Akshaya RaneWest Virginia university

Aspen Winter ConferenceFebruary 14, 2017

COSMOLOGICAL FRB SIMULATIONS

Outline

• Energy, luminosity and redshift distributions

• Contributions to DM

• FRB widths and fluxes

• Simulation procedure

• Results

• Conclusions

Aspen Winter Conference, 2017Akshaya Rane

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

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

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

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

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

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

MCMC Results

Akshaya Rane Aspen Winter Conference, 2017

(Rane et al., in prep)

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)

Best-fit model

Akshaya Rane Aspen Winter Conference, 2017

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

Thank you!

Simulation procedure

Detection criteria

• The S/N for optimal detection:

• Case 1:

• Case 2:

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.

Comparing with the repeater

Akshaya Rane Aspen Winter Conference, 2017