来自脉冲星的引力波，具有测量的制动指数
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Eur. Phys. J. C (2016) 76:481
DOI 10.1140/epjc/s10052-016-4327-y
Regular Article - Theoretical Physics
Gravitational waves from pulsars with measured braking index
José C. N. de Araujo
a
, Jaziel G. Coelho
b
, Cesar A. Costa
c
Divisão de Astrofísica, Instituto Nacional de Pesquisas Espaciais, Avenida dos Astronautas 1758, São José dos Campos,
SP 12227–010, Brazil
Received: 28 April 2016 / Accepted: 22 August 2016 / Published online: 31 August 2016
© The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract We study the putative emission of gravitational
waves (GWs) in particular for pulsars with measured braking
index. We show that the appropriate combination of both GW
emission and magnetic dipole brakes can naturally explain
the measured braking index, when the surface magnetic field
and the angle between the magnetic dipole and rotation axes
are time dependent. Then we discuss the detectability of these
very pulsars by aLIGO and the Einstein Telescope. We call
attention to the realistic possibility that aLIGO can detect
the GWs generated by at least some of these pulsars, such as
Vela, for example.
1 Introduction
Recently, gravitational waves (GWs) have finally been
detected [1]. The signal was identified as coming from the
final fraction of a second of the coalescence of two black
holes (BHs), which resulted in a spinning remnant black
hole. Such an event had been predicted (see e.g., [2]) but
never been observed before.
As is well known, pulsars (spinning neutron stars) are
promising candidates for producing GW signals which would
be detectable by aLIGO (Advanced LIGO) and AdV Virgo
(Advanced Virgo). These sources might generate continuous
GWs whether they are not perfectly symmetric around their
rotation axes.
The so-called braking index (n), which is a quantity
closely related to the pulsar spindown, can provide informa-
tion as regards the pulsars’ energy loss mechanisms. Such
mechanisms can include GW emission, among others.
Until very recently, only eight of the ∼2400 known pulsars
have braking indices measured accurately. All these brak-
ing indices are remarkably smaller than the canonical value
a
e-mail: [email protected]
b
e-mail: [email protected]
c
e-mail: cesar[email protected]
(n = 3), which is expected for pure magneto-dipole radiation
model (see e.g., [3–9]).
Several interpretations for the observed braking indices
have been put forward, like the ones that propose either accre-
tion of fall-back material via a circumstellar disk [10], rela-
tivistic particle winds [11,12], or modified canonical models
to explain the observed braking index ranges (see e.g., [13–
15], and references therein for further models). Alternatively,
it has been proposed that the so-called quantum vacuum fric-
tion (QVF) effect in pulsars can explain several aspects of
their phenomenology [16]. However, so far no developed
model has yet explained satisfactorily all measured braking
indices, nor any of the existing models has been totally ruled
out by current data. Therefore, the energy loss mechanisms
for pulsars are still under continuous debate.
Recently, Archibald et al. [17] showed that PSR J1640-
4631 is the first pulsar having a braking index greater than 3,
namely n = 3.15 ± 0.03. PSR J1640-4631 has a spin period
of P = 206 ms and a spindown rate of
˙
P = 9.758(44) ×
10
−13
s/s, yielding a spindown power
˙
E
rot
= 4.4×10
36
erg/s,
and an inferred dipole magnetic field B
0
= 1.4×10
13
G. This
source was discovered by using X-ray timing observations
with NuStar and a measured distance of 12 kpc (see [18]).
The braking index of PSR J1640-4631 reignites the ques-
tion about energy loss mechanisms in pulsars. With the
exception of this pulsar, all other eight, as previously men-
tioned, have braking indices n < 3 (see Table 1), which
may suggest that other spindown torques act along with the
energy loss via dipole radiation. Recently, we showed that
such a braking index can be accounted for if the spindown
model combines magnetic dipole and GW brakes (see [19]).
Therefore, each of these mechanisms alone cannot account
for the braking index found for PSR J1640-4631.
Since pulsars can also spindown through gravitational
emission associated to asymmetric deformations (see e.g.,
[20,21]), it is appropriate to take into account this mechanism
in a model which aims to explain the braking indices which
have been measured. Thus, our interest in this paper is to
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