters, and 2) reduce the potential for modeling biases between our host galaxy population and the general galaxy population at large.

In Figure 7.7 we show the distribution of host galaxy masses versus luminosity distance (left) and SN absolute magnitude (right). The color and symbol schemes are the same as Figure 7.1. Leftward arrows denote upper limits on the host galaxy mass. The green diamonds right panel of Figure 7.7 show the mean host galaxy

199 10 mass and SN Ia absolute magnitude for galaxies above and below 10 M⊙ for the full sample. The diﬀerence in the mean absolute magnitudes between the two mass bins is 0.110 0.062. Thus, the SN Ia in more massive galaxies are indeed marginally ± fainter than the SNe Ia in the lower mass galaxies. This is consistent with previous studies (e.g., Sullivan et al. 2010; Pan et al. 2014), which found that low stretch (i.e., fainter) SNe Ia are found in more massive galaxies. However, the overall amplitude of this eﬀect is not large, and would only result in a < 20% enhancement of low mass ∼ galaxies over high mass galaxies, all else being equal.

In Figure 7.8 we show the cumulative distribution of host galaxy masses. In the left panel, we show all 476 galaxies in the ASAS-SN Bright Supernova Catalogs (gray solid line) the 403 galaxies hosting SNe Ia either discovered or recovered by ASAS-SN (black solid line), and the volume limited (z 0.02) subset of 114 galaxies ≤ hosting SNe Ia either discovered or recovered by ASAS-SN. The mass distributions are quite similar, but the volume limited sample has a mild enhancement of low mass galaxies compared to the full sample of discovered/recovered SN Ia hosts.

In the right panel we compare the total and volume limited samples recovered by ASAS-SN (black solid and dashed histograms, respectively) to the distribution of host galaxy masses from other low redshift supernova surveys. The green and blue histograms show the results from the distribution of SN Ia host galaxy masses from PTF (Pan et al. 2014) and the volume limited LOSS sample (Li et al. 2011b), respectively. The gray dashed line shows the galaxy mass function from Bell et al. (2003). The host galaxy mass distributions from the ASAS-SN sample (and to a lesser extent the PTF sample) are much more sensitive to lower mass galaxies. This is principally due to the fact that LOSS was a targeted SN survey and preferentially observed large galaxies. The LOSS survey was instrumental in demonstrating that that lower mass galaxies produce a larger number of SNe Ia than higher mass

200 galaxies, but they only included galaxies with stellar masses down to 109.5. ∼ Additionally, the ASAS-SN sample has a signiﬁcantly larger number of SNe than the other surveys. The beneﬁt of using an unbiased SN survey to conduct a census SN host galaxies is quite clear; SNe occur in galaxies that simply are not monitored in traditional targeted surveys.

In order to obtain the speciﬁc SN Ia rate, we need to apply several corrections to the host galaxy mass distribution, and we follow the same procedure used to compute the relative luminosity function. First, we need to increase the weights of the galaxies hosting faint SNe. We compute these weights from the completeness corrections presented in Section 7.2. Additionally, we need to correct for time dilation and the fact that the luminous SNe can be observed to greater distances. We ﬁnd that there is at most only a modest correlation between the SN luminosity and host galaxy stellar mass, and thus do not implement any explicit correction for this relationship. In short, we use Equation 7.2 to sum over the host galaxies in each stellar mass bin, using the properties of the individual SNe to compute the appropriate weights. Finally, we need to assume a form for the underlying galaxy stellar mass function. We adopt the g-band derived stellar mass function from Bell et al. (2003), which we have converted to a Salpeter IMF by scaling their masses by 0.15 dex. For each bin, we divide the weighted histogram by the integral of − M2 the stellar mass function over the width of the bin (i.e., M1 MdMdn/dM) and 10 R normalize to the 10 M⊙ bin to obtain the relative SN Ia rate per unit stellar mass.

Figure 7.9 shows this normalized speciﬁc SN Ia rate as a function of host galaxy mass over the range 6.25 log(M /M⊙) 12.25. The black circles show ≤ ⋆ ≤ the rate calculated using the full ASAS-SN sample, and the red squares show the rate calculated from the volume limited sample. The dashed blue line shows the analytic ﬁt to the Li et al. (2011a) results from Kistler et al. (2013). At the high

201 mass end (9.5 < log(M⋆/M⊙) < 11.5), we find remarkably good agreement with the ∼ ∼ results from Kistler et al. (2013). Moving towards lower masses, the Kistler et al. (2013) curve suggests a flattening in specific SN Ia rate, but this is largely due to their assumed analytic form. The ASAS-SN data show that the specific SN Ia rate

7 continues to rise towards lower mass galaxies, down to stellar masses of 10 M⊙. ∼ That is, progressively lower mass galaxies produce more SNe Ia per unit mass than more massive galaxies. This trend is consistent with previous studies (e.g., Sullivan et al. 2006; Li et al. 2011a; Graur & Maoz 2013), but this has never been shown for low redshift galaxies spaning such a broad range of masses. For both the full

8 and volume limited samples, we ﬁt a power law to the bins above 10 M⊙ normalized α 10 M to unity at 10 M⊙, such that r = 10 . We ﬁnd αfull = 0.45 0.04 and 10 M⊙ − ± α = 0.51 0.05, which are show by the black and red dashed lines for the full vol. − ± sample and volume limited subsample, respectively. This values are in agreement with the results from Li et al. (2011a). Our results show that the the dependence of the SN Ia rate on host galaxy mass extends to much lower masses than previously known.

The enhanced speciﬁc SN Ia rate at low masses could be due to an underestimation of the stellar mass function at low masses. However, the results from Baldry et al. (2012) show that the faint end slope of the stellar mass function remains relatively constant even down to the lowest masses considered here. We also consider the dependence of the relative rate on speciﬁc SFR. Given the relatively loose constraints on the SFR, we split our sample into a star forming subsample (sSFR> 11) and a passively evolving sample (sSFR< 11). We compute the − − relative rates following the same procedure as outlined above, but include an additional factor in the weights accounting for the fractions of blue and red galaxies

9 as a function of stellar mass. At low masses (M⋆ < 10 M⊙) the galaxy population ∼

202 is dominated by star forming galaxies with relatively few passive galaxies, while at high masses the opposite is true. We derive the correction factors by computing the fraction of early and late type galaxies the stellar mass functions presented in Bell et al. (2003). Our procedure assumes that the the mapping in Bell et al. (2003) between early and late type galaxies is reasonably consistent with our division between passive and star forming galaxies, which is not necessarily the case.

8.5 However, Baldry et al. (2012) argue that below 10 M⊙, the relative populations ∼ of blue and red galaxies are not all that well constrained, and at very low masses

7.5 (e.g., < 10 M⊙) the fractions of red and blue galaxies may be comparable. Given ∼ these uncertainties, we adopt a maximum correction factor for the low mass galaxies

9 ﬁxed to the value computed at 10 M⊙. We show the SN Ia rate in actively star forming galaxies relative to that in passive galaxies in Figure 7.10. We ﬁnd no strong evidence that the relative SN Ia rate strongly depends on star formation activity. In

10 11 the high mass galaxies where most of the SNe Ia originate (M 10 10 M⊙), ⋆ ∼ − the actively star forming galaxies appear to produce marginally more SNe Ia than the passive galaxies of the same mass. This is consistent with previous findings Mannucci et al. (2005); Graur et al. (2017, e.g.,). On the other hand, at lower masses, the active galaxies become less efficient at producing SNe Ia than passive galaxies. However, in both cases there is little evidence that the ratio of the relative rates in the two samples differs from unity. In any case, a careful assessment of this behavior requires more robust measurements of SFRs, and a more thorough treatment of the relative galaxy stellar mass functions.

7.4. Conclusions

We leveraged the statistical power of three years of discoveries presented in the ASAS-SN Bright Supernova Catalogs in order to construct a sample of SNe Ia that

203 is largely unbiased with respect to host galaxy properties and nearly complete within 100 Mpc. We derived the relative completeness of the V-band component of ∼ ASAS-SN as a function of apparent magnitude which, combined with the the peak V-band magnitudes from the catalogs, we used to construct the relative luminosity function of SNe Ia in the low redshift universe. We used archival photometric data from the near-UV, optical and near-IR to derive masses and star formation rates for the SN Ia host galaxy population. Finally, we used this host data in conjunction with the individual SN data to derive the relative SN Ia rate as a function of host galaxy properties.

We show that the specific SN Ia rate increases in progressively lower mass galaxies, and that this trend persists in the galaxies for which this measurement was not previously possible. We find that low mass galaxies produce 10 20 times more − SNe Ia per unit stellar mass than their more massive counterparts. We find marginal evidence for a dependence of the specific SN Ia rate on sSFR, but in order to constrain the (s)SFR dependence of the SN Ia rate, additional follow-up observations are needed. Quantitative, rather than qualitative, measurements of SFR and ideally chemical abundances are necessary for characterizing how the SN Ia rate depends on these galaxy properties. Given the low redshift nature of the sample, obtaining optical photometry and medium resolution spectroscopy for 100% of the host ∼ galaxies would be a large undertaking, but feasible, especially for a volume limited or dutifully selected subsample. Similarly, multiple efforts are underway to monitor low redshift SN Ia (Foley et al. 2018, Chen et al., in preparation), which will be invaluable for studying the relationships between SN Ia light curve properties and their host galaxies in this revolutionary SN Ia sample.

204 Redshift 0.00 0.02 0.04 0.06 0.08

-21

= 17.0 -20 mlim

V -19 M

-18

-17 Discovered or Recovered (N=409) Not Recovered (N=67) Subclass SN Ia (39/9 Rec. / Not Rec.) Peculiar SN Ia (6/2 Rec. / Not Rec.) -16 0 50 100 150 200 250 300 350 400

DL [Mpc]

Fig. 7.1.— SN Ia peak absolute magnitudes after applying corrections for Galactic reddening and redshift (K correction), versus luminosity distance (redshift is shown on the top axis). The dashed gray curve denotes the detection threshold for a survey with a limiting magnitude mV = 17.0 mag, assuming no extinction along the line of sight. The vertical gray dashed line denotes the distance limit used to construct our volume limited sample. Black (red) symbols show SNe recovered (not recovered) by ASAS-SN. Circles and squares denote normal SNe Ia and those belonging to a Ia subclass, respectively. The small points denote peculiar SNe Ia (including Ia-02cx) that we exclude from our analysis.

205 101 Observed Simulated Euclidean 100 ) V m

≤ 10−1 peak N(m 10−2

10−3 13 14 15 16 17

Fig. 7.2.— Cumulative number of SNe as a function of apparent magnitude. The black histogram shows the observed distribution, the gray dashed line shows the expected number in a Euclidean universe, and the green histogram shows the results from our simulation. We normalize the Euclidean and simulated curves to the number of observed SNe discovered brighter than mV = 16. Using the diﬀerential form of this distribution, we derive the completeness as a function of apparent magnitude by computing the ratio of the number of observed SNe to the number of expected SNe at a given brightness.

206 0.4 Full Sample 100 Vol. Limited Sample

0.3 10−1

0.2 10−2 Relative Abundance Diﬀerential Fraction 0.1

−3 Full Sample 10 Vol. Limited Sample 0.0 −16 −17 −18 −19 −20 −21 −17 −18 −19 −20 −21

MV MV

Fig. 7.3.— Left: the observed distributions of SN Ia absolute magnitudes. The volume limited sample has a larger fraction of relatively faint SNe than the full sample. Right: True relative luminosity function (i.e. corrected for completeness, redshift, and luminosity bias). The dashed lines show our best ﬁt luminosity functions to the two samples.

2MASS+WISE

Normal SN Ia

PanSTARRS

Fig. 7.4.— Left: the breakdown of the SN Ia types included in our analysis. The overall sample comes from the ASAS-SN Bright Supernova Catalogs (Holoien et al. 2017a,b,c). The SNe Ia excluded from our analysis were either not recovered by ASAS-SN, or were peculiar in type. Right: the breakdown of the archival data used to model the SN Ia host galaxies. The galaxies which hosted unrecovered or peculiar SNe Ia are excluded. A small number of galaxies were lacking the data needed for a robust mass estimate; their masses should be be regarded as upper limits only. For every host galaxy, we incorporate the 2MASS+WISE data in the modeling whenever possible. When reliable SDSS photometry is not available, we use PanSTARRS stack data or, for the galaxies outside the PanSTARRS footprint (δ < 30◦), the masses − are modeled from the 2MASS+WISE data only.

208 12 1

0 11

− ] [Galspec] 1 1 − yr ) [Galspec] 10 ⊙ ⊙ −

M 2 / ⋆

− log(M 9 3 log (SFR) [M

−4 8 8 9 10 11 12 −4 −3 −2 −1 0 1 −1 log(M⋆/M⊙) [this work] log (SFR) [M⊙ yr ] [this work]

Fig. 7.5.— Stellar masses (left) and SFRs (right) derived here compared to the MPA- JHU Galspec estimates. We ﬁnd generally good agreement, although our SFRs are less constrained and may be systematically lower in high SFR galaxies.

209 ASASSN-16dn ASASSN-15od ASASSN-15cz 2

1 ] 1 − 0 (8.0, -1.07) (9.7, -0.03) (11.1, 0.12) yr

⊙ ASASSN-15uk ASASSN-14in ASASSN-16eq -1

-2

log (SFR) [M (7.8, -1.41) (9.7, -0.78) (10.8, -0.49) -3 ASASSN-15fy ASASSN-14bb ASASSN-16na

-4

7 8 9 10 11 12

(6.5, -1.65) (9.7, -1.48) (10.9, ---) log(M⋆/M⊙)

Fig. 7.6.— Left: Comparison of all host galaxies in our sample (colored symbols) with the MPA-JHU Galspec galaxies (gray contours) in the M⋆ SFR plane. The green line shows our division between actively star forming galaxies− (blue symbols) and passive galaxies (red symbols), corresponding to a sSFR < 11. Right: PanSTARRS images for a sample of host galaxies, demonstrating the diversity− of our host galaxy sample. The image scale corresponds to a proper distance of 20 kpc on a side. The numbers in parentheses are log(M⋆/M⊙) and log(SFR), respectively. The images are ordered such that stellar mass is increasing rightward, and star formation rate is increasing upward.

210 400 -22

350 -21

300 -20 250 V 200 -19 M [Mpc] L D 150 -18

100 -17 50

0 -16 6 7 8 9 10 11 12 6 7 8 9 10 11 12

log(M⋆/M⊙) log(M⋆/M⊙)

Fig. 7.7.— Left: luminosity distance versus host galaxy stellar mass. The color and symbol scheme is the same as Figure 7.1. Right: SN Ia peak absolute magnitudes versus host galaxy stellar mass. The green diamonds show the mean absolute 10 magnitude for all galaxies hosting recovered SNe Ia above and below 10 M⊙. The error bars show the range of masses and the standard deviation of the absolute magnitudes in the two samples. The diﬀerence in the mean absolute magnitudes of the two samples is 0.110 0.062. ±

211 1.0 Bright SNe Ia [N=476] 1.0 LOSS [Li et al. 2011; N=66] Recovered SNe Ia [N=403] PTF [Pan et al. 2014; N=82] Recovered SNe Ia [N=403] 0.8 Recovered SNe Ia [z<0.02; N=114] 0.8 Recovered SNe Ia [z<0.02; N=114] Mass Function (Bell et al. 2003) ) ) ⋆ 0.6 ⋆ 0.6 < M < M ( (

f 0.4 f 0.4

0.2 0.2

0.0 0.0 7 8 9 10 11 12 7 8 9 10 11 12

log(M⋆/M⊙) log(M⋆/M⊙)

Fig. 7.8.— Left: cumulative distribution of host galaxy masses for the entire Bright Supernova Sample (solid gray histogram), the host galaxies with SNe Ia either discovered or recovered by ASAS-SN (solid black histogram), and the low redshift host galaxies with SNe Ia either discovered or recovered by ASAS-SN (dashed black histogram). Right: cumulative distribution of SN Ia host galaxies from various surveys. The black histograms show the host galaxies with SNe Ia recovered by ASAS-SN. The blue histogram shows the volume limited SN Ia host galaxy sample from Li et al. (2011b), the green histogram shows the distribution of SN Ia host galaxies from PTF (Pan et al. 2014), and the gray dashed line shows the cumulative galaxy mass function of all galaxies from Bell et al. (2003). The ASAS-SN sample includes a larger fraction of low mass galaxies than other low redshift SN surveys.

212 103 Full Sample [N=403] Vol. Limited [z<0.02; N=114] Kistler et al. 2013

102

101

100 Relative Speciﬁc SN Ia Rate

10−1 6 7 8 9 10 11 12

log(M⋆/M⊙)

Fig. 7.9.— The SN Ia rate per unit stellar mass as a function of host galaxy mass, 10 relative to the rate at 10 M⊙. The black points are calculated using the full sample of host galaxies with SNe Ia either discovered or recovered by ASAS-SN; the red points are calculated from the volume limited sample. Error bars correspond to the 84% confidence intervals computed from the Gehrels (1986) approximations for binomial statistics. The dashed blue curve shows the Kistler et al. (2013) analytic fit to the LOSS SN Ia host galaxy sample in (Li et al. 2011a). The black and red dashed lines show the approximate dependence of the specific SN Ia rate for the two samples, 10 assuming a power law normalized to unity at 10 M⊙.

213 101

100 passive r / active r 10−1

10−2 7 8 9 10 11 12

log(M⋆/M⊙)

Fig. 7.10.— The ratio of the SN Ia rate in actively star forming galaxies to that in passive galaxies, as a function of host galaxy stellar mass.

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