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Acta Polytechnica Vol. 51 No. 2/2011

X-ray Transient Sources (Multifrequency Laboratories)
The Case of the Prototype A0535+26/HDE 245770

F. Giovannelli, L. Sabau-Graziati

Abstract

The goal of this paper is to discuss the behaviour of the X-ray transient source A0535+26 which is considered for
historical reasons and for the huge amount of multifrequency data, spread over a period of 35 years, as the prototype of
this class of objects. Transient sources are formed by a Be star — the primary — and a neutron star X-ray pulsar —
the secondary — and constitute a sub-class of X-ray binary systems.
We will emphasize the discovery of low-energy indicators of high-energy processes. They are UBVRI magnitudes

and Balmer lines of the optical companion. Particular unusual activity of the primary star — usually at the periastron
passage of the neutron star – indicates that an X-ray flare is drawing near. The shape and intensity of X-ray outbursts
are dependent on the strength of the activity of the primary.
We derive the optical orbital period of the system as 110.856 ± 0.02 days. By using the optical flare of December 5,

1981 (here after 811205-E) that triggered the subsequent X-ray outburst of December 13, 1981, we derive the ephemeris
of the system as JD Popt−outb = JD0(2,444,944) ± n(110.856 ± 0.02). Thus the passage of the neutron star at the
periastron occurs with a periodicity of 110.856 ± 0.02 days and the different kinds of X-ray outbursts of A0535+26 —
following the definitions reported in the reviewbyGiovannelli & Sabau-Graziati (1992) —occur just after ∼ 8 days. The
delay between optical andX-ray outbursts is just the transit time of thematerial coming out from the optical companion
to reach the neutron star X-ray pulsar.
The occurrence of X-ray “normal outbursts”, “anomalous outbursts” or “casual outbursts” is dependent on the

activity of the Be star: “quiet state: steady stellar wind”, “excited state: stellar wind plus puffs of material”, and
“expulsion of a shell”, respectively. In the latter case, the primary manifests a strong optical activity and the consequent
strong X-ray outburst can occur in any orbital phase, with a preference at the periastron passage of the neutron star,
because of its gravitational effects on the Be star.

Keywords: X-ray/Be systems,X-raypulsars, be stars, optical, spectroscopy, photometry,X-rays, individual: A0535+26
≡ 1A 0535+26 ≡ 4U 0538+26 ≡ 1H 0536+263 ≡ 1RXS J053855.1+261843, individual: HDE 245770 ≡ BD+26◦ 883 ≡
V 725 Tau ≡ AAVSO 0532+26 ≡ SAO 77348.

1 Introduction
The trivial definition of X-ray binaries (XRBs) is that
they are binary systems emitting X-rays. However it
has been largely demonstrated that X-ray binary sys-
tems emit energy in IR, Optical, UV, X-ray, Gamma-
ray energy ranges, and they sometimes also show
valuable radio emission. They can be divided into
different sub-classes
• High Mass X-ray Binaries (HMXB), in which

the optical companion is an early type giant
or supergiant star and the collapsed object is
a neutron star or a black hole. They are con-
centrated around the galactic plane. The mass
transfer usually occurrs via stellar wind; they
show hard pulsed X-ray emission (from 0.069 to
1413 s) with KT ≥ 9 keV; typical X-ray lumi-
nosity ranges from 1034 to 1039 erg s−1, and the
ratio of X-ray to optical luminosity is ∼ 10−3–10.
HMXBs can be divided into two sub-classes

• Hard Transient X-ray Sources (HXTS)
in which the neutron star is eccentri-

cally (e ∼ 0.2–0.5) orbiting around a V-III
luminosity-class Be star (Porb > 10 days);
they show strong variable pulsed hard X-
ray emission (LXmax/LXmin > 100) with
KT ≥ 17 keV;

• Permanent X-ray Sources (PXS), in which
the neutron star or black hole is circularly
orbiting (e ∼ 0) around a giant or super-
giant OB star (Porb < 10 days); they show
an almost steady permanent pulsed hard X-
ray emission (LXmax/LXmin � 100);
• Obscured Sources, which display a

huge amount of low energy absorption
produced by the dense wind of the su-
pergiant companion;

• Supergiant Fast X-ray transients
(SFXT), a new subclass of transients in
which the formation of transient accre-
tion discs could be partly responsible
for the flaring activity in systems with
narrow orbits.

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Acta Polytechnica Vol. 51 No. 2/2011

• Low Mass X-ray Binaries (LMXB), in which the
optical companion is a low-mass-late-type star
and the collapsed object is a neutron star or a
black hole (Porb from 41 min to 11.2 days). They
are concentrated around the galactic plane and
especially in the galactic center. The mass trans-
fer in these systems usually occurs via Roche
lobe overflow. Their emission in the soft X-ray
range is usually not pulsed with KT ≤ 9 keV.
Their X-ray luminosity ranges from 1036 to 1039

erg s−1 and LX/Lopt ∼ 102–104; many LMXBs
show Quasi Periodic Oscillations (QPOs) be-
tween 0.02 and 1 000 seconds, and a few of them
also show pulsed X-ray emission, such as Her X1,
4U 1626-27 and GX 1+4;

• Cataclysmic Variables (CVs), in which the opti-
cal companion is a low-mass-late-type star and
the compact object is a white dwarf. The de-
tected CVs are spread roughly around the solar
system at a distance of 200-300 pc. The orbital
periods range from tens of minutes to about ten
hours. The mass transfer occurs either via Roche
lobe overflow or via accretion columns or in an
intermediate way, depending on the value of the
magnetic field. Typical X-ray luminosity ranges
from 1032 to 1034 erg s−1. An updated review
on CVs is that of Giovannelli (2008);

• RS Canum Venaticorum (RS CVn) type sys-
tems, in which no compact objects are present
and the two components are an F or G hotter
star and a K star. Typical X-ray luminosity
ranges from 1030 to 1031 erg s−1. In the cur-
rent literature they are usually excluded from
the class of X-ray binaries, since historically they
were discovered as X-ray emitters only with the
second generation of X-ray experiments.

For a general review of XRBs, see the paper by
Giovannelli & Sabau-Graziati (2004). XRBs are the
best laboratory for the study of accreting processes
thanks to their relatively high luminosity in a large
part of the electromagnetic spectrum. For this rea-
son, multifrequency observations are fundamental in
understanding their morphology and the physics gov-
erning their behaviour. Because of the strong in-
teractions between the optical companion and the
collapsed object, low and high energy processes are
strictly related. It is often easier to perform obser-
vations of low energy processes (e.g. in the radio,
near-infrared (NIR) and optical bands), since the ex-
periments are typically ground-based, unlike observa-
tions of high energy processes, for which experiments
are typically space-based.

X-ray/Be binaries are the most abundant group
of massive X-ray binaries in the galaxy, with a to-
tal inferred number of between 103 and 104. Those
which occasionally flare-up as transient X-ray/Be
systems are only the “tip” of this vaste “iceberg”

of systems (van den Heuvel and Rappaport, 1987).
The mass loss processes are due to the rapid rota-
tion of the Be star, the stellar wind and, sporadi-
cally, to the expulsion of a casual quantity of mat-
ter essentially triggered by gravitational effects close
to the periastron passage of the neutron star. The
long orbital period (> 10 days) and the large eccen-
tricity of the orbit (> 0.2) together with the tran-
sient hard X-ray behavior are the main characteris-
tics of these systems. Among the whole sample of
galactic systems containing 114 X-ray pulsars (John-
stone, 2005), only few have been extensively studied.
Among these, the system A 0535+26/HDE 245770
is the best known, thanks to concomitant favorable
causes, which have enabled thirty five years of coordi-
nated multifrequency observations, most of them dis-
cussed by e.g. Giovannelli & Sabau-Graziati (1992),
Burger et al. (1996), Piccioni et al. (1999). Accretion
powered X-ray pulsars usually capture material from
the optical companion via the stellar wind, since this
primary star generally does not fill its Roche lobe.
However, in some specific conditions (e.g. the pas-
sage at the periastron of the neutron star) and in
particular systems (e.g. A 0535+26/HDE 245770),
the formation of a temporary accretion disk around
the neutron star behind the shock front of the stel-
lar wind is possible. This enhances the efficiency of
the process of mass transfer from the primary star
onto the secondary collapsed star, as discussed by
Giovannelli & Ziolkowski (1990) and by Giovannelli
et al. (2007) in the case of A 0535+26.

Optical emission of HMXBs is dominated by the
emission of the optical primary component, which is
not, in general, strongly influenced by the presence
of the X-ray source. The behavior of the primary
stars can be understood in the classical (or almost)
framework of the astrophysics of these objects, i.e. by
studying their spectra, which will provide indications
on mass, radius, and luminosity. The two groups
of HMXBs differ because of the different origin of
the mass loss process: in the first group, the mass
loss process occurs via a strong stellar wind and/or
because of an incipient Roche lobe overflow; in the
second group, the mass transfer is probably partially
due to the rapid rotation of the primary star and par-
tially due to a stellar wind and sporadically due to
expulsions of a casual quantity of matter, essentially
triggered by gravitational effects because of perias-
tron passage, where the effect of the secondary col-
lapsed star is more marked. A relationship between
the orbital period of HMXBs and the spin period of
X-ray pulsars is shown in Fig. 1 (updated from Gio-
vannelli & Sabau-Graziati, 2001 and from Corbet,
1984, 1986). We can recognize three kinds of systems,
namely disk-fed, wind-fed [Ppulse ∝ (P orb)4/7], and
X-ray/Be systems [Ppulse ∝ (P orb)2].

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Acta Polytechnica Vol. 51 No. 2/2011

Fig. 1: Spin period vs orbital period for X-ray pulsars. Disk–fed systems are clearly separated by systems having as
optical counterparts either OB stars or Be stars (Giovannelli & Sabau-Graziati, 2001)

Most of the systems having a Be primary star
are hard X-ray (KT > 10 KeV) transient sources
(HXTS). They are concentrated on the galactic plane
within a band of ∼ 3.9◦. The orbits are quite ellip-
tic and the orbital periods are large (i.e. A 0538-
66: e = 0.7, Porb = 16.6 days (Skinner et al.,
1982); A 0535+26: e = 0.47 (Finger, Wilson & Hage-
don, 1994), P = 111.0 days (Priedhorsky & Terrell,
1983). The X-ray flux during the outburst phases
is of the order 10–1 000 times greater than during
quiescent phases. For this reason, on the contrary,
the stars belonging to the first class which do not
present such strong variations in X-ray emission can
be named “standard” high mass X-ray binaries. In X-
ray/Be systems, the primary Be star is relatively un-
evolved and is contained within its Roche lobe. The
strong outbursts occur almost periodically in time
scales of the order of weeks or months. Their dura-
tion is shorter than the quiescent phases. During X-
ray outbursts, spin-up phenomena in several systems
have been observed (i.e. A 0535+26 and 4U 1118-61
(Rappaport & Joss, 1981)). The observed spin-up
rates during the outbursts are consistent with tor-
sional accretion due to an accretion disk (e.g. Ghosh,
1994). The formation of a temporary accretion disk
around the collapsed object should therefore be pos-
sible during the outburst phases (e.g. Giovannelli &
Ziolkowski, 1990).

The number of X-ray pulsars increases slowly
with time, thanks to new detections performed at
various new generation observatories. There were
95 (Giovannelli & Sabau-Graziati, 2000) in 2000
and the orbital periods were known only for about
three dozen of them. They contain the group

of permanent HMXBs and the group of transient
HMXBs (X-ray/Be systems), whose components are
an X-ray pulsing neutron star — the secondary —
and a giant or supergiant OB or a Be star, re-
spectively — the primary. Moreover, some low-
mass X-ray Binaries (LMXBs) containing an X-
ray pulsar, and some pulsars belonging to Magel-
lanic Clouds were also contained in the sample of
95 systems. In 2005, there were 114 known X-
ray pulsars (Johnston, 2005). 47 X-ray pulsars
have been detected in the SMC (Corbet et al.,
http://lheawww.gsfc.nasa.gov/users/corbet/pulsars/).
Recently, Rajoelimanana, Charles & Udalski (2010)
listed 49 optical counterparts of SMC X-ray pulsars
detected by MACHO and OGLE. There are 20 sys-
tems with known Pspin, while there are 23 systems
with known Porb, 6 of which are uncertain.

In this paper we will discuss the history of the dis-
covery of optical indicators of high energy emission
in the prototype system A0535+26/HDE 245770, up-
dated to the March–April 2010 event, when strong
optical activity occurred roughly 8 days before the
X-ray outburst (Caballero et al., 2010a) that was pre-
dicted by Giovannelli et al. (2010).

2 The X-ray/Be System
A0535+26/HDE 245770

A 0535+26/HDE 245770 is a typical X-ray/Be run-
away system (van Oijen 1989), whose components are
a 104 s X-ray pulsar (Rosenberg et al. 1975) and an
O9.7 IIIe star (Giangrande et al. 1980). The X-ray

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Acta Polytechnica Vol. 51 No. 2/2011

Fig. 2: X-ray flux versus time of A 0535+26. X-ray measurements are reported with red lines and asterisks, upper
limits with green arrows, and predicted fluxes with light blue stars. Periods of real detected X-ray outburst and optical
measurements are also marked (Giovannelli, 2005)

pulsar is spinning up with a pulse period derivative
Ṗ/P = −4.9×10−4 yr−1 (Coe et al. 1990), with alter-
nating phases of spin-down during X-ray outbursts.
The X-ray pulsar A0535+26 has a magnetic field of
∼ 1013 G (Grove et al. 1995). The orbital period
has been determined by many authors, using various
methods: 111d.0±0d.4 (Priedhorsky & Terrell 1983),
111d.38±0d.11 (Motch et al. 1991), and 110d.3±0d.3
(Finger, Wilson & Hagedon 1994) from X-ray data,
and 110d.0 ± 0d.5 (Coe et al., 2006) from the increas-
ing X-ray activity associated with the periastron pas-
sage of the neutron star. These values agree with the
value reported by Guarnieri et al. (1985) from long-
term optical photoelectric data (109d.8 ± 2d.0). The
orbital eccentricity of the system is 0.47 (Finger, Wil-
son & Hagedon 1994). The terminal velocity of the
stellar wind from the star with significant optical out-
put is ∼ 630 km s−1 (Giovannelli et al. 1982), and
its mass loss rate is ∼ 10−8 M� yr−1 (Giovannelli et
al. 1984a; de Loore et al. 1984).

The X-ray pulsar is close to its equilibrium state
(Bisnovatyi-Kogan 1991; Li & van den Heuvel 1996),
which could be a reason why some of the expected X-
ray outbursts have failed to occur. This was noted at
the end of the 1980s, as discussed by Giovannelli &
Zió�lkowski (1990, and references therein), or in the
mid-nineties, as found by the RXTE satellite (see
http://space.mit.edu/XTE). The O9.7 IIIe companion
does not normally fill its Roche lobe (de Loore et al.
1984), although a temporary accretion disc can be
formed around the neutron star when it is close to
periastron (Giovannelli & Zió�lkowski 1990; Giovan-
nelli et al., 2007).

Complete reviews of the A0535+26/HDE 245770
system can be found in the papers by Giovannelli et
al. (1985), Giovannelli & Sabau-Graziati (1992), and
Burger et al. (1996).

2.1 Historical Multifrequency
Observations of A 0535+26/HDE
245770

The most studied HMXB system, for historical rea-
sons and due to concomitant favourable causes, is
the X-ray/Be system A 0535+26/HDE 245770. By
means of long series of coordinated multifrequency
measurements, very often simultaneously obtained,
it was possible to:
• identify the optical counterpart HDE 245770 of

the X-ray pulsar;
• identify various X-ray outbursts triggered by dif-

ferent states of the optical companion and influ-
enced by the orbital parameters of the system;

• identify the presence of a temporary accretion
disc around the neutron star at periastron.

Multifrequency observations of this system star-
ted soon after its discovery as an X-ray pulsar by
the Ariel-5 satellite (Rosenberg et al., 1975). The
error box of the X-ray source contains 11 stars up
to 23rd magnitude; these include the 9 mag Be star
HDE 245770. The a priori probability of finding a
9 mag star in such a field is 0.004, so that Margon
et al. (1977) suggested this star as a probable op-
tical counterpart of A0535+26. But in order to re-
ally associate this star with the X-ray pulsar, it was
necessary to find a clear signature proving that the

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Acta Polytechnica Vol. 51 No. 2/2011

two objects would belong to the same binary system.
This happened thanks to a sudden insight of one of
us (FG), who predicted the fourth X-ray outburst
of A 0535+26 around mid December 1977. For this
reason, Giovannelli’s group was observing in optical
HDE 245770 around the predicted period for the X-
ray outburst of A 0535+26. Figure 2 shows the X-
ray flux intensity of A 0535+26 as deduced by vari-
ous measurements available at that time, with obvi-
ous meaning of the symbols used (Giovannelli, 2005).
FG’s intuition was sparked by looking at the rise of
the X-ray flux (red line) and at the 24th May 1977
measurement (red asterisk): he assumed that the ev-
ident rise of the X-ray flux would have produced an
outburst similar to the first one, which occurred in
1975. Then with a simple extrapolation he predicted
the fourth outburst, similar to the second: and this
happened!

Optical photoelectric photometry of HDE 245770
showed significant light enhancement of the star rel-
ative to the comparison star BD +26 876 between
Dec 17 and Dec 21 (here after 771220-E) and suc-
cessive fading up to Jan. 6 (Bartolini et al., 1978),
whilst satellite SAS-3 was detecting an X-ray flare
(Chartres & Li, 1977). The observed enhancement
of optical emission followed by the flare-up of the X-
ray source gave a direct argument strongly support-
ing the identification of HDE 245770 — later nick-
named Flavia’ star by Giovannelli & Sabau-Graziati
(1992) — with A 0535+26.

Soon after, with spectra taken at the Loiano 152
cm telescope with a Boller & Chivens 26767 grat-
ing spectrograph (831 grooves/mm II-order grating:
39 Å mm−1) onto Kodak 103 aO plates, it was pos-
sible to classify HDE 245770 as O9.7IIIe star. This
classification was so good that it survives even to the
recent dispute attempts made with modern technol-
ogy. The mass and radius of the star are 15 M� and
14 R�, respectively; the distance to the system is
1.8 ± 0.6 kpc (Giangrande et al., 1980).

UV spectra taken with the IUE enabled the red-
dening of the system to be determined as E(B-
V)= 0.75 ± 0.05 mag, the rotational velocity of the
O9.7IIIe star (vrot sin i = 230±45 km s−1), the termi-
nal velocity of the stellar wind (v∞ � 630 km s−1),
the mass loss rate (Ṁ ∼ 10−8 M� yr−1 in quies-
cence (Giovannelli et al., 1982). During the Octo-
ber 1980 strong outburst, the mass loss rate was
Ṁ ∼ 7.7 × 10−7 M� yr−1 (de Martino et al., 1989).

2.2 Optical and Ultraviolet
indicators of X-ray outbursts in
A0535+26/HDE 245770

Giovannelli et al. (1985) and Guarnieri et al. (1985)
found UV and optical features of HDE 245770 as in-

dicators of the X-ray activity of A 0535+26. They
found experimentally that the X-ray flaring activity
of A 0535+26 is preceded by modifications in the
optical spectrum of the companion HDE 245770, of
about one week (≈ 0.6 × 106 s). This roughly cor-
responds to the transit time of puffs of material ex-
pelled by the Be star at ∼ 300 km s−1 in order to
reach the neutron star, being the dimensions of the
orbit of ∼ 1.34 AU (de Loore et al., 1984). The Hγ
line seems to be the best indicator of the activity
going on. Moreover, enhancements of optical lumi-
nosity were observed on four occasions before X-ray
outbursts (Bartolini et al., 1983; Maslennikov, 1986).
Narrow absorption components present in the blue
wings of the Si IV and C IV resonance lines indicate
a variable mass loss superimposed on a steady wind
of ∼ 10−8 M� yr−1 (Giovannelli et al., 1984a; de
Loore et al., 1984). They are strong probes in study-
ing the physics and dynamics of the mass transfer
at periastron and the subsequent X-ray flaring. X-
ray outbursts are triggered by the eccentric orbital
motion (Porb ∼= 111 days: ≈ 107 s). Then, multifre-
quency monitoring of this system and of a number
of other X-ray/Be systems around the passage at the
periastron could give a conclusive answer to many of
the open problems on the Be/X-ray transients.

From two outburst decays with exactly the same
shape, shown in Fig. 3 (Bartolini et al., 1983) it is
possible to derive the optical period of the system
(Porb−opt = 110.856 ± 0.02 days. This value is in
agreement with the many values available in the lit-
erature, but it has the advantage that it has been
derived by two simple optical measurements. We will
use such a period in the following in order to discuss
the flaring activity of the system.

Fig. 3: Decay from two outbursts of optical luminosity of
HDE 245770: the first on February 24, 1976, the second
on December 20, 1977 (Bartolini et al., 1983).

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Acta Polytechnica Vol. 51 No. 2/2011

Fig. 4: C IV resonance line of Flavia’ star with narrow absorption components marked with red arrows. The data comes
from the IUE short wavelength high resolution spectra. Clockwise from the upper right panel, the spectra were taken by
Giovannelli on November 1, 1981 (X-ray quiescence), October 26, 1980 (X-ray outburst decay), January 23, 1984 (X-ray
outburst), and November 10, 1983 (X-ray quiescence), respectively

Fig. 5: Typical Hα, Hβ and Hγ lines of Flavia’ star be-
fore X-ray activity of the neutron star. The fluxes are
normalized to the continuum. The left and right pan-
els report spectra taken at Haute Provence and Loiano
Observatories, respectively (Giovannelli et al., 1984a)

Figure 4 shows the narrow absorption compo-
nents in the C IV resonance line in the high res-
olution IUE spectra of Flavia’ star. The velocity

of the “puffs” of material expelled by the star is
∼ 350±50 km s−1, roughly coincident with that mea-
sured in the optical spectra (∼ 300 ± 50 km s−1).
Then, the transit time from the primary to the sec-
ondary is about 7–8 days, being the dimension of the
system of ∼ 1.34 AU (Giovannelli et al., 1984a; de
Loore et al., 1984; Guarnieri et al., 1985b).

Figure 5 shows typical Hα, Hβ and Hγ lines of
Flavia’ star before X-ray activity of the neutron star.
The spectra were taken at the Haute Provence and
Loiano Observatories (Giovannelli et al., 1984a).

Figure 6 shows the optical outburst 811205-E
(Guarnieri et al., 1985b) — marked with a red line —
which occurred 8 days before the X-ray outburst of
December 13, 1981 (Nagase et al., 1982) — marked
with a blue line — and was just 13 cycles after
771220-E), when, through enhanced optical activity,
Bartolini et al. (1978) discovered the firm associa-
tion between the X-ray pulsar and the O9.7 IIIe star.
Around the strong X-ray outburst — October 9–24,
1980: JD 2444522 – 2444537 – (marked with the blue
rectangle in Fig. 6) scarce optical measurements are
available. However, such a strong X-ray outburst oc-
curred between the 9th (JD 2444500.6) and 10th (JD
2444611.4) cycle after 771220-E. This will be com-
mented in the conclusions.

We use 811205-E to give the optical ephemerides
of the binary system that is in our opinion the most
reliable. They are:

JDopt−outb = JD0(2,444,944) ± n(110.856 ± 0.02)
days.

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Acta Polytechnica Vol. 51 No. 2/2011

Fig. 6: Optical outburst onDecember 5, 1981 (811205-E)
(Guarnieri et al., 1985b) —markedwith a red line —oc-
curred 8 days before the X-ray outburst of December 13,
1981 (Nagase et al., 1982) — marked with a blue line —
and was just 13 cycles after the 771220-E. Around the
big X-ray outburst – October 9–24, 1980: JD 2,444,522 –
2,444,537 – (markedwith the blue rectangle) scarce opti-
cal measurements are available

Figure 7 shows 1983–1986 X-ray outbursts of
A0535+26. The long 1983 October 1–18 [(JD
(5609–5626) + 2,440,000] X-ray outburst started just
in the 6th orbital period after the 811205-E (or the
19th cycle after 771220-E). No clear optical measure-
ments were available. However, looking at the V
light curve (obtained with the observations at the
1.5 m Loiano telescope), it is possible to note a

small decay followed by a further increase, better
detected by the Byurakan telescope (see Fig. 8) —
this means that the O9.7 IIIe star was experienc-
ing a stronger mass loss process than the usual pro-
cess — which could be responsible for the prolonga-
tion of the X-ray outburst. The 1984 February 1–4
[JD (5732–5735) + 2,440,000] X-ray outburst (mea-
sured with the ASTRON satellite by Giovannelli et
al., 1984b; 1986a,b), probably started a few days ear-
lier. Indeed the two available measurements (Febru-
ary 1 and 4) clearly show a decay. The 20th cycle
after the 771220 E is placed just at JD 5720. At
this moment the V magnitude of the optical com-
panion was just in a phase of decay. The follow-
ing 1986 October 28–November 1 X-ray outburst, de-
tected only twice on those dates, occurred again af-
ter the 29th cycle (JD 2,446,718) from the 771220-
E. Also in this case, the V magnitude of the optical
companion was in a decay phase after a relative maxi-
mum. These three latter events strongly support that
the real orbital period of the system is 110.856 days,
which scans the periastron passage of the neutron
star, and the X-ray outbursts are triggered with a
delay of ∼ 8 days — the transit time of the expelled
material from the primary for reaching the secondary.
In the case of Be star in “quiescence (steady stellar
wind)”, the X-ray outburst has an intensity ≈ 0.1–0.5
Crab (normal outbursts); in the case of “moderate
activity (steady stellar wind plus puffs of material
expelled)”, the intensity of the X-ray outburst is
≈ 0.5–1 Crab (anomalous or noisy outbursts); in the
case of the “expulsion of a shell” from the primary,
preferably triggered near the periastron passage, a
very strong X-ray outburst (> 1–∼ 4 Crab) occurs
and its duration is typically very long (≈ 10–20 days)
(casual outbursts).

Fig. 7: 1983–1986 X-ray outbursts of A0535+26. The red lines indicate the 6th, 7th, and 16th optical cycles after the
811205-E. The blue rectangles and the blue lines indicate X-ray outbursts

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Acta Polytechnica Vol. 51 No. 2/2011

Fig. 8: UBVRI observational campaign of Flavia’ star and X-ray observations with ASTRON satellite between Septem-
ber 1983 and April 1984 (Giovannelli et al., 1984b). Blue stars represent X-ray measurements during two outbursts
(Giovannelli & Sabau-Graziati, 1992 and references therein). Red lines indicate the 19th and 20th cycles after 771220-E

Figure 8 shows the UBVRI observational cam-
paign of Flavia’ star at the Stenberg, Loiano, Byu-
rakan and Tirgo telescopes and X-ray observations
with the ASTRON satellite between September 1983
and April 1984 (Giovannelli et al., 1984b). The blue
stars represent X-ray measurements during two out-
bursts (Giovannelli & Sabau-Graziati, 1992 and ref-
erences therein). The optical outburst occurred on
October 3, 1983 (JD 2,445,611) — practically in the
19th cycle after the 771220-E (or the 6th cycle af-
ter 811205-E) — just 8 days before the X-ray max-
imum (JD 2,445,619). The successive X-ray out-
burst occurred just one cycle later [JD (5732–5735)
+ 2,440,000] with the probable maximum just at JD
5726; the 20th optical cycle after the 771220-E (or
the 7th cycle after 811205-E) was at JD 5720 (also
visible in Fig. 7).

Figure 9 shows X-ray outbursts of A0535+26 in
different epochs. Red lines mark the time of the op-
tical cycles after 811205-E. The X-ray activity starts
roughly 8–12 days after the periastron passage of the
neutron star. The strong X-ray outbursts, named
casual, also occur preferably close to the periastron.

Finally, Fig. 10 shows strong optical activity of
Flavia’ star detected at the Loiano 1.5 m telescope
through Hα, Hβ and Hγ and He I lines (Giovannelli
et al., 2010). Such activity predicted the incoming X-
ray outburst of A0535+26 (Caballero et al., 2010c),
as shown in Fig. 11.

Figure 11 shows the March–April 2010 X-ray
outbursts of A0535+26. The X-ray activity starts
roughly 8 days after the 93rd cycle from the 811205-E
(Caballero et al., 2010a). The strong optical activity
of Flavia’ star (Giovannelli et al., 2010) was detected
∼ 10 days before the maximum of the X-ray outburst
(Caballero et al., 2010c).

3 Discussion and conclusions
We think we have clearly demonstrated that the op-
tical orbital period of the A0535+26/Flavia’ star
system is Porb−opt = 110, 856 ± 0.02 days. With
this periodicity, the system scans the neutron star
passage at the periastron with impressive precision.
This passage is roughly 8 days before any kind of
X-ray outbursts: normal, anomalous (or noisy) and
casual outbursts, with some exceptions of the lat-
ter that can also occur outside this phase. An
example of this could be October 9–24, 1980 (JD
2,444,522–2,444.537) a casual X-ray outburst appar-
ently occurred between the 9th (JD 2,444,500.6) and
10th (JD 2,444,611.4) cycle after the 771220-E (see
Fig. 6). However, according to the available measures
(Giovannelli & Sabau-Graziati, 1992 and references
therein), the X-ray outburst started 22 days after the
periastron passage. However, the first X-ray measure
gives an intensity of 1.1 Crab, and the maximum of
this strong outburst seems to be placed on October 10

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Acta Polytechnica Vol. 51 No. 2/2011

Fig. 9: X-ray outbursts of A0535+26 in different epochs. Red lines mark the time of the optical cycles after 811205-E.
The X-ray activity starts roughly 8–12 days after the periastron passage of the neutron star. Also in the case of strong
X-ray outbursts, named casual, they occur preferably close to the periastron. Upper left and right panels are adapted
fromVioles et al. (1982), andGiovannelli &Sabau-Graziati (1992), respectively; middle left and right panels are adapted
from Finger, Wilson & Hagedon (1994), and Caballero (2009), respectively; lower left and right panels are adapted from
Caballero et al. (2010b, and Caballero et al. (2010c), respectively

29



Acta Polytechnica Vol. 51 No. 2/2011

Fig. 10: Strong optical activity of Flavia’ star detected at the Loiano 1.5 m telescope through Hα, Hβ and Hγ and He I
lines. The fluxes are normalized to the continuum (Giovannelli et al., 2010)

Fig. 11: March–April 2010 X-ray outbursts of A0535+26. The thin red line marks the time of the 93rd optical cycles
after 811205-E. The bold red line marks the detected strong activity of Flavia’ star

(1.5 Crab). The decay of the outburst extends until
October 24 (0.4 Crab) — the last measure available.
Then if we extrapolate the same shape of the decay to
the rise of the outburst, we could have had the same
intensity as on October 24 roughly on September 27
(JD 2,444,509). This date is just about 8 days after
the 9th cycle after the 771220-E! This could support
the idea that all the outbursts are triggered around
the periastron passage, even those referred to as ca-
sual (strong).

In conclusion, we have demonstrated that the op-
tical ephemerides of the system can be given by

JDopt−outb = JD0(2,444,944) ± n(110.856 ± 0.02)
days.

Then the periastron passage of the neutron star is
scanned every 110.856 days, and the X-ray outbursts
are triggered starting from that moment and occur
roughly after 8 days — the transit time of material
expelled from the primary to reach the secondary.
In the case of Be star in “quiescence (steady stellar
wind)”, the X-ray outburst has an intensity ≈ 0.1–0.5
Crab (normal outbursts); in the case of “moderate
activity (steady stellar wind plus puffs of material

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Acta Polytechnica Vol. 51 No. 2/2011

expelled)”, the intensity of the X-ray outburst is
≈ 0.5–1 Crab (anomalous or noisy outbursts); in the
case of the “expulsion of a shell” from the primary,
preferably triggered near the periastron passage, a
very strong X-ray outburst (> 1–∼ 4 Crab) occurs
and its duration is typically very long (≈ 10–20 days)
(casual outbursts).

Therefore, continuous long-term monitoring of
A0535+26/Flavia’ star at least in optical and X-ray
could definitively prove our conclusions. We believe
that this behaviour of A0535+26/Flavia’ star system
is typical for all the X-ray/Be systems for which we
wish methodical multifrequency monitoring.

In conclusion, with this paper we want to give
a hint to the community to think again about the
mechanisms responsible for outbursts in X-ray pul-
sars, and about new overall models of X-ray/Be sys-
tems.

Acknowledgement

We are pleased to thank the organizers of the Karlovy
Vary 7th INTEGRAL/BART Workshop. One of us
(FG) wishes to thank the LOC for logistical support.

This research has made use of NASA’s Astro-
physics Data System.

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Franco Giovannelli
E-mail: franco.giovannelli@iasf-roma.inaf.it
INAF – Istituto di Astrofisica Spaziale e Fisica Cos-
mica – Roma,
Area di Ricerca di Roma-2
Via del Fosso del Cavaliere 100, I 00133 Roma, Italy

Lola Sabau-Graziati
INTA – Dpt de Programas Espaciales y Ciencias del
Espacio
Ctra de Ajalvir Km 4 – E 28850
Torrejón de Ardóz, Spain

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