1. Exploring  -ray emission models using millisecond pulsars in the Second Fermi Pulsar Catalog Alice K. Harding With T. Johnson, C. Venter, E. Grove Latest results from the neutron-star laboratory, Amsterdam, May 2013

2. Why MSPs are special Smaller light cylinders: Radio emission beams at relatively higher altitudes Radio beams wider: Visible for larger impact angle |  | =  -  More complicated B-field structure: Relatively more diverse profiles? More massive: Increased E-field?

3. Millisecond pulsar profile types  -ray peak(s) lag main radio peak – Similar to young pulsars – “Class I”  -ray peaks aligned with radio peaks – Nearly exclusive to MSPs – “Class II”  -ray peak(s) lead main radio peak(s) – Exclusive to MSPs – “Class III” 2 nd Fermi LAT Pulsar Catalog (Abdo et al. 2013) PRELIMINARY Johnson et al. (2013) (See talk of P. Ray)

4. Accelerator/ emission geometries Accelerator/ emission geometries (different from Watters et al. 2009)

5. Radio emission geometries

6. Sky distribution of intensity Retarded dipole field (Deutsch 1955) Constant emissivity in corotating frame Grid of model parameters Find best joint radio /  -ray fits using log(likelihood)

7. Modeling MSP gamma-ray and radio profiles Johnson et al. (2013)  = 74 o, 88 o  = 55 o, 68 o  = 55 o, 60 o  = 43 o, 45 o TPC Model OG Model TPC Model OG Model PRELIMINARY Outer gap and Two-pole caustic models “Class I” OG TPC PRELIMINARY 68% 95% 99%

8. Maximum likelihood fits of aligned MSPs  = 88 o, 72 o  = 88 o, 85 o  = 56 o, 52 o  = 85 o, 87 o  ray and radio emission both caustic but with different altitude ranges: R  min = R ns, R ncs R  max = 0.85, 0.8 R LC J1939+2134 R r min = 0.75, 0.9 R LC R r max = 0.95,1.05 R LC Johnson et al. (2013) Altitude-limited Two-pole caustic, Outer Gap and low-altitude Slot Gap consistent with caustic s  -ray radio 0% radio polarization PRELIMINARY “Class II”

9. Modeling MSP gamma-ray and radio profiles  = 51 0  = 85 0 PRELIMINARY Johnson et al. (2013) Pair-starved polar cap (PSPC) model “Class III”

10. MSP pulsar light curve fits Johnson et al. (2013) Two-pole caustic better fits LCs with off-peak emission Outer gap better fits LCs with no off-peak emission PRELIMINARY

11. Fermi pulsar light curve best fits Johnson et al. (2013) Results of fits for all MSPs in Second Pulsar Catalog (2PC) No model best fits all light curves Two-pole caustic and outer gap geometry fit comparable % Radio uncertainty (x2): changes in ,  < 30 o (less for class II & III)  -ray background level (5%): small effect in -ln(L): may change best-fit model Increasing radio lag (0.1): changes in ,  < 10 o Systematic bias checks Systematic bias checks MSPs (40)

12. Which MSPs are pair-starved? Which are aligned? Class I – standard OG or TPC Class II – aligned  -ray/radio Class III – pair starved polar cap (PSPC) Johnson et al. (2013)

13. Best-fit inclination vs. observer angle Johnson et al. (2013)

14. Best-fit inclination angle vs. spindown Johnson et al. (2013) PRELIMINARY

15. Class II: Maximum and Minimum Altitudes Johnson et al. (2013) PRELIMINARY

16. Johnson et al. (2013) Average f  TPC (std only): OG (std only): PSPC: alTPC: alOG: all TPC (std + al): all OG (std + al): laSG:  -ray luminosity vs. spindown power L  corrected for best-fit f  * f  = 1 from 2PC 0.76 0.72 1.03 0.86 0.62 0.78 0.70 1.8

17. Conclusions  -ray and radio light curve fits for 40 MSPs in 2PC Classes Trends Future Broad distribution of , clustering at larger  (caustics) Larger  for OG: visibility TPC: smaller  for larger Edot (larger |  |) Class II emission altitudes: Radio more limited, higher up, contained within  -ray region (within errors) Clustering around  = 10%; L  ~ Edot; < 1 for TPC / OG 27 class I – best fit by TPC (15) or OG (12); need mix of these two models 6 class II – best fit by alTPC (1), alOG (4), or laSG (1) 7 class III – best fit by PSPC model No clear separation of classes; class II – low P; class III – low B LC New B-field geometries (offset dipoles; finite conductivity magnetospheres) Higher-altitude and more complex radio beams