COSMOLOGICAL FRB SIMULATIONSaspen17.phys.wvu.edu/Rane.pdf · 2017. 2. 28. · Akshaya Rane Aspen...
Transcript of COSMOLOGICAL FRB SIMULATIONSaspen17.phys.wvu.edu/Rane.pdf · 2017. 2. 28. · Akshaya Rane Aspen...
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Akshaya RaneWest Virginia university
Aspen Winter ConferenceFebruary 14, 2017
COSMOLOGICAL FRB SIMULATIONS
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Outline
• Energy, luminosity and redshift distributions
• Contributions to DM
• FRB widths and fluxes
• Simulation procedure
• Results
• Conclusions
Aspen Winter Conference, 2017Akshaya Rane
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Redshift distribution
• Assume FRBs are uniformly distributed
• Generate co-moving distances within a co-moving volume up to 𝑧 = 2.5: 0 < 𝑟 < 1
• Compute z from 𝐷𝑐(𝑧) (Hogg 1999):
H0 = 68.0 km s-1 Mpc-1 , Ωm = 0.32, and Ωл =0.68
Aspen Winter Conference, 2017Akshaya Rane
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Energy and luminosity distributions
• Model A: 𝜎𝐸 , 𝜎𝐿
Energy, Luminosity: Gaussian distributions
• Model B: 𝐸, 𝐿𝑚𝑖𝑛, α
Energy: Constant
Luminosity: Power law distribution
• Model C: 𝜎𝐸 , 𝐿𝑚𝑖𝑛, α
Energy: Gaussian distribution
Luminosity: Power law distribution
Akshaya Rane Aspen Winter Conference, 2017
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DM contributions
H0 = 68.0 km s-1 Mpc-1 , Ωm = 0.32, Ωл =0.68, 𝑛𝑒,0 = 2 × 10
−7𝑐𝑚−3
𝐷𝑀𝐼𝐺𝑀
𝐷𝑀ℎ𝑜𝑠𝑡
(Zheng et al. 2014)
𝐷𝑀𝑀𝑊
Akshaya Rane Aspen Winter Conference, 2017
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FRB widths
• In a simple empirical model:
𝐸 = 𝐿𝑊𝑟𝑒𝑠𝑡
• The effective observed pulse width (ms):
• Dispersion delay: 𝛥𝜈 and 𝜈 in MHz
• Scattering:
• Sampling time (Parkes HTRU survey): 𝑡𝑠𝑎𝑚𝑝 = 64 𝜇𝑠
(Lorimer et al. 2013)
Akshaya Rane Aspen Winter Conference, 2017
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FRB fluxes
• Peak flux averaged over a certain bandwidth (Following Lorimer et al. 2013):
• Peak observed flux:
• Detection criteria: S/N > 9.0
Akshaya Rane Aspen Winter Conference, 2017
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Likelihood
• For every simulated FRB: DM, Speak,obs, Wobs• For every known FRB: DM, Speak,obs, Wobs• Probability of getting the modeled number of FRBs in cell i
𝑝𝑖 =𝑁𝑖
𝑁𝑠𝑖𝑚
• The likelihood function
Cell i
Akshaya Rane Aspen Winter Conference, 2017
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MCMC Results
Akshaya Rane Aspen Winter Conference, 2017
(Rane et al., in prep)
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Maximum Likelihood Estimation
A1-Gaussian distributed E and L around 𝜎𝐸 , 𝜎𝐿 (No Scattering in MW)A2-Gaussian distributed E and L around 𝜎𝐸 , 𝜎𝐿 (Scattering in MW + host)B1-Constant E and power law in L with 𝐿𝑚𝑖𝑛, α (No scattering in MW)B2-Constant E and power law in L with 𝐿𝑚𝑖𝑛, α (Scattering in MW + host)C1-Gaussian distributed E around 𝜎𝐸 and power law in L with 𝐿𝑚𝑖𝑛, α (No scattering in MW)C2-Gaussian distributed E around 𝜎𝐸 and power law in L with 𝐿𝑚𝑖𝑛, α (Scattering in MW + host)
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Best-fit model
Akshaya Rane Aspen Winter Conference, 2017
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Conclusions
• The observed distributions of DM, flux, and widths are consistent with a distribution of sources at cosmological distances with uniform co-moving density out to z=2.5
• Models with power law in L and constant E and Gaussian distributed E are almost indistinguishable
• The estimated bolometric luminosities for the repeater are consistent with the range of luminosities in our best-fit model
• FRBs unlikely to be standard candles!
Akshaya Rane Aspen Winter Conference, 2017
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Thank you!
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Simulation procedure
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Detection criteria
• The S/N for optimal detection:
• Case 1:
• Case 2:
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Maximum likelihood using MCMC
• Initiate Markov chain with
• Choose from a Gaussian distribution with = 0.1
• Compute Metropolis ratio:
• If stay at current position
• Repeat this process until the chain converges.
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Comparing with the repeater
Akshaya Rane Aspen Winter Conference, 2017