Searching  for  Radio  Pulsars
David  Champion
Max-­‐Planck-­‐Ins=tut  für  Radioastronomie

Outline
•   Finding  the  first  pulsar
•   Radio  telescopes  and  data   recording  systems
•   Searching  for  pulsars
–   Where  do  you  search
–   ScaEering
–   Fourier  transforms
–   Dispersion
–   Accelera=on  searching
–   Processing  the  data
–   SiGing  the  results
•   Latest  surveys
–   Current  survey  details
–   Highlights
•   Single  pulse  searches
–   Fast  Radio  Bursts
•   Near  future  (now)
–   Extending  the  accelera=on  search
–   Fast  Folding  Algorithm
–   Phased  Array  Feeds
–   Ultra-­‐broadband  receivers
•   The  Square  Kilometre  Array

New discoveries advance our knowledge
Rotating radio transients, 2006.
First globular cluster PSR, 1987.
First millisecond PSR, 1982.
Double PSR, 2004.
(most precise test of GR!)
Fermi points to 32 millisecond
PSRs, 2009...
Credit: Michael Kramer
First binary pulsar, 1974.
(Noble prize for inferring the existence of GW!)
First exoplanet found around a PSR, 1992
Radio magnetars, 2006.
First pulsar discovery by the general public, 2010.
Eatough

Observing  pulsars

Why  the  radio?

ADC
Baseband  recording
0
LO
1
0
0
BB
LSB IF USB
LO
2
RF
Freq
Freq
Freq

The  Radio  Sky
Hazlam et al

Mul=beam  Systems

Searching  for  pulsars

Where  do  you  search?
•   Pulsars  are  incredibly  weak  and  can  only  be  detected  within  our  local
Galaxy,  The  Milky  Way  (rela=vely  nearby)

Where  do  you  search?
•   Pulsars  are  incredibly  weak  and  can  only  be  detected  within  our  local
Galaxy,  The  Milky  Way  (rela=vely  nearby)
C. Ng

Where  do  you  search?
•   Pulsars  are  incredibly  weak  and  can  only  be  detected  within  our  local
Galaxy,  The  Milky  Way  (rela=vely  nearby)
C. Ng

Where  do  you  search?
•   Pulsars  are  young  objects  associated  with  the
Galac=c  plane
•   Recycled  pulsars  are  found  at  greater  scale  height   and  in  globular  clusters
•   MSPs  are  more  difficult  to  find  in  the  Galac=c   plane
•   Pulsars  have  been  found  in  the  Magellanic  clouds
•   A  large  collec=ng  area  and  large  beam  make   single  dishes  ideal

ScaEering  and  frequency  selec=on
•   Cannot  be  corrected  for
•   Worse  at  low   frequencies
•   Worse  in  the  plane
•   Pulsars  stronger  at  low   frequencies
•   DM  and  scaEering  weaker   at  high  frequencies
•   Compromise  of  1.4  GHz   oGen  used
Lorimer and Kramer

Radiometer  equa=on
•   S min
–  sensi=vity  (1  Jy  =  1  x  10 -­‐26   W  m -­‐2   Hz -­‐1 )
•   Beta  –  digi=sa=on  factor
•   S/N min
•   T sys
–  signal  to  noise
–  system  temperature
•   G  –  gain
•   n p
–  number  of  polarisa=ons
•   t int
–  integra=on  =me
•   Delta  f  –  bandwidth
•   W  –  pulse  width
•   P  –  pulse  period
S min
= β
(S / N
G n min p t int
)T
Δ f sys
W
P − W

Searching  for  periodic  signals

Fourier  transform
•   Uses  a  superposi=on  of   sine  waves  to  describe  a   repea=ng  signal
•   The  sine  waves  will  be   harmonically  related
•   The  fast  Fourier   transform  (FFT)  is  an   efficient  algorithm  to   compute  the  discrete
Fourier  transform

Fourier  transform
•   Uses  a  superposi=on  of   sine  waves  to  describe  a   repea=ng  signal
•   The  sine  waves  will  be   harmonically  related
•   The  fast  Fourier   transform  (FFT)  is  an   efficient  algorithm  to   compute  the  discrete
Fourier  transform

Searching  for  periodic  signals
FFT
Time domain Frequency domain
•   Single  pulses  are  very  weak  in  the  =me  series.
•   FFTs  are  used  to  detect  periodic  signals.
•   Harmonic  summing  increases  delectability  of  low  duty  cycle  pulsars.
•   To  detect  MSPs  (~500  Hz)  typical  sample  =mes  are  ~64  μs  (~7800  Hz).
•   Increased  observa=on  =me  (4300  s)  and  bandwidth  (~340  MHz)  gives  improved   sensi=vity.
•   Typical  FFT:  15,000,000  samples  -­‐>  60  MB
•   Radiometer  equa=on:
S min
= β
(S / N
G n min p t int
)T sys
Δ f
W
P − W
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Searching  for  periodic  signals
•   Single  pulses  are  very   weak.
•   FFTs  are  used  to  detect   periodic  signals  in  the
=me  series.
•   Harmonic  summing   increases  delectability  of   low  duty  cycle  pulsars.
CSIRO.
Measuring the mass of Jupiter using pulsars

A  pipeline
Prepare the data
RFI removal
FFT
Harmonic summing
Sift and fold the candidates

Dispersion
•   Radio  frequency   dependent  delay  in  the   arrival  =me  of  pulses
•   Caused  by  free  electrons   along  the  line  of  sight
•   High  frequencies  arrive   before  low  frequencies
•   Strongest  in  the  plane
•   Limits  the  volume  in  which   we  are  sensi=ve  to  pulsars

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Dealing  with  dispersion
•   Use  a  filterbank  to  split   bandwith  into  channels
•   Corrected  by  adding  a   progressive  =me  delay
•   Dispersion  is  ini=ally  unknown,
~1500  of  trials  required
•   Large  data  files  (18  GB)  make   dedispersion  a  slow  process
•   Subbanding  and  treeing   techniques  radically  speed  up   the  process
•   Downsampling  occurs  at  the   diagonal  DM  (when  intra   channel  smearing  =  2*tsamp)
Lorimer and Kramer

Modern  filterbank  backends
•   Firmware  can  be  reprogrammed  for  variable   sampling  =me  and  number  of  channels
•   Bandwidths  of  300  MHz  at  1.4  GHz
•   Covered  by  512  channels
•   Sampling  =mes  of  50  μs
•   32  bit  data
•   Observa=ons  produce  many  GBs  per  hour

A  pipeline
Prepare the data
RFI removal
Dedisperse
FFT
Harmonic summing
Sift and fold the candidates x1500
New DM

Searching  for  binaries

Eatough
•   In binary systems spin period can change over the observation due to the Doppler effect.
•   In a standard pulsar search spin frequency is smeared over a number of spectral bins.
FFT

•   Pulsars  in  a  binary  orbit  are   accelerated.
•   Accelera=on  smears  out  the   pulse  over  the  period  of  the   observa=on..
•   By  searching  in  accelera=on   space  the  signal  strength  can  be   recovered.
•   Equivalent  can  be  done  in
Fourier  space
•   Number  of  trials  is  propor=anal   to  1/Tsamp  and  Tobs^2
Eatough
Accelera=on  searches
ν (t) = ν
0
(1 − V (t) / c)
Doppler formula
V ( t ) = Ω b a p sin i
(
1 − e
2
)
[ cos( ω + A
T
) + e cos ω ]
Line of sight velocity from Keplers laws.
Search in five dimensional parameter space. Not possible!
V (t) = V
0
+ a
0 t + j
0 t
2
2!
+ ...
If the observation time is significantly shorter than the orbital period, can make linear approximation i.e. search for constant accelerations.
Resample then FFT

Eatough 2009
Range  of  accelra=on
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CSIRO.
Measuring the mass of Jupiter using pulsars
Accelera=on  searches
•   Pulsar  in  a  binary  orbit  are   accelerated.
•   Accelera=on  smears  out  the   pulse  over  the  period  of  the   observa=on.
•   The  pulsar  becomes  less   detectable.
•   By  searching  in  accelera=on   space  the  signal  strength  can   be  recovered.
•   Longer  observa=on  would   require  a  second  deriva=ve.

A  pipeline
Prepare the data
RFI removal
Dedisperse x1000
Remove acceleration
FFT
Harmonic summing
New acceleration x1500
New DM
Sift and fold the candidates

•   Accelera=on  search  works  only  if   T obs
≤ P orb
/ 10
•   Number  of  trials  is  propor=onal  to  1/Tsamp  and  Tobs^2
•   For  our  long  observa=ons  we  must  segment  the  data  and  search  each   segment  independently.
•   Each  search  is  sensi=ve  to  different  binary  systems.
70 min
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Orbits  detectable
•   P
MinOrb
=  10  T
Obs
(depending  on  orbital  phase,   eccentricity  etc)
•   For  HTRU-­‐S  P
MinBin
=  12  hr
•   Splipng  observa=ons  increases  sensi=vity  to   short  orbital  periods  (and  helps  with   computer  power)
•   Some  power  can  be  regained  by  incoherent   addi=on  of  parts  (e.g.  stack  slide)

Processing  the  Data

•   1  Petabyte  =
1,024  Terabytes  =
1,048,576  Gigabytes
•   250  of  the  largest  hard   drives
•   6,600  iPods
•   223,100  DVDs
•   1,431,700  CDs
•   745,645,000  Floppy   disks
•   140,737,488,000  sides   of  paper

www.einsteinathome.org
…mit dem Bildschirmschoner Pulsare finden
Wex

Graphics  Processor  Unit
•   Designed  to  render  3D  objects  in   real=me  to  display
•   Primarily  used  for  gaming
•   Graphics  rendering  is  a  highly   parallel  process
•   GPUs  were  designed  with  large   numbers  of  individually  slow   processors
•   RAM  on  board  GPU  accessible  to  all   processors
•   Moving  data  between  GPU-­‐RAM   and  CPU-­‐RAM  slow
•   Non-­‐graphics  usage  lead  to  the   development  of  General  Purpose
GPUs  (GPGPUs)

The  GPU  pipeline
•   Project  lead  by  Swinburne
University  in  Melbourne
•   PhD  students:  Ben  Barsdell  &  Paul
Coster
•   Post  Doc:  Ewan  Barr  (MPIfR  PhD   student)
•   Staff:  MaEhew  Bailes  and  Willem   van  StraEen
•   CUDA  /  C++
•   Designed  to  find  pulsars  in   rela=vis=c  orbits
•   CUDA  and  Thrust  libraries
•   Modular
•   Algorithms  based  on  well  known
Sigproc  pulsar  soGware
•   Designed  to  run  on  an  arbitrary   number  of  GPUs  with  processing
=me  decreasing  linearly  with  #GPUs

SiGing  the  results

A  pipeline
Prepare the data
RFI removal
Generate time series for each DM x1000
Remove acceleration
FFT
Harmonic summing
New acceleration x1500
New DM
Sift and fold the candidates

Visualisa=on

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Latest  surveys

High  =me  resolu=on  Universe  surveys
•   Recent  improvements  in  hardware  that  u=lize  field  programmable  gate   arrays  to  produce  high  resolu=on  digital  filterbanks.
•   Dispersion  smearing  across  individual  frequency  channels  reduced.
Analogue filterbank
W eff
= W int
•   BeEer  sensi=vity  distant,  highly  dispersed  MSPs!
+ τ + τ + τ + τ + τ + τ
•   HTRU  -­‐  Collabora=on  between  pulsar  groups  in  UK  (Uni.  Manchester),
Australia  (Swinburne/CASS),  Germany  (MPIfR-­‐Bonn),  Italy  (Cagliari)  to   perform  an  all-­‐sky  survey  to  find  highly  dispersed  MSPs  missed  in  previous   surveys!

Eatough
High  =me  resolu=on  Universe  surveys
•    Some  numbers  on  the  new  hardware…
Number of frequency channels
Channel bandwidth
Parkes analogue filterbank.
Parkes/Swinburne
BPSR digital filterbank.
96 1024
3 MHz 0.3 MHz
Dispersion smearing
(central channel)
10 us per
DM unit
1.3 us per
DM unit
•    We  are  finding  new  pulsars!  16     from  Effelsberg,  +100  at  Parkes.  Diamond     planet,  magnetar,  Cosmological  bursts,
Eccentric  binary  MSP  in  the  North….
BPSR, Parkes.

Discovery  highlights
•   A  pulsar  with  a   diamond  planet
•   A  magnetar  in  the   radio
•   3  extra-­‐galac=c  bursts
•   Several  precise  =mers
•   An  MSP  in  an   eccentric  orbit

Fast  Radio  Bursts

Single  pulse  searches
•   Some  pulsars  emit  single   strong  pulses
•   Not  frequent  enough  to   be  seen  in  FFT
•   Search  for  single   dispersed  pulses  using   boxcars  of  various  widths
•   Hope  to  find  several   pulses  at  the  same   dispersion
CSIRO.
Insert presentation title, do not remove CSIRO from start of footer

Search  pipeline
Prepare the data
RFI removal
Dedisperse
FFT
SP search New boxcar x1500
New DM
Harmonic summing
Sift and fold the candidates

Lorimer  and  Keane  Bursts

Extra-­‐galac=c  burst  discoveries
FRB: Fast Radio Burst, 4 detections in 11% of full sky
Thornton et al. 2013

4  FRBs
Thornton et al. 2013

FRB  110220
Thornton et al. 2013

Real=me  transient  pipeline
Swinburne Thornton et al. 2013

Loca=ons  of  the  bursts
Thornton et al. 2013

DMs  of  the  bursts
Thornton et al. 2013

DM  and  redshiG
Thornton et al. 2013

Near  Future
(now)

Extending  the  accelera=on  search
•   The  Porb/Tobs  ra=o  can  be  increased  by  including  the   accelera=on  deriva=ve,  jerk
V (t) = V
0
+ a
0 t + j
0 t
2
2!
+ ...
•   Increases  sensi=vity  by  having  a  greater  amount  of  data   added  coherently
•   Number  of  trials  is  propor=onal  to  1/Tsamp  and  Tobs^3
•   There  is  some  covariance  with  accelera=on  that  will  increase   the  trial  spacing  of  both

A  pipeline
Prepare the data
RFI removal x1500
Dedisperse x1000
Remove acceleration x1000
Remove jerk
FFT
Harmonic summing
New jerk
New DM
New acceleration
Sift and fold the candidates

FFT  Sensi=vity  Limita=ons
•   FFT  sensi=vity  degrades  for   long  period  pulsars
–   Smaller  number  of  pulses
–   Red  noise  contamina=on
•   Demonstrated  in  PALFA   survey  results
–   Lazarus  et  al.  (in  prep)
•   Actual   S min
determined  via   synthe=c  profile  injec=on
•   Theore=cal   S min
determined   via  radiometer  equa=on:
S min
= β
(
S
G
N min
)
T sys n p t int
Δ f P
W
− W
Figure from Lazarus et al. (in prep), showing difference between actual vs. theoretical sensitivity in
PALFA survey (FWHM = 2.6%)
Andrew David Cameron

The  Fast  Folding  Algorithm  -­‐  FFA
•   Why  not  just  fold  trial  periods  directly?
–   Prohibi=vely  computa=onal  expensive
–   Increasing  processing  power  makes  large  period  searches  viable
•   Enter  the  Fast  Folding  Algorithm  (FFA)
–   First  proposed  by  Staelin,  1969
–   Improves  folding  efficiency  from  O(N 2 )  to  O(NlogN)
•   BeEer  suited  to  longer  periods
–   Computa=onal  expense  decreases  with  long  periods
•   Highly  parallelisable
–   Well  suited  to  GPU  implementa=on  –  further  speed  boost
Andrew David Cameron

The  Fast  Folding  Algorithm  -­‐  FFA
1   2   3   4   5   6   7   8
1
4
7
2
5
8
3
6
9
10   11   12
0
1
0
1
1  +  4   2  +  5   3  +  6
1  +  5   2  +  6   3  +  4
7  +  10   8  +  11   9  +  12
7  +  11   8  +  12   9  +  10
9
0
10   11   12
1+4+
7+10
2+5+
8+11
3+6+
9+12
Period
3
1
1+4+
8+11
2+5+
9+12
3+6+
7+10
3 1/3
1
1+5+
8+12
2+6+
9+10
3+4+
7+11
3 2/3
2
1+5+
9+10
2+6+
7+11
3+4+
8+12
4

Phased  Array  Feeds
•   ~100  elements
•   The  elements  are  phased-­‐up   to  produce  ~36  beams   instantaneously
•   300  MHz  BW
•   Increases  survey  speed  by   factor  of  4.5
•   Also  increases  data-­‐rate
•   48  FPGAs,  96  digi=zers
•   Beamforming  requires  another   bunch  of  FPGAs
•   300  MHz  x  10bits  x  96   elements  x  2  pol  =  70  GB/s
•   AGer  beamforming  22  GB/s
•   This  is  per  dish!
•   Real-­‐=me  RFI  rejec=on

Ultra  Broadband  Receivers
•   Tradi=onal  receivers  have
~300  MHz  BW
•   UBB  has  nearly  2.5GHz  BW
•   Increases  sensi=vity  to  weak   pulsars  without  increasing   integra=on  =mes
•   Dispersion  becomes  a  major   factor
•   Split  the  broad  BW  into  many   subbands  and  sample  at  BB
•   Significant  compu=ng  power   required  to  record  data

Looking  further  ahead

The  Square  Kilometre  Array
•   An  large  array  of  small  telescopes   with  1sq  km  collec=ng  area
•   Thousands  of  dishes  required
•   A  mixture  of  technologies  at   different  frequencies
•   Located  in  Southern  Africa  and  in
Western  Australia
•   Germany  is  now  a  member  of  the
SKA
•   >100  peteflops  required
•   Many  PB/s
•   Phase  1  =  20%
•   Located  in  two  cores  with  smaller   sta=ons  spread  over  the  con=nents
•   Will  require  real=me  pulsar   searching

Summary
•
•
•   Gain,  BW,  obs  =me  are  key  to   sensi=vity
Searching  for  pulsars
–   Search  in  our  galaxy   new  technology  finds  new   pulsars
•   Fast  radio  bursts
–   Hot  topic!
–   ScaEering  limits  the  low  frequencies   •   Near  future  (now)
–   FFTs  to  find  periodic  signals
–   Extending  the  accelera=on  search
–   Dispersion  and  accelera=on  need  to  be   searched
–   Computa=onal  power  limits  the  search   space
–   ANNs  used  to  siG  results
–   Fast  Folding  Algorithm
–   Phased  Array  Feeds
–   Ultra-­‐broadband  receivers
•   The  Square  Kilometre  Array
Latest  surveys   –   Will  provide  huge  gain!
–   Searching  the  same  area  with