The Instrumental Effects on VLBI Polarization in Event ...€¦ · The Instrumental E ects on VLBI...
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The Instrumental Effects on VLBI Polarization inEvent Horizon Telescope Baselines
Michael Kosowsky1,2
Mentors: Vincent Fish2, Rusen Lu2
1Brandeis University
2MIT Haystack Observatory
August 8, 2013
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Targets
Sgr A∗ M87
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EHT StationsCARMA SMT
SMA JCMT
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EHT Telescopes
www.maps.google.com
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VLBI Polarization
I We observe in 230 GHz (1.3 mm)
I Polarimetry teaches about B-fields in target sources
I Atmosphere is highly variable at 230 GHz - can’t use absolutephases.
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VLBI Polarization Equations
Parallel polarization ratio:
R1R∗2
L1L∗2=
G1R
G1L
G ∗2R
G ∗2L
e2i(−φ1+φ2)
Cross-polarization ratio:
L1R∗2
R1R∗2
=G1L
G1R
[P∗
21
I12
e2i(φ1) + D1L + D2R∗ e2i(φ1−φ2)
]Cyan are parallel hands.Magenta are cross hands.Green are antenna gains.Violet are field rotation angles.Orange are antenna polarization.Red are source polarization.Blue are source intensity.
Roberts, Wardle, & Brown. 1994. ApJ., 472, 718
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Circle Plots
L1R∗2
R1R∗2
=G1L
G1R
[P∗
21
I12
e i(2φ1) + D1L + D∗2R e i(2φ1−2φ2)
]
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Circle Plots
L1R∗2
R1R∗2
=G1L
G1R
[P∗
21
I12
e i(2φ1) + (D1L + D∗2R)
]
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MCMC Simulations - CARMA-CARMA
Phased CARMA R/L gain amplitude Phased CARMA R/L complex gain
Reduced χ2 = 1.596
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MCMC Simulations - SMT-CARMA
Reduced χ2 = 4.743 Clearly, 3C279 doesn’t fit.
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MCMC Simulations - SMT-CARMA, Only Good Sources
Reduced χ2 = 1.599
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Checking MCMC Consistency
Reduced χ2 = 17.571 Clearly, the points do not fit.
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Conclusions
I MCMC works well as a fitting tool for our data
I We have good estimates for the gains and D-terms of theCARMA and SMT stations
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Future Work for MCMC
I Include HI stations
I Reverse fit - assume D-terms to find source polarization
I Baseline-dependent source polarization
I Look at data over time
I Global fit of everything
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Acknowledgements
I NSF
I Vincent Fish and Rusen Lu
I Sheperd Doeleman
I Kazunori Akayama
I The EHT Group
I Phil Erickson, K.T. Paul and Heidi Johnson
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CARMA-CARMA MCMC Results
Parameter Value
G1R/G1L 1.0288
Ψ1R −Ψ1L 11.6052◦
G2R/G2L 0.9398
Ψ2R −Ψ2L −167.2085◦
|D1R + D∗2L| 0.0283
φ(D1R + D∗2L) 3.6562◦
|D1L + D∗2R | 0.0260
φ(D1L + D∗2R) 179.8692◦
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SMT-CARMA MCMC Results
Phased CARMA ValueGR/GL 0.9979ΨR − ΨL 11.9603◦
DR amp 0.0397DR phase 60.9276◦
DL amp 0.0130DL phase 117.1770◦
Comp. CARMA ValueGR/GL 0.9668ΨR − ΨL −166.7028◦
DR amp 0.0215DR phase 147.7472◦
DL amp 0.0334DL phase 74.6544◦
SMT ValueGR/GL 1.0133ΨR − ΨL 104.1871◦
DR amp 0.0684DR phase 50.6288◦
DL amp 0.1049DL phase 102.3045◦
Phased CARMA ValueGR/GL amp 1.0122ΨR − ΨL 8.9545◦
DR amp 0.0509DR phase 120.0533◦
DL amp 0.0502DLphase −4.7177◦
Comp. CARMA ValueGR/GL amp 0.9606ΨR − ΨL −169.5825◦
DR amp 0.0874DR phase −170.2907◦
DL amp 0.0764DL phase 33.4524◦
SMT ValueGR/GL amp 0.9914ΨR − ΨL 102.1956◦
DR amp 0.1478DR phase 87.0353◦
DL amp 0.1573DL phase 107.4904◦
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VLBI Polarization Equations
R1R∗2
L1L∗2=
G1R
G1L
G ∗2R
G ∗2L
e2i(−φ1+φ2)
L1R∗2
R1R∗2
=G1L
G1R
[P∗
21
I12
e i(2φ1) + D1L + D∗2R e i(2φ1−2φ2)
]L1R
∗2
L1L∗2=
G ∗2R
G ∗2L
[P∗
21
I12
e i(2φ2) + D1L e i(−2φ1+2φ2) + D∗2R
]R1L
∗2
L1L∗2=
G1R
G1L
[P12
I12
e i(−2φ1) + D1R + D∗2L e i(−2φ1+2φ2)
]R1L
∗2
R1R∗2
=G ∗
2L
G ∗2R
[P12
I12
e i(−2φ2) + D1R e i(2φ1−2φ2) + D∗2L
]