Testing gravity theories with pulsar-white dwarf systems - Paulo C. C. Freire Max-Planck-Institut für Radioastronomie Bonn, Germany
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Testing gravity theories with pulsar-white dwarf
systems
Paulo C. C. Freire
Max-Planck-Institut für Radioastronomie
Bonn, Germany
558. WE Heraeus-Seminar, 31st March – 4th of April 2014, Bad Honnef, Germany
Gravity (not the movie)
Nature s most fundamental and mysterious force
Electromagnetism
UQFTGR
Gravity
? Weak Nuclear Force
Strong Nuclear Force
QFT
To achieve a full, coherent picture of the Universe, we must understand gravity.
Do we understand it? GR cannot be the ultimate gravity theory (because of
singularities, incompatibility with GR).
Reasons to doubt…
We don‘t know many things:
What caused cosmic inflation?
What is Dark Matter?
What is Dark Energy?
Cosmic "makeup". Credit: ESA/Planck
• Instead of this many new fields, could our understanding of gravity be at fault?
• MANY alternative theories of gravity have been proposed to explain these phenomena.
• Thus, falsifying or confirming such theories has implications beyond the study of gravity – also for
the study of the origin, evolution and contents of our Universe.
Testing general relativity
• Einstein published the field
equations of general relativity in
November 1915.
• General relativity has since passed
all experimental tests!
• Until 1974, all tests of this theory
were made in the Solar System
(very weak fields, very low
velocities).
• But what if the fields are much
stronger? What if we have
objects moving much faster, and
with much stronger gravitational
fields? – After all, this is what made
Newtonian gravity fail…
Neutron stars
Neutron stars are the remnants of
extremely massive stars. Towards the
end of their lives they explode as
Supernovae!
Neutron stars • The result is a sphere of neutrons with a radius of about 11-13 km, and about 460000 times the Earth’s mass • Gravitational binding energy: about −40 000 Earth masses! • Density in the core is several hundred million tons per cubic cm – significantly higher than at the atomic nucleus!
Neutron stars
Credit: Jim Lattimer
The equation of state for matter at these densities is not known! Very hot topic of research at the
moment.
The discovery of pulsars • In August 1967, Jocelyn Bell, then a graduate student at Cambridge, finds a radio signal in the constellation Sagitta (the Little Arrow) pulsating with a period of 1.33 seconds. She found this to appear 4 minutes earlier every day, indicating a sidereal source. • For this discovery, Anthony Hewish earns the Nobel Prize in Physics 1974. • Sound of PSR B1919+21, as observed at Arecibo on the 13th of June 2006:
The discovery of PSR B1913+16 In 1974, Russel Hulse and Joe Taylor discovered PSR B1913+16, in the constellation Aquila (the Eagle), during a systematic 430-MHz survey of the Galactic plane at Arecibo. First binary pulsar!
PSR B1913+16
• The pulsar and the companion star are
orbiting the common center of mass. The
orbital period is 7h45m and the eccentricity is
0.61.
• This is an astrophysically clean system – no
companion is detected, implying that the
companion is another neutron star.
• We have two point masses with motion
influenced solely by their mutual gravitation,
and one of them is pulsing with the stability of
an atomic clock!
• This is a wonderful laboratory for testing GR
in a completely new regime!Interlude - Pulsar timing Norbert Wex
Pulsar timing
Fold Fold
Model
TOA ResidualThe pulsar model – for isolated pulsars • Phase (at epoch) • Period • Period derivative • RA • Dec • Proper motion • Parallax
Correcting for Earth motion
Residuals in binary pulsars
• In a binary pulsar, having a clock in the
system allows us to measure the range
relative to the center of mass of the binary. If
the timing has a precision of 1µs, that implies
that for each measurement we range the
pulsar’s position in its orbit with a precision of
300 m! – a relative precision of ~10−8 in this
case.
• This is makes pulsar timing thousands of
times more precise for measuring orbital
parameters than Doppler measurements.
• This feature is unique to pulsars, and is the
fundamental reason why they are superior
astrophysical tools.
• This is the reason why I am giving this talk
here!PSR B1913+16 • Five Keplerian parameters can be easily measured: orbital period (Pb), projected size of the orbit, in light seconds (x), eccentricity (e), longitude of periastron (ω) and time of passage through periastron (T0). A non-changing Keplerian orbit is exactly what is predicted by Newtonian gravity. • Without access to information on transverse velocities, the individual masses of the components (m1 and m2) and the inclination of the system (i) cannot be measured, but… • The mass function, a relation between these three quantities, can be measured to excellent precision, as it depends on two observable parameters: • One equation, three unknowns! L
PSR B1913+16
• IF the system is compact and eccentric,
the timing precision allows the
measurement of several relativistic
effects.
• The periastron of PSR B1913+16
advances 4.226607(7) degrees/year.
The daily periastron advance is the
same as Mercury’s perihelion advance
in a century…
• The Einstein delay was also measured:
γ = 0.004294(1) s, due to slowdown of
time near the companion!PSR B1913+16 • These two effects provide two more equations and determine the mass and inclination of the system! This happens because, according to General relativity, they depend on the known Keplerian parameters and the masses of the two objects: • 3 equations for 3 unknowns! J
PSR B1913+16
• The masses of the individual
components (and, from the mass
function, the inclination of the
system!) are only well determined if
we assume that General relativity
applies.
• This was at the time the most
precise measurement of any mass
outside the solar system.
Weisberg, J.M., and Taylor, J.H., “The Relativistic Binary Pulsar B1913+16”, in
Bailes, M., Nice, D.J., and Thorsett, S.E., eds., Radio Pulsars: In Celebration of
the Contributions of Andrew Lyne, Dick Manchester and Joe Taylor – A Festschrift
Honoring their 60th Birthdays, Proceedings of a Meeting held at Mediterranean
Agronomic Institute of Chania, Crete, Greece, 26 – 29 August 2002, ASP
Conference Proceedings, vol. 302, (Astronomical Society of the Pacific, San
Francisco, 2003).PSR B1913+16 • A third relativistic effect is measurable: The orbital period is becoming shorter! • General relativity predicts this to be due to the loss of energy caused by emission of gravitational waves. This depends only on quantities that are already (supposedly!) known: • Prediction: the orbital period should decrease at a rate of –2.40247 × 10−12 s/s (or 75 µs per year!) • Test not possible in the Solar System.
PSR B1913+16
• Orbital decay detected!
• Rate is –2.4085(52) x 10–12 s/s. The agreement
with GR prediction is perfect!
• GENERAL RELATIVITY GIVES A SELF-
CONSISTENT ESTIMATE FOR THE MASSES
OF THE TWO COMPONENTS OF THE
BINARY!
Weisberg, J.M., and Taylor, J.H., “The Relativistic Binary Pulsar B1913+16”, in Bailes, M.,
Nice, D.J., and Thorsett, S.E., eds., Radio Pulsars: In Celebration of the Contributions of
Andrew Lyne, Dick Manchester and Joe Taylor – A Festschrift Honoring their 60th Birthdays,
Proceedings of a Meeting held at Mediterranean Agronomic Institute of Chania, Crete,
Greece, 26 – 29 August 2002, ASP Conference Proceedings, vol. 302, (Astronomical
Society of the Pacific, San Francisco, 2003).Gravitational Waves Exist!!
Pulsar timing arrays
• Interestingly, pulsar timing might allow a direct detection of low-frequency (~10−9 Hz) gravitational
waves!
• These are produced by the mergers of binary supermassive black holes, which are a
consequence of galaxy mergers and evolution.
See David Champion’s Talk
&
Nicolas Caballero’s posterparameters g (the gravitational redshift and time 5-day GBT observing sessions at 820 MHz. On the entries in table S1. The final weighted root
dilation parameter) and s and r (the Shapiro- the time scale of the long-term profile evolution mean square post-fit residual is 54.2 ms. In
delay parameters) are asymmetric in the masses, of B, each 5-day session represents a single- addition to the spin and astrometric parameters,
and their values and interpretations differ for A epoch experiment and hence requires only a the Keplerian parameters of A’s orbit, and five
and B. In practical terms, the relatively low single set of profile templates. The value of xB PK parameters, we also quote a tentative de-
timing precision for B does not require the obtained from a fit of this parameter only to tection of a timing annual parallax that is con-
inclusion of g, s, r, or Ṗb in the timing model. the two 5-day sessions is presented in Table 1. sistent with the dispersion-derived distance.
We can, however, independently measure ẇ wB , Because of the possible presence of unmod- Further details are given in (16).
The double pulsar
obtaining a value of 16.96- T 0.05- yearj1, eled intrinsic pulsar timing noise and because Tests of general relativity. Previous obser-
vations of PSR J0737-3039A/B (8, 9) resulted
in the measurement of R and four PK param-
• Foreters:
theẇ,J0737−3039 double
g, r, and s. Relative to these pulsar
earlier
system, wemeasurement
results, the now haveprecision7 mass for these
parameters from PSR J0737-3039A/B has in-
constraints (previously mentioned,
creased by up to two orders of magnitude. Also,
plus
we mass
have nowratio andthe2orbital
measured constraints
decay Ṗb . Its
from Shapiro
value, measured delay)
at the 1.4% level after only 2.5
years of timing, corresponds to a shrinkage of
the pulsars’ separation at a rate of 7 mm per day.
Therefore, we have measured five PK parame-
• Thistersmeans, 5 tests
for the system ofTogether
in total. GR – with the
mass ratio R, we have six different relationships
including some of the most precise
that connect the two unknown masses for A and
ever!
B with the observations. Solving for the two
masses using R and one PK parameter, we can
then use each further PK parameter to compare
its observed value with that predicted by GR for
• These
the givennow twoinclude the best
masses, providing four test of
indepen-
GR’s
dent predictions for quadrupolar
tests of GR. Equivalently, one can display
these tests elegantly in a ‘‘mass-mass’’ diagram
GW emission
(Fig. – oneoforder
1). Measurement the PKofparameters
magnitude
gives curves on better thanthat
this diagram forare,the
in general,
original
differentbinary pulsar!
for different theories of gravity but
should intersect in a single point (i.e., at a pair
of mass values) if the theory is valid (12).
As shown in Fig. 1, we find that all mea-
For update on PSR J0737-3039,
sured constraints are consistent with GR. The
most precisely measured PK parameter current-
Fig. 1. Graphical summary of tests of etGRal.parameters.
Kramer Constraints
2006, Science,
see Michael Kramer’s Talk
314, 97 on the masses of the two stars (A and
ly available is the precession of the longitude of
periastron, ẇ. We can combine this with the
B) in the PSR J0737-3039A/B binary system are shown; the inset is an expanded view of the region of theory-independent mass ratio R to derive the
principal interest. Shaded regions are forbidden by the individual mass functions of A and B because sin masses given by the intersection region of theirBeyond the double pulsar
coupling function
where A,which B, C is a quadratic
denote a prioripolynomial
three bodies, in but
the Bscalar
= C field
is ϕ: higher-order
a(ϕ) = terms
2 relativistic periastron advance, proportional to
(ϕ − ϕ0 ) + βallowed.
0 (ϕ − ϕThe0 ) /2 [12, 14, 15]. The parameter α0 defines the linearFig. matter-
7 with respect
PPN PPN
lar coupling(2constant
+ 2γ and − ββ0 the ) in the PPNcoupling
quadratic formalism, becomes
of matter to now
two ascalar particles,
A comment on
combination of the above expressions, explicitly written in The mass
ile higher-order vertices are neglected. In this sense, this is a natural extension of of the wh
Could Einstein still be wrong?
BD gravity.
eq. (9.20a) of Damour & Esposito-Farèse (1992). optical data of Pap
But the most spectacular deviation from GR is that The difference is a n
In presence of such
scalar wavesnon-perturbative strong-field
are now also emitted deviations
by any binary away from GR,take
system, we can
into account
• Many alternative theories of gravity predict violation of the strong equivalence principle (SEP).
ve a situation where
thus the effective
contributing to coupling
the observedstrength of the of
variation neutron
the star, αA , ismatter-scalar
orbital of order coup
This leads to several important effects:
period.
ty, even if the For asymmetric
scalar-matter coupling,systems, notably the neutron
α0 , is unobservably small in star-
the Solar System§.
Figure 7 show
ch an effect white
leads dwarf binary studied
to a violation of SEPinthat the present
requirespaper, the main
test systems quadratic
which contain a matter-s
1. Dipolar gravitational
contribution wave
comes emission
from dipolar(tightwaves:
orbits) whatever the value
utron star.
The structure dependence of the effective 2 gravitational constant G , the
hasnonperturbativ
the
D G ∗ Mc q 1 + e /2 2 AB
Ṗb = −2πnb (αp − αc ) , (21) Esposito-Farèse (19
nsequence that the pulsar cdoes qnot 3 + 1fall
(1 −ine the
2 ) same way as its companion in the
5/2
are now derived eit
vitational field of a third body, which in our case is the Galaxy. One finds
where the eccentricity e is negligible in our case. [The lowest- PSRforJ1738+0333.
a
sar with2. a Orbital
weakly polarization (Nordtvedtcompanion,
self-gravitating effect,2for widesince
orbits) α " 1, that [11]
order expansion of (αp − αc ) in powers of0the sensitivities to provide the best
2 changed: PSR J114
∆p − ∆c # α0 (αp − αc ) in
s p,c is denoted as κ D S # eq. (12)−above.
α0 (α p α 0 ) . In the present sec- (4)
tion, we are numerically taking into account the full nonlin- is more constrainin
hile |α0 | < 0.003 by the Cassini
ear dependence on the experiment [4], αp canThe
bodies’ self-gravity.] of order unity forand
be companion’s PSR J1738+03
neutron
rs, as outlinedscalar charge
above. α ≈
Although α thebecause
effect of
is its small
greatly binding
suppressed energy,
by a small β0 > 0.7.
factor α , The same
3. Violation of local Lorentz Invariance of gravity.
c 0 0
while the pulsar’s scalar charge αp may be of order 1 in The special case β0
The quantity α A ≡ ∂
some ln MA /∂ϕ
theories 0 measures
even if α0 ≈ the0 effective
(Damour strength of the coupling between
& Esposito-Farèse oryaofself-
gravity) is in
vitating bodyare
• They A, absent
with total mass Mrelativity.
in general A , and the scalar field
Detecting them ϕ. would
It is equivalent to the negative
falsify GR! ratio
is still more sensiti
1993, 1996b). The orbital decay from dipolar gravitational
otal scalar charge to total mass. For a weakly self-gravitating body αA3 # α0 . converts into ωBD
wave emission (eq. (21)), which is of order O(1/c ), is thus
generically muchonlarger thanofthe usual quadrupole of the precision of
of orderof the binary.
• First two effects depend difference compactness between members
O(1/c5 ). An observed Ṗb consistent with general relativity same constraint in t
therefore strongly constrains scalar-tensor theories. considered in Alsin1. Limits on Dipolar GWs
• PSR J1738+0333 is a 5.85-ms pulsar in
a 8.5-hour, low eccentricity orbit. It was
discovered in 2001 in a Parkes Multi-
beam high-Galactic latitude survey
(Jacoby 2005, Ph.D. Thesis, Caltech).
• Companion WD detected at optical
wavelenghts, and relatively bright!
All pictures in this section: Antoniadis et al. (2012), MNRAS, 423, 3316Optical observations of PSR J1738+0333 • The WD is bright enough for a study of the spectral lines! • Together with WD models, these measurements allow an estimate of the WD mass: 0.181+0.007−0.005 M .
Optical observations of PSR J1738+0333 • Shift in the spectral lines allows an estimate of the mass ratio: q = 8.1 ± 0.2. • This allows an estimate of the orbital inclination (32.6 ± 1.0°) and the pulsar mass: 1.46+0.07−0.06 M . • Results in Antoniadis et al. 2012, MNRAS, 423, 3316.
and their un
ṖbInt = −25.9 ± 3.2 fs s−1 . (5)
Prediction:
3.3 Excess orbital decay 4 GENER
From the values for q and mc in Paper I we can estimate the In order to u
• Once the component masses are known, we can estimate the rate of orbital decay due to xs
orbital decay caused by the emission of quadrupolar GWs Ṗb in eq. (7
quadrupolar GW emission predicted
for a low-eccentricity system, by GR:
as predicted by GR: — we now
GR 192 π 5/3 q be contribut
Ṗb # − (nb T" mc )
5 (q + 1)1/3 xs Ṁ
Ṗb = Ṗb +
+1.5 −1
= −27.7−1.9 fs s , (6)
Ṁ
… which is a change on the −3orbital period of −0.86 µs per year! where Ṗ b i
where T" ≡ GM" c = 4.925490947 µs (Lorimer & Kramer tribution fro
Int
2005). Subtracting this from Ṗb (eq. (5)) we obtain the mainly by
• In“excess”
the presence of dipolar
orbital GW relative
decay emission this
to quantity must be larger
the prediction (in absolute value) - If αp ~1,
of GR,
then about 100000 times larger! multipole m
xs +3.7 −1 Ġ
Ṗb = 2.0−3.6 fs s . (7) Ṗ b is a con
• Can such a small change in the orbital period be detected? tions of New
This is consistent with zero. As discussed in Section 4, this Cavendish e
implies that GR passes the test posed by the orbital decay of cal” terms,
PSR J1738+0333. We illustrate this match in Fig. 5, where of gravity ot
we see that the mass/inclination constraints, derived from
ṖbInt using eq. (6) (i.e., assuming that GR is the correct the-
2Timing of PSR J1738+0333
10 years of timing with Parkes and Arecibo were necessary to measure this number precisely!
Relative Intensity
0 100 200 300 400 500
Bin Number. rate.
e This distance, when combined with the known temper-
d ature and photometric properties of the white dwarf, pro-
d
o
The (awesome) power of pulsar timing
duces an estimate for its radius that is very similar to that
derived from its the spectrum (see Paper I). This suggests
f that our value for the distance is likely to be accurate given
, o the
Spin present
period (attiming uncertainties. This
MJD 54600.0001776275): is important because
0.005850095859775683 ± 0.000000000000000005 s
the distance (and the proper motion, also presented in Ta-
- ble 1) are necessary for a correct estimate
o Orbital period: 8h 30m 53.9199264 ± 0.0000003 s
of the intrinsic
- orbital decay of the system ṖbInt , as discussed below.
r Following the analysis by Verbiest, Lorimer, &
y o Semi-major axis of the pulsar’s orbit, projected along the line of sight: 102957453 ± 6 m.
McLaughlin (2010), we find that there are no significant bi-
e ases affecting this parallax measurement.
- o Eccentricity: ( 3 ± 1) × 10−7
-
- o 3.2
Proper Intrinsic
motion: 7.037orbital decay
± 0.005 mas yr−1, 5.073 ± 0.012 mas yr−1.
o
t The intrinsic orbital decay of the system can be obtained
Parallax:
o from the0.68 ± 0.05 mas.
observed orbital period variation (Ṗb ) by subtract-
s ing the kinematic effects (Shklovskii 1970; Damour & Taylor
, o 1991):
Orbital decay: −(25.9 ± 3.2) × 10−15 ss−1 (or 0.8 ± 0.1 µs yr−1!). GR Does it again!!!!
e ṖbInt = Ṗb − ṖbAcc − ṖbShk . (1)
t
e The same equation applies to any quantity with the dimen-
IntFor Scalar-Tensor theories of gravity, this is the
most constraining binary pulsar test ever!
0|
LLR Precision of the limits on JFBD
100
theory will soon surpass the
Cassini test!
B1534+12
10 SEP See results in Freire et al. 2012,
J0737–3039 MNRAS, 423, 3328.
B1913+16
10
LLR
J1141–6545
Cassini
J1738+0333
10
See Gilles Esposito-
10
Farèse’s Talk
0
−6 −4 −2 0 2 4 6Also for TeVeS and friends!
0|
• Tensor-Vector-Scalar theories
100 (based on Bekenstein’s 2004
TeVeS theory) can also be
constrained, but in this case PSR
B1534+12 J1738+0333 is not enough.
10
SEP
J0737–3039
• Improvements in the timing
B1913+16
precision of the double pulsar
Tuned (PSR J0737−3039) will be
TeVeS 10
essential to constrain regions near
LLR linear coupling. To be published
J1141–6545
soon (Kramer et al 2014).
J1738+0333
Inconsistent 10
TeVeS • TeVeS and all non-linear friends
will soon be unnaturally fine-
tuned theories.
10
See Gilles Esposito-Farèse’s Talk
0
−6 −4 −2 0 2 4 6-
ing campaign with Arecibo, the GBT, and Westerbork (which ob- tem using high-precision three-body integ
tational equations of motion matched t
2. The Nordtvedt effect
where this other motion was coming from. It turns out that there
is an older, cooler, 0.4 solar mass white dwarf orbiting that in- better than a part in 10,000, the inclina
ner binary every 327 days, making a hierarchical triple system. are measured to about a hundredth of
gravitational interactions are se
icance over time scales as sho
In addition, the inner white dw
cally bright, and members of o
beautiful photometric and sp
vations of it, measuring its ra
matches predictions from puls
gravity and temperature. We hav
pulsar with the VLBA and a ca
portant calibration point for w
The system is already one of
system, which is dramatically
non-compactness of the bodies)
ing observations may allow hig
Figure caption: A schematic of the millisecond pulsar triple-system parts of General Relativity and i
• The GBT 350-MHz drift-scan survey found a pulsar in a hierarchical triple, PSR J0337+1715!
Grav for gravitational wave det
(Ransom et al., 2014, Nature, 505, 520) complicated evolution of the sy
“deaths” of three main-sequenc
fodder for astrophysical studies
sense of scale, the distance from the Earth to the Sun is about 500 light-
• This will be the best SEP test(lt-sec),
seconds ever while
– See the why
radiusinofFreire, Kramer
the Sun itself is only&2.3
Wex 2012, CQGra,
lt-sec. 29r40073. Local Lorentz Invariance of gravity
2
!˙
ity
Important for Gravity! See Enrico Barausse’s talk
tr i c
cen
d ec
e
serv
ob
êw / ↵1
PSR B1937+21: P = 1.56 ms
FIG. 1. Angle notations and the α2 -induced precession of the pulsar spin s around w, which is the pulsar velocity with respect
to the preferred frame. The coordinate system (I0 , J0 , K0 ) is defined in [10].
I. PULSARS AND TESTS OF GRAVITY THEORIES
The first pulsar was discovered in 1967 [1]. Since then, more than two thousands of pulsars are revealed by
international surveys through radio, X-ray and γ-ray observations. Among them, several pulsars have achieved
great contribution to our understanding of astronomy, as well as fundamental physics, such as the first millisec-
ond pulsar (MSP), PSR B1937+21 [2], the Hulse-Taylor binary pulsar, PSR B1913+16 [3], and the double pulsar,
PSR J0737−3039A/B [4–6]. These celestial objects are intriguing in multiple aspects, e.g., the long-term stable ro-
tation excessing the precision of atomic clocks, the high interior density excessing that of nuclear matter, the high
[ Damour & Esposito-Farèse 1992 ] magnetic field excessing the quantum critical value [7].
One of the most important contributions of pulsars is their unique role in tests of gravity theories. To illustrate two
examples: i) the Hulse-Taylor pulsar provided the first evidence for the existence of gravitational waves [8]; ii) the
double pulsar provided the most accurate test of Einstein’s general relativity in the strong field to 0.05% precision [6].
PSR J1738+0333 In this letter, we report a new limit of the parameterized post-Newtonian (PPN) parameter α2 from solitary pulsars,
which surpasses the best limit from the Solar system obtained 25 years ago [9].
II. PREFERRED FRAME EFFECTS AND PULSAR SPIN PRECESSION
T = 10.0 yr Universal matter distribution might single out a preferred frame, if gravitational interaction is mediated by an
New tests of LLI of gravity with binary pulsars 29
extra vectorial or tensorial component in addition to the symmetric metric tensor [11]. The preferred frame effects
!˙ = 1.56 deg/yr [calculated] (PFEs) are predicted by many alternative gravity theories, like vector-tensor theories [11], Einstein Æther theories [12],
Standard Model Extension of gravity sector [13]. In the parameterized post-Newtonian (PPN) formula [11, 14], PFEs
are characterized by two parameters, α1 and α2 . In GR, α1 = α2 = 0.
Observational implications of PFEs are studied by several authors through different aspects, and are constrained to
J1012+5307 and e J1738+0333,
= (3.5 ± 1.1) ⇥ 10we7 have full spatial velocity information. For a
where high precision from geophysics, Solar system, and pulsar timing [15–18]. Currently, the best limits on α1 and α2 come
from the orbital dynamics of small-eccentricity neutron star (NS) white dwarf (WD) binary PSR J1738+0333 [18]
and the alignment of the Sun’s spin with the orbital angular momentum of the Solar system [9], respectively.1 The
frame at rest with respect to the CMB, the best limit we obtain is
PSRs B1937+21 and J1744-1134 combined
best limit of α1 is −0.4+3.7
−3.1 × 10
−5
(95% C.L.) from strong field regime [18], while for α2 , |α2 | < 4.8 × 10−7 (95%
C.L.) from the weak field regime [9]. We will focus on α2 later.
Nordtvedt [9] used the current alignment of the Sun’s spin with the orbital angular momentum of the Solar system,
and limited |α2 | < 4.8 × 10−7 (95% C.L.). However, the crucial assumption that the Sun’s spin was aligned with the
9
↵
ˆ1 = 0.4+3.7
3.1 ⇥ 10
5
(95% C.L.) , |↵
ˆ 2 | < 6.6 ⇥ 10 (95%
(49)C.L.)
Solar system angular momentum is not well justified. A weaker limit on α2 comes from Lunar Laser Ranging, which
[ Shao & Wex 2012 ] 1
[ Shao et al., inα prep.
Be aware of a non-standard renormalization of α2 in [9], αNordtvedt
[16].
]
= 1 standard
which avoids the probabilistic considerations of previous methods, and clearly surpasses 2 2 2
the current best limits obtained with both, weakly (Solar system) and strongly (binaryThe strong-field frontier
PSR J0348+0432
• This is a pulsar with a
spin period of 39 ms
discovered in a GBT 350-
MHz drift-scan survey
(Lynch et al. 2013, ApJ.
763, 81).
• It has a WD companion
and (by far) the shortest
orbital period for a pulsar-
WD system: 2h 27 min.
Credit: Norbert WexPSR J0348+0432
Recent optical measurements at the
VLT find a WD mass of 0.172 ± 0.003
M¤ and a pulsar mass of 2.01 ± 0.04
M¤ (Antoniadis et al. 2013, Science,
340, n. 6131).
• Most massive NS with a precise mass
measurement.
• Confirms that such massive NSs exist
using a different method than that
used for J1614−2230. It also shows
that these massive NSs are not rare.
• Allows, for the first time, tests of
general relativity with such massive
NSs! Prediction for orbital decay: −8.1
µs /year
Credit: Luis Calçada, ESO. See video at:
http://www.eso.org/public/videos/eso1319a/Measurement of orbital decay
.
q Pb
q
MWD MWD
.
Pb
With Arecibo, GBT and Effelsberg, we have now measured the orbital decay: (−8.6 ± 1.4) µs/year.
Complete agreement with GR!This is important – system is unique! Figure by Norbert Wex. See http://www3.mpifr-bonn.mpg.de/staff/pfreire/NS_masses.html
Strong non-linear deviations from GR
seriously constrained!
• This is the first time we do a GR test with
such a massive NS: Previously, only 1.4
M¤ NSs had been used for such tests!
• This constrains the occurrence of strong
non-linear deviations from GR, like
spontaneous scalarization (e.g., Damour
& Esposito-Farèse, 1996, Phys. Rev. D.,
54,1474) – at least at large PSR-WD
separations!
• Such phenomena simply just could not be
probed before.Implications for GW detection • This measurement also increases our confidence in the GR templates to be used soon to search for NS- NS and NS-BH mergers - for the whole range of NS masses. • For a NS-NS merger, only a small fraction of a cycle can be lost while it is in the LIGO/Virgo bands • … unless there are short-range, high frequency effects!
Constraints on the equation of state
Mass measurement of PSR J0348+0432 has direct implications for the EOS of dense matter!
PSR J0348+0432
PSR J1614−2230
PSR J1903+0327
See John Antoniadis’ TalkSummary • Double neutron stars have provided extremely precise tests of the properties of strong-field gravity. • MSP-WD systems, with their astounding timing precision, are now being used to test GR, opening a new era in pulsar tests of gravity theories. Because of the asymmetry of the components and the timing precision, these tests are very constraining for alternative theories of gravity. • Strong complementarity with work on the double pulsar – together can rule out e.g., TeVeS! This has implications for our knowledge of the laws and contents of the Universe. • New SEP test with the triple system around the corner. • Best limits on all gravitational LLI parameters now derived from pulsar observations. These, together with previous limits, have serious implications for alternative theories of gravity! • We have done the first ever test of GR in a new regime of gravitational fields. Spontaneous scalarization seriously constrained!
Thank you!
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