ì  A Bayesian approach to multi-messenger astronomy

范锡龙  (Xi-­‐Long  Fan)  湖北第二师范学院(Hubei  University  of  Educa;on)  

 LIGO@tsinghua  

Short  Gammy  Burst Host  galaxy Compact  Binary  Coalescence

Detection  >  GW  Astronomy

Aasi  et  al,  arXiv:1304.0670  (2013)

Singer  et  al.  ApJ  2014

GW：

EM：

Abadie  et  al.  2011

~20  Mpc  50        Mly

~  15  Kpc ~  200  Mpc

Gravitational wave astronomy    in  my  mind  

ì How  to  confirm  the  joint  detec;on  by  two  sets  of  data  (GW  and  EM)?  ì  Do  these  data  respond  to  one  physical  rela;on?    

ì What  can  we  learn  from  this  joint  detec;on?    ì  Beyond  confirming  detec;on,  what  is  the  new    

knowledge  for  both  research  fields?      

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GW<-­‐-­‐-­‐-­‐>    Gamma-­‐Ray  Burst

ì  GW burst

Collapsar

Long GRB

h^p://ucolick.org/~acucchia/Gamma-­‐ray_Bursts.html Image:  W.  Benger,  AEI/ZIB

n  GW inspiral

NS/BH Merger

Short GRB

引力波<-­‐-­‐-­‐-­‐>    伽玛爆

Why need galaxy catalogue？

Binary  (NS-­‐NS  /NS-­‐BH) Burst

Poor GW localization >10 deg2 (in Ad LIGO－Virgo sky box ～500 galaxies！) Where is the GW source？

Rank    galaxies  within  GW  error  box.    Nu^all  &  Su^on  rank  sta;s;c  :    Loca;on,    distance  and  B  band  luminosity  of  galaxies    

Veitch  et  al.  2012    Wen,  Fan,  Chen  2008

GRB<-­‐-­‐-­‐-­‐>  Galaxy

Fan, Yin, Matteucci 2010

Morphology/metallicity

Berger  2011

SFR Metallicity Age

Long  GRB  ,  host  by  faint,  metal  poor,  star  forming  hosts  (Irs)?  Short  GRB,  host  by  old  popula;ons?    

GW  <-­‐-­‐-­‐-­‐>    GRB  <-­‐-­‐-­‐-­‐>  galaxy

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ì  Observa;onal  triangle

GRB  070201,    M31  and    no  Ns-­‐Ns    Merger  in  M31  Abbo^  et  al.  2008  

GRB

galaxy?

Location Distance

Energy source

Host properties

GW

Fan, Messenger & Heng, ASSP, 2014

Our  Bayesian  approach    

ì  Develop  Bayesian  approach  to  combine  GW  observa;ons  with  non-­‐GW  (EM,  neutrinos,  others…)  informa;on/observa;ons    ì  Gives  the  posterior  probability  on  desired  parameters  from  joint  

observa;ons  ì  Model  selec;on  (on-­‐going  project)  

ì  Loca;ng  host  galaxies  of  GW  sources  seemed  like  an  interes;ng  applica;on      ì  Applicable  to  joint  observa;ons  with  EM,  plus  other  applica;ons  (eg.  

Cosmology)  

ì  As  a  first  test  of  our  proposed  method,  we  focus  on  CBC  sources  because  they  give  nicer  error  regions  and  also  provide  a  distance  es;mate        (first  detec;on!  )  

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A Bayesian approach : Joint  observations  with  GW  ì  D  represents  the  gravita;onal  wave  data  

ì  S  represents  the  non-­‐GW  observa;ons  

ì  in  this  case,  S  represents  the  galaxy  catalogues  used  

ì  γ  represents  the  common  parameters  between  the  D  and  S  data  ì  here,  γ  corresponds  to  the  RA,  dec  and  distance  

ì  want  to  obtain  posterior  probability  on  common  parameters  

ì  use  Bayes  theorem  to  write  down  an  expression  for  this  

9 posterior

parameter priors likelihood

evidence

p(�|S,D, I) =p(�|S, I)p(D|S, �, I)

p(D|S, I)Fan,  Messenger  &  Heng.  ApJ,  2014

A Bayesian approach (i) : Joint  galaxy  observations  with  GW

ì  We  choose  to  call  the  galaxy  catalogue  prior  the  MMPF    ì  So,  if  we  have  the  correct  MMPF  func;on,  the  GW  is  most  likely  to  originate  from  the  

host  galaxy  with  the  largest  value  in  the  posterior  probability  ì  rank  poten;al  GW  host  galaxies  based  on  this  probability  

=p(�|S, I)p(�|D, I)

p(�|I)

= f(�)p(�|D, I)

p(�|I)

prior on sky location with your favorite galaxy catalogue and model

p(�|S,D, I) =p(�|S, I)p(D|I)

p(�|D, I)p(D|I)p(�|I)

inference on sky location from GW parameter estimation with your favorite pipeline

The  final  posterior  probability  of  common  parameters:  

A  few  things  to  note  

ì  The  derived  expression  is  applicable  to  any  joint  GW/non-­‐GW  observa;ons  ì  in  fact,  it  is  applicable  to  any  observa;ons  that  

involve  two  independent  measurements  with  common  parameters  

ì  Since  we  do  not  know  which  galaxies  are  more  likely  to  host  GW  progenitors,  we  basically  create  our  own  MMPF    ì  insert  your  favorite  model  as  the  MMPF  ì  MMPF    is  easily  updated  with  new  informa;on   11

The  current  MMPF

ì  Only  use  sky  loca;on  、distance  and    blue  band  luminosity  

ì  Based  on  Gravita;on  Wave  Galaxy  Catalog  (White  et  al  2011)    ignoring  the  completeness  within  100  Mpc  

ì  d^2  distribu;on  beyond  100  Mpc    

ì  Ignore  EM  data  error  

ì  Ignore  source  offset  effect    

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Simulation  and  analysis  details  ì  To test the effectiveness, we use the GWGC catalogue and inject NS-

NS signals into simulated Advanced HLV noise ì  NS mass prior: 1.3 to 1.5 solar masses ì  all other parameters had the usual ranges (eg. -1 < cos i < 1)

ì  We run 1000 realisations where each involves an injection with random parameter values and located at a randomly selected galaxy and 7000 realisations beyond GWGC distance cut (with relevant MMPF function weighting)

ì  Parameters for the injected signals were recovered using LALinference with the same priors from which the injection parameters were selected ì  assumed unknown but within allowed ranges

ì  Note that the code was modified so that the prior on the distance was only accounted for by the galaxy catalogue

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Cumulative probability

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p50 =NX

i

pi � 50%

For example

So, ~8.5% of injections have 50% of the probability included in the top 10 ranked galaxies

where pi is the probability of each galaxy

1/8=0.125 Need  new  gravita;on  wave  galaxy  catalog！

Learn  more：Inclination angle

ì  Inference on the host galaxy provides a distance which can be used to obtain a better estimate on the inclination angle

Other  simulations:flexibility  of  our  method  

ì  We  have  also  performed  studies  using  injec;ons  (<10  Mpc  in  Nearby  galaxy  catalog)  where  the  host  galaxies  are  weighted  by  the  K  band  and  recovered  with  an  MMPF  func;on  weighted  by  either  the  K  band  or  the  B  band  

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Nearby galaxy catalogue used to obtain K band info, simulation for initial LIGO-Virgo network

K band based MMPF B  band  based  MMPF

inj_LK >B_LK A_LB>inj_LB

A Bayesian approach (ii): Joint  sGRB  observations  with  GW

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S-­‐GRB

L-­‐GRB

Simulation  and  analysis  details  ì  inject NS-NS signals into simulated Advanced HLV noise

ì  source sky (α,β) is randomly chosen in the sky map of GRB ì  Distance : 200 Mpc ì  cosine inclination angle cos ι is randomly chosen between cos θjet and 1 ì  all other parameters are from the usual ranges

ì  SGRB data: ì  the prior of half-opening angle of SGRB jet θjet is the uniform distribution

between 5◦ to 30◦ ì  Set a SGRB sky map with the injection location as the central (1 sqr

degree!) ì  Parameters for the injected GW signals were recovered using LALinference

with the same priors from which the injection parameters were selected ì  assumed unknown but within allowed ranges

ì  Note that the code was modified so that the prior on the distance was only accounted for by the galaxy catalogue

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Task:  merger  time  parameter  

ì  Time  window  between  GRB  and  GW:    ì  Baret  et  al  2011  

ì  Lalinference    ì  the  ;me  of  coalescence  was  assumed  uniform  on  the  ;me  

window  ±40msec  around  the  true  injected  value.    

ì  Ignore  the  GRB    ;me  parameter/data  

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Preliminary  results

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Need  to  know:    Sky  loca;on  error  of  sGRB?

Summary  and  future  work  

ì  SGRB  sky  map  will  not  improve  the  distance  es;ma;on  ì  The  (improved)  distance  es;ma;on  is  dominated  by  the  prior  

of  SGRB    open  angle  ì  Inclina;on  angle  is  improved  ì  Need  to  include  the  merger  ;me  parameter    ì  Need  to    test  the  improvement  on  SGRB  luminosity  es;ma;on  

ì  Based  on    distance  es;mate  ì  Include    more  complete  GRB            data    and  model    ì  Include    host  galaxy?      

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Take  home  message

ì  Detec;on  very  soon!  

ì  GW  astronomy,  new  window!  (Pls  test  our  Bayesian  approach!)  

ì  Need  combina;on  of  technological  innova;ons  ,  data  analysis,  astronomy  and  physics    (people  work  together!)