Bayesian inference from all-sky SETI surveys Claudio Grimaldi C. - - PowerPoint PPT Presentation

Claudio Grimaldi

Bayesian inference from all-sky SETI surveys

• C. Grimaldi, Sci. Rep. 7, 46273 (2017)
• C. Grimaldi, G.W. Marcy, N.K. Tellis, F. Drake, PASP 130, 054101 (2018)
• C. Grimaldi, G.W. Marcy, PNAS 115, E9755 (2018)

Bayes rule

Bayes’ theorem gives a recipe to update the initial hypothesis (prior) about the probability of occurrence of an event in response to new evidence (data)

• Alan Turing used a Bayesian system to crack the Enigma

Code

• Bernard Koopman used Bayes rule to hunt U-boats
• used to find missing aircrafts (Air France AF447, Malaysia

Airlines MH370)

• medicine,

weather forecasting, financial risk analysis, cosmology, spam filtering, machine learning, AI, …

real-world applications Bayes rule is a pervasive tool for decision making based

• n incomplete information

Bayes’ theorem gives a recipe to update the initial hypothesis (prior) about the probability of occurrence of an event in response to new evidence (data)

The present state of SETI is better described by almost complete ignorance rather than incomplete information.

• no evidence that life exists beyond Earth
• the fraction of the SETI search space explored is similar to that of a glass of

water to the Earth’s ocean (Tarter - 2010)

• UPDATE: The fraction of the SETI search space explored is similar to that of

a Jacuzzi to the Earth’s ocean (Wright, Kanodia, Lubar - 2018)

• less than 0.1% of stars within 160 ly harbor detectable trasmitters as

powerful as the Arecibo radar (or more) in the frequency range 1.1-1.9 GHz (Enriquez et al. 2017) suggesting that the number of Arecibo-like emitters in the Milky Way is between 0 and 107.

Incomplete information in SETI is an euphemism

… but the data gathered by large-scale SETI projects can potentially enable us to infer the population of ET emitters by Bayesian analysis

Necessary conditions for signal detection

• the Earth must be within the domain covered by

the EM emissions

• telescopes must be targeting the emitters
• the emitted signal strength must be above the

detection threshold

Necessary conditions for signal detection

• the Earth must be within the domain covered by

the EM emissions

• telescopes must be targeting the emitters
• the emitted signal strength must be above the

detection threshold

• The thin disk of the Milky Way has a radius of

about 60 kly

• The Earth lies approximately on the galactic plane,

at 27 kly from the galactic center

• any radio wavelength photon emitted before

tM=87,000 years ago is absolutely undetectable

Necessary conditions for signal detection

• the Earth must be within the domain covered by

the EM emissions

• telescopes must be targeting the emitters
• the emitted signal strength must be above the

detection threshold

• q = fraction of Ns stars in the Galaxy that harbor

emitters whose signal is no older than tM = 87,000 yr

• L = average lifetime of the emissions

mean number of signals crossing Earth emitted from the entire Milky Way mean number of signals crossing Earth emitted from the entire Milky Way

Necessary conditions for signal detection

• the Earth must be within the domain covered by

the EM emissions

• telescopes must be targeting the emitters
• the emitted signal strength must be above the

detection threshold

Emitters may transmit narrow directional beams as a more efficient way to communicate (less power required) qshell: fraction of stars emitting isotropic shell signals for a solid angle covering the size of the solar system at a distance of 10 ly qbeam: fraction of stars emitting randomly oriented beams

Necessary conditions for signal detection

• the Earth must be within the domain covered by

the EM emissions

• telescopes must be targeting the emitters
• the emitted signal strength must be above the

detection threshold

Ro

ATA MeerKAT VLA SKA1, SKA2

Necessary conditions for signal detection

• the Earth must be within the domain covered by

the EM emissions

• telescopes must be targeting the emitters
• the emitted signal strength must be above the

detection threshold

Ro probability density of stars

fraction of stars within Ro:

• bservational radius:

effective luminosity of the emitter minimum detectable flux

mean number of detectable signals:

Probability that there are k=0, 1, 2, … signals crossing Earth from emitters within Ro

Bayesian analysis

= prior PDF that there are in average signals from the entire Galaxy that cross the Earth, regardless of whether we can detect them or not. = new evidence on the number of detected signals acquired from new data Posterior PDF of given Prior PDF Likelihood function = prior PDF that there are in average signals from the entire Galaxy that cross the Earth, regardless of whether we can detect them or not. = new evidence on the number of detected signals acquired from new data Posterior PDF of given Prior PDF Likelihood function

Earth

Ro

Earth

Ro

Earth

Ro

= non-detection = at least one

detection

= exactly one

detection

likelihood function

Bayesian analysis

= prior PDF that there are in average signals from the entire Galaxy that cross the Earth, regardless of whether we can detect them or not. = new evidence on the number of detected signals acquired from new data Posterior PDF of given Prior PDF Likelihood function = prior PDF that there are in average signals from the entire Galaxy that cross the Earth, regardless of whether we can detect them or not. = new evidence on the number of detected signals acquired from new data Posterior PDF of given Prior PDF Likelihood function

Prior PDF

We don’t know even the scale of (the average number of signals at Earth) the most noninformative prior is a log-uniform PDF: The detection threshold of previous all-sky surveys is about Smin = 10-23 W/m2 (within 1-2 GHz) past SETI surveys have detected no signals within

2x1013 W

σ: signal-to-noise ratio (15) Ssys : system equivalent flux density (Jy=10-26 W/m2Hz) t : integration time (10 min) ∆ν: bandwidth (0.5 Hz)

Bayesian inference from all-sky observations of narrowband signals within 1-2 GHz

disk-like model for the star distribution

Breakthrough Listen goal: 1 million nearby stars (contained within a sphere of radius Ro=500 ly)

Bayesian inference from all-sky observations of narrowband signals within 1-2 GHz

non-detection

• ne detection

at least one detection

LE=LArecibo

Breakthrough Listen goal: 1 million nearby stars (contained within a sphere of radius Ro=500 ly) What if Ro extends up to the galactic center?

Bayesian inference from all-sky observations of narrowband signals within 1-2 GHz

non-detection

• ne detection

at least one detection

LE=LArecibo LE=LArecibo

Bayesian inference from all-sky observations of narrowband signals within 1-2 GHz

• ne detection

non-detection at least one detection

Bayesian inference from all-sky observations of narrowband signals within 1-2 GHz

Conclusions

• At present there is almost complete ignorance about the possible population of ET

emitters in the Galaxy

• A statistical Bayesian approach is still possible by considering possible outcomes of future

extensive SETI all-sky surveys

• It is unlikely that there are Arecibo-like emitters in the Galaxy If no signals are discovered

within about 40 kly from Earth

• If a signal is discovered within 1000 ly from Earth it is almost certain that there are more

than 100 Arecibo-like emitters in the Galaxy, yet to be discovered

• Improved statistical modelling: adding other galactic components (e.g. globular clusters),

periodic signals, distributed emitter luminosities (power law), frequency dependent SEFD, correlation (signal longevity – luminosity), fractal distribution of emitters, local universe beyond the Milky Way, micrometer-submicrometer wavelength emissions

• Improved Bayesian analysis: model selection, adaptive distribution of emitters, iterative

Bayesian inference, targeted searches, false positive/negative results (e.g. scintillation), wideband emissions

Outlook

Geoff Marcy - UC-Berkeley Nathaniel Tellis - UC-Berkeley Frank Drake - SETI Institute Amedeo Balbi – Uni Tor Vergata - Rome Avik Chatterjee – SUNI Syracuse

remerciements

Andrew Siemion- UC-Berkeley Emilio Enriques- UC-Berkeley Eric Korpela- UC-Berkeley Jill Tarter– SETI Institute Dan Werthimer– UC-Berkeley