I primi passi della Radio Astronomia

Primordial Gravitational
Wave detection: the role
of the pulsar timing arrays
ANDREA POSSENTI
INAF – Osservatorio Astronomico di Cagliari
on behalf of the Epta-Leap collaboration
Outline
1. Pulsar Timing Concepts
2. Pulsar Timing Array and GW detection
3. Ongoing experiments and perspectives
28 Aug 2009 - CMS
1.
Pulsar Timing Concepts
28 Aug 2009 - CMS
What is a Radio Pulsar
@Kramer
A PULSAR is a rapidly rotating and highly
magnetized neutron star, emitting a pulsed radio
signal as a consequence of a light-house effect
Timing idea: observations
Performing repeated observations of the Times of Arrival
(ToAs) at the telescope of the pulsations from a given pulsar
and
searching the ToAs for systematic trends on many different
timescales, from minutes to decades
Timing of a radio pulsar: operations
for getting a ToA
@ Lorimer
The dedispersion
Single pulse profile
vs
integrated profile
Determination of the TOPOCENTRIC
Times of Arrival (ToAs)
ToA uncertainty (ω = width of the pulse, P=pulsar period):
Timing idea: modeling
if a physical model adequately describes the systematic trends in
the ToAs, it is applied with the smallest number of parameters
otherwise
if a physical model is not adequate,
it is extended (adding parameters) or rejected in favour of
another model
when a model finally describes accurately the observed ToAs, the
values of the model’s parameters shed light onto the physical
properties of the pulsar and/or of its environment
Timing key quantity: the residuals
Given the full set of parameters (a1, a2, …, an) of a model, the i-th
residual ri is the difference in rotational phase Φ (with -0.5<ri<+0.5)
between the observed phase of arrival of the i-th pulse and the
phase of arrival of that pulse as predicted by the model
ri = Φobserved (i-th pulse) – Φmodel(a1, a2, …, an)(i-th pulse)
In an iterative procedure, one least-square fits on suitable
subsets of the possible parameters (a1, a2, …, an) of the model,
in the aim to remove apparent trends and thus eventually to
approach ri << 1
Timing analysis: removing trends
Thanks to the least-square fit
procedure, one can
iterativelly solve for
rotational, positional and
kinematic parameters as well
as for binary keplerian (when
applicable) and sometimes
post-keplerian parameters
Timing analysis quality: rms
Good timing solution → no evident trend and ri << 1 for all observed pulses
The quality of the timing solution is usually given in term
of the root mean square rms of the residuals:
the smaller rms is, the smaller physical effects
can be measured
High precision pulsar timing: which targets?
Ordinary pulsars:
~ 1650 known objects;
NSage < few 107 yr
NOT SUITABLE FOR
HIGH PRECISION
TIMING
log
relatively long pulses
&
rotational irregularities
Recycled pulsars:
~ 140 known objects;
NSage > 108-109 yr
The most rapidly rotating
are known as millisecond
pulsars
ATNF Pulsar Catalogue
Recycling scenario: A died pulsar is spun up and rejuvenated by
an evolving binary companion, and eventually shines as a
millisecond pulsar, often still orbiting the companion star
[Bisnovati-Kogan & Kronberg 1974, Alpar et al. 1982]
High precision timing: a prototype source
• P = 2.9471 ms
• Pb = 1.5334 d
• x = ap sin(i) = 1.8980 lt-s
•e = 1.3 · 10-7
• s = 0.9982
• r = 1.004 μs
• Parkes timing with CPSR2
Rms residuals:
daily (~2 hr): 74 ns
•From Shapiro delay:
i = 86.58  0.1 deg
mc = 0.204  0.002 Msun
• From mass function:
mp = 1.438  0.024 Msun
[Jacoby et al. 2005]
PSR J1909-3744
Atomic clocks vs MSP timing
[ Lorimer 2008 ]
…a subsample of the millisecond pulsars shows a rotational
stability comparable to (or, over few yrs timescale, better than)
the best atomic clocks
2.
Pulsar Timing Array and
GW detection
28 Aug 2009 - CMS
Pulsars as GW detectors
Source
of GWs
The Pulsar-Earth path can be used as the arm of
a huge cosmic gravitational wave detector
Perturbation in space-time can be
detected in timing residuals over a
suitable long observation time span
Radio
Pulsar
Sensitivity (rule of thumb):
hc(f)~
σ TOA
T
Earth
where
hc(f) is the dimensionless strain at freq f
σTOA is the rms uncertainty in Time of Arrival
T is the duration of the dataspan
An instructive application
[ Jenet et al 2004 ]
The radio galaxy 3C66 (at z = 0.02) was claimed to harbour a
double SMBH with a total mass of 5.4 · 1010 Msun and an
orbital period of order ~yr [ Sudou et al 2003]
Timing residuals from PSR B1855+09 exclude
such a massive double BH at 95 c.l.
The GW back(fore?) grounds: some sources
Expected (?) amplitudes and
spectral shape
hc(f)~Af
2
0, H
h

A  10 16  10 15
;@f
GW ( f )  f
 1 yr ;   2 / 3
2 2 
 f
( 2 / 3) 
hc(f)~Af
merging massive BH binaries
in early galaxy evolution


M
f 
 9

10 yr 10 M sun 
1
[ e.g. Phinney 2001; Jaffe & Backer 2003;
Jaffe & Backer 2003, Sesana,Vecchio et al 2008]

Kind of sources
1/ 2


a


 0.01pc 
A  10 17  10 15
;@f
 1 yr ;   1
early universe
and inflationary era
h02, H GW ( f )  f 22   f 0
[ e.g. Grishchuck 2005; Boyle & Buonanno 2008]
hc(f)~Af

3/ 2
A  10 16  10 14
;@f
 1 yr ;   7
6
2
h02, H GW ( f )  f 22   f (1/ 3)
[ e.g. Caldwell et al 96; Maggiore 2000; Damour & Vilenkin 2005]
string cosmology
and cosmic strings
The “best” case for a single source
Remembering the approx formula
hc(f)~
σ TOA
T
one can estimate that for detecting the expected GW background from merging
of SMBHs (strain amplitude hc ~ 10-16-10-15) would require at least a timing
stability σTOA < 10-100 ns over few years
The best result so far using a single source is from 8-yr timing of PSR
B1855+09 at Arecibo implying limit for f~7 nHz [ Kaspi et al 94]
hc <~ 10-13
ΩGW h0,H2 (1/8 yr) <~ 1.1 10-7
Extended dataset led to ΩGW h0,H2 (1/17 yr)<~ 2 10-9 [Lommen et al 2002] but not
confirmed yet by independent analyses [Jenet et al 2006].
Subject to uncontrollable timing noise effects!
A pulsar timing array (PTA)
Using a number of pulsars distributed across the sky it is possible
to separate the timing noise contribution from each pulsar from the
signature of the GW background, which manifests as a local (at
Earth) distortion in the times of arrival of the pulses which is
common to the signal from all pulsars
A pulsar timing array (PTA)
A(t) dimensionless amplitude of the GW at time t
Ni(t) intrinsic timing noise of the i-th pulsar at time t
αi geometric term dependent on pulsar sky coord and GW prop&polar vectors
νi rotation frequency of the i-th pulsar
δνi fractional frequency shift detected in the i-th pulsar
i
  i A(t )  N i (t )
i
By cross-correlating ‹brackets…› the observations of i-th and j-th pulsars, one gets
 i j A (t )   i A(t ) N j (t )   j A(t ) N i (t )  N i (t ) N j (t )
2
Since GW amplitude and intrinsic timing noise are uncorrelated the
latter 3 terms tend to become negligible while the dataspan (i.e. number
of observations) and the number of pulsars become large enough
A pulsar timing array (PTA)
Idea first discussed by Romani [1989] and Foster & Backer [1990]
 Clock errors
Pulsar b
All pulsars have the same TOA variations: Pulsar a
Monopole signature
 Solar-System ephemeris errors
Dipole signature
 Gravitational waves background
θab
Quadrupole signature
1  cos ab
3 1  cos ab
1 1  cos ab
1 1
 ( ab )  (
) log(
) (
)    ab
2
2
2
4
2
2 2
Hellings & Downs [1983]: correlation that an isotropic and stocastic GWB leaves on the
timing residuals of 2 pulsars a and b separeted by an angle θab in sky
Can separate these effects provided there is a
sufficient number of widely distributed pulsars
[ adapted from Manchester ]
Pulsar timing arrays: sensitivity curve
A too simple (interpretation of the) sensitivity curve…
Limited by total
Tobs≈ few yrs ≈
few 108 sec
Limited by interval
btw observations:
days→weeks ≈
106-107 sec
White timing noise
contribution
For pulsar with white
timing noise, best
sensitivity for f≈1/Tobs
More realistic sensitivity curves can be obtained only using data
analysis of simulated data
Pulsar Timing array(s): the frequency space
Note the complementarity in explored frequencies with respect
to the current and the future GW observatories, like LIGO,
advLIGO, advVIRGO and LISA
PTA
Adv LIGO/VIRGO
LISA
CMB-POL
Data analysis methodologies
Spherical harmonic decomposition
[Burke 1975, Dettweiler 1979, Jaffe & Backer 2003, Demorest et al 2005]
Two point correlation
Correlating the time derivative of the
residuals [Hellings & Downs 1983]
Directly correlating the time residuals
[Jenet et al 2005]
Bayesian analysis
[van Haasteren, Levin, McDonald, Lu 2008]
Robust: deals easily with unevenly sampled data, variable number of tracked
pulsars, etc.
Marginalisation: deals easily with all systematics of known functional form,
including the timing model
Capable to simultaneously measure the amplitude and the shape of the GWB
Data analysis methodologies
Bayesian analysis of the timing residuals of an ensemble of pulsars
[van Haasteren, Levin, McDonald, Lu 2008]
[@ van Haasterann 2008]
Sanity check tests:
Useful for optimizing PTA(s) experimental setup
Duration of the experiment
>≈ 5-10 yr
[@ van Haasteren 2008]
Number of pulsars
≈ 20-25
Typical rms of the timing data
S/N>2
rms < 200 ns
Rate of data taking
3.
Ongoing experiments and
perspectives
28 Aug 2009 - CMS
I. Current projects: PPTA
Parkes Pulsar Timing Array: PPTA
@ M.Burgay
Australian based, using Parkes 64m dish
Running since ~ 2003 and currently achieving the
best results so far
[ @ D.Manchester ]
The currently used set of observed millisecond
pulsars in the PPTA australian project
P < 20 ms and not in globular clusters
hc [1/(1 yr)]< 1.1 × 10-14
gw[1/(8 yr)]h0,H2 < 1.2  10-8
[ Hobbs et al. Dec 2008 ]
With ~ 2 yr of useful data
and 7 MSPs used (5 with
a rms < 300 ns)
For full PPTA (rms of 100 ns
over 5 yr for many MSPs)
Factor >10 improvement on
hc and on Ωgw limits
II. Current projects: NANOGrav
North American Nanohertz Observatory for
Gravitational Waves: NANOGrav
USA & Canada based, using the excellent Arecibo 300m
dish and GBT 101m dish and state-of-art backends
Running only since ~ 2008
@ Cornell
@ NRAO
III. Current projects: EPTA-LEAP
European Pulsar Timing Array
+
Large European Array for Pulsar
European based
Running since ~ 2006
The partner institutions
ASTRON,Un.Leiden,Un.Amsterdam NL
University of Manchester, JBO, GB
INAF Osservatorio Astronomico di Cagliari, ITA
Nancay Observatory, FR
Max-Planck Institut fur Radioastronomie, GER
The telescopes
Effelsberg(100 m)-Westerbork(96 m)-Nancay (92 m)-Lovell(76 m)-Sardinia(64 m)
The people
GB
–
Ben Stappers
Andrew Lyne
Mark Purver
Chris Jordan
Sotirios Sanidas
FR
Ismaël Cognard
Gilles Theureau
Grégory Desvignes
Robert Ferdman
–
ITA
–
Andrea Possenti
Marta Burgay
Nichi D’Amico
Maura Pilia
GER
Michael Kramer
Axel Jessner
Kosmas Lazaridis
–
NL
Jason Hessels
Gemma Janssen
Yuri Levin
Rutger van Haasteren
Current limits from EPTA data
Using the data from 6 pulsars:
J1640+22 (dataspan 12 yr ; rms=1.6μs) J1855+09 (dataspan 23 yr ; rms=1.70 μs)
J1713+0747 (dataspan 11 yr ; rms=0.73 μs) J1744-1134 (dataspan 10 yr ; rms=0.55 μs)
J1909-1134 (dataspan 4 yr ; rms=0.11 μs) J1918-0642 (dataspan 7 yr ; rms=2.24 μs)
@ van Haasteren
…and applying a Bayesian analysis [e.g. van Haasteren 2009]
…only a factor ≈ 1.7 worse than
hc [1/(1 yr)]< 1.9 × 10-14 the current published PPTA limit
Long term advantages of EPTA
 Larger total number of TOAs
 Commensurate scheduling will allow for improved binary
and yearly phase coverage
 A wide range of frequencies can be sampled and then
compared in quasi-simultaneous sessions
 Simultaneous same frequency observations can be used to
check polarisation calibration and overall timing offsets
 Telescope, Instrumentation, or Observatory clock based
errors can be quickly identified and corrected
+
 The data will be combined with those provided by
LEAP…
LEAP
Phased array of the 5 major European telescopes
Funded by the EU Research Council: 2.5 M€
People involved: 2 staff, 2 senior postDoc and 2 junior postDoc
Duration: 5 years since mid 2009
Sensitivity equivalent to illuminated Arecibo
But able to see much more or the sky
~ a factor 10
Adapted from Verbiest et al [2009]
Expected sensitivity of EPTA+LEAP after 5 yrs of
observations will largely improve the current best limits for
the GW Background Amplitude
Timing array(s): what is going on…
 The
establishment of the IPTA (International Pulsar Timing
Arrays) is underway
 New more sensitive back-ends adopted at various sites
 Better understanding of the impact of the variations
occurring in the dispersive effects (i.e. of the DM of the pulsars)
 Investigations on the possible occurrence of limits to the
achievable rms
E.g. Verbiest et al [2009]: an rms of 80 ns may be attained over 5 yr of obs for few
pulsars, provided (i) more sensitive observing systems are used, and (ii) enhanced
techniques for the mitigation of frequency dependent effects will be introduced. It will
also be important (iii) to discover additional bright millisecond pulsar with a stability
comparable to the best available examples, like PSR 1909-3744 and J1713+0747
 Better modeling of the red noise component in the timing
residuals , e.g. along the lines of van Haasteren [2009]
Effelsberg
@ van Haasteren
Westerbork
Careful analysis of the “red” component of the timing noise was performed while
calculating the current upper limit for a GWB signal in the Epta data
[van Haasteren 2009]
Timing array(s): the future
@ Stappers
Current projects are evolving in pace with predictions. Then at least
very significant limits on GWB (and hopefully a detection) will be
achieved within 5-10 years
A detailed scientific investigation of the GWBackground is warranted with SKA