Suzaku Discovery of Hard X-ray Pulsations from the Rotating Magnetized White Dwarf, AE Aquarii

1 MB·English

by  Yukikatsu Terada

PASJ:Publ.Astron.Soc.Japan,1–??,
(cid:13)c 2008.AstronomicalSocietyofJapan.
Suzaku Discovery of Hard X-ray Pulsations from the Rotating
Magnetized White Dwarf, AE Aquarii
Yukikatsu Terada,1 Takayuki Hayashi,2 Manabu Ishida,3 Koji Mukai,4
TadayasuDotani,3 Shunsaku Okada,3 Ryoko Nakamura,3
Sachindra Naik,5 Aya Bamba,3 and Kazuo Makishima,6,7
1Department of Physics, Science, Saitama University, Saitama 338-8570
2Science of Physics, Tokyo Metroporitan University,
1-1 Minami-Osawa, Hachioji-si, Tokyo, 192-0397, Japan
8 3Department of High Energy Astrophysics,
0 Institute of Space and Astronautical Science (ISAS),
0 Japan Aerospace Exploration Agency (JAXA),
2
3-1-1 Yoshinodai, Sagamihara, Kanagawa 229-8510, Japan
n 4Exploration of the Universe Division, Code 660,
a NASA/GSFC, Greenbelt, MD 20771, USA
J 5Physical Research Laboratory, Ahmedabad 380 009, India

4 6Makishima Cosmic Radiation Laboratory, RIKEN,
2
2-1, Hirosawa, Wako-shi, Saitama 351-0198, Japan

7Department of Physics, Graduate School of Science,
]
h University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
p [email protected]
-
o
(Received 2007 September18; accepted 2007 November14)
r
t
s Abstract
a
[ The fast rotating magnetized white dwarf, AE Aquarii, was observed with Suzaku, in October 2005

and October2006with exposuresof 53.1and42.4ks,respectively. In additionto clearspin modulationin
2
v the 0.5–10 keV band of the XIS data at the barycentric period of 33.0769±0.0001s, the 10–30 keV HXD
6 data in the second half of the 2005 observation also showed statistically significant periodic signals at a
1 consistentperiod. Onthatoccasion,the spin-foldedHXDlightcurveexhibitedtwosharpspikesseparated
7 by ∼0.2 cycles in phase, in contrast to approximately sinusoidal profiles observed in energies below ∼ 4
2
keV. The folded 4–10 keV XIS light curves are understood as a superposition of those two types of pulse
.
1 profiles. The phase averaged 1.5–10 keV spectra can be reproduced by two thermal components with
1 temperatures of 2.90+0.20 keV and 0.53+0.14 keV, but the 12-25 keV HXD data show a significant excess
−0.16 −0.13
7 above the extrapolated model. This excess can be explained by either a power-law model with photon
0 index of1.12+0.63 orathirdthermalcomponentwithatemperatureof54+26 keV.Atadistanceof102pc,
: −0.62 −47
v the4–30keVluminositiesofthethermalandtheadditionalcomponentsbecome1.7+1.3 and5.3+15.3×1029
−0.6 −0.3
Xi erg s−1, respectively. The latter corresponds to 0.09% of the spin down energy of the object. Possible
emission mechanisms of the hard pulsations are discussed, including in particular non-thermal ones.
r
a Key words: acceleration of particles – stars: white dwarfs – X-rays: individual (AE Aquarii)
2πR
1. Introduction V ∼ BR
(cid:18) P (cid:19)
Since the discovery of cosmic-rays by Hess in 1912,the −1 2
P B R
originofsuchhigh-energyparticlesandthe mechanismof ∼6×1016 V (1)
(cid:18)1s(cid:19) (cid:18)1012G(cid:19)(cid:18)106cm(cid:19)
their acceleration have remained a long-standing issue in
astrophysics. Among varioustypes of astrophysicalparti- where R is a typical radius from the NS center at which
cleaccelerationsites,oneimportantprototypeisrotation- the electric acceleration takes place.
poweredpulsars,namelyfastrotatingneutronstars(NSs) Magnetized white dwarfs (WDs) are similar systems to
with strong magnetic field of ≥ 1012 G. They are con- pulsars; rotating compact objects with strong magnetic
sidered to accelerate particles using their rotation as the fields. Since a typical magnetized WD has P ∼5×103
ultimate energy source, and strong electric fields as the s, B ∼106 G, and R≥ 109 cm, we expect V ∼ 1013 V
acceleration tool. The electrostatic potential, induced by fromequation(1). Therefore,magnetizedWDsshouldbe
the strong surface field, B, and the fast rotation with a a promising candidate of new particle acceleration sites,
period, P, is expected to amount to although efficiencies of the particle acceleration and the
2 Y. Terada et al. [Vol. ,
subsequent radiation could be different between pulsars away due to propeller effects. These observed properties
and WDs. altogether suggest strongly that AE Aqr is a promising
Non-thermalincoherentradioemissionhasinfactbeen site of particle acceleration, as pointed out by de Jager
detected from seven WDs via systematic radio surveys (1994).
(Nelson and Spencer 1988; Beasley et al. 1994; Pavelin The hard X-ray band is most suited to the search for
et al. 1994; Bond et al. 2002; Mason and Gray 2007). the expectednon-thermalsignals,becausethatparticular
SomeobjectslikeAEAquarii(Bastianetal. 1988;Abada- band is expected to receive the largest number of non-
Simon et al. 1993) and AM Herculis (Chanmugam and thermal high-energy photons without being hampered by
Dulk 1982; Dulk et al. 1983) show signs of coherent ra- the soft X-rays arising from accretion. In the present pa-
dio emission. Then, higher-energy photons in the X-ray per, we report on the first successful detection of pulsat-
to gamma-raybands mayalsobe generatedviasuchnon- inghardX-raysfromthe mostpromisingobject,AEAqr,
thermalprocessesascurvatureradiationlikeinNSs,non- achievedwithSuzaku(Mitsudaetal. 2007),whichcarries
thermal bremsstrahlung, and inverse Compton scattering two instruments; the X-rayCCDcameracalledthe X-ray
of soft photons (Chanmugam and Brecher 1985; Cheng ImagingSpectrometer(XIS;Koyamaetal. 2007)withthe
and Ruderman 1991; Ikhsanov and Biermann 2006), X-ray telescope (XRT; Serlemitsos et al. 2007) and the
as well as electron-positron annihilation lines and γ-ray Hard X-ray Detector (HXD;Takahashi et al. 2007). The
emission via the π0 decay chain. In fact, some au- emission is likely to be of non-thermal origin, thus rein-
thorsreportedTeVgamma-rayemissionfromAEAquarii forcing the view that MCVs are indeed particle accelera-
and AM Herculis during optical flares (Meintjes et al. tors.
1992;Meintjes et al. 1994;Bhat et al. 1991). Therefore,
high energy electrons with energies reaching 1-100 MeV 2. Observation and Data Reduction
are thought to be present in these WDs (Abada-Simon
2.1. Suzaku Observation of AE Aqr
et al. 1993; Meintjes and Venter 2003).
The object AE Aquarii (hereafter AE Aqr), located WeobservedAEAqrwithSuzakutwiceduringtheper-
at a distance of d = 102+42 pc (Friedjung 1997), is a formance verification phase. The first observation was
−23
magnetized cataclysmic variable (MCV) belonging to the performed from 2005 October 30 02:13 UT to November
DQ Herculis (or intermediate polar) class. It is spinning 2 01:02 UT (sequence number 400001010), and the sec-
near break up (de Jager 1994) with a spin period of ond one from 2006 October 25 5:25 UT to 09:11 UT on
P = 33.0767 s (Patterson 1979), which is the second the next day (sequence number 400001020). The obser-
sp
fastest value among MCVs. This fast rotation, combined vations were carried out at the “HXD nominal” pointing
with the surface field intensity of B∼105–6 G which is a position (i.e., with the target on the nominal optical axis
typical value among intermediate polars, yields via equa- of the HXD). Although the HXD has no imaging capa-
tion (1) an induced potential of V ≃1014–15 V, which is bility, the full field of view of its PIN diodes (1.0 degrees
probablyoneofthehighestfoundamongMCVs. Inaddi- square)containednohardX-rayobjectsintheSwiftBAT
tion, AE Aqr has been in a spin-downstate over the past catalog. On both occasions, the XIS was operated in the
27 years, at a rather high rate of 1.8×10−6 s yr−1 (de normal mode with the “1/8 window” option, which gives
Jager et al. 1994; Mauche 2006). The value implies a atimeresolutionof1s,withoutchargeinjectionfunction.
huge spin-down luminosity of 6×1033 erg s−1 (de Jager The HXD was operated in the nominal mode; in the sec-
1994;deJageretal. 1994). Theobjectisoneofthe most ond observation,however,a quarter of the 64 PIN diodes
asynchronouscataclysmicvariableswithanorbitalperiod were operated with a reduced voltage of 400 V, rather
of P =35567s=9.88hr (Casareset al. 1996;de Jager than the nominal 500 V.
orb
et al. 1994). Flares reported in the radio band (Bastian
2.2. Data Reduction
etal. 1988;Abada-Simonetal. 1993)areconsistentwith
synchrotronemission(MeintjesandVenter 2003),andthe We used the datasets produced by the Suzaku pipe-
pulsatingTeVgamma-rays(Meintjesetal. 1992;Meintjes line processing version 1.2.2.3 with the calibration-
et al. 1994) are sometimes coincident with optical flares. version of hxd20060829, xis20060913, xrt20060720, and
AccordingtosoftX-rayobservations(EzukaandIshida xrs20060410,usingtoolsinHEADASpackageversion6.2.
1999; Itoh et al. 2006), the plasma temperature of thin WeusedXSPECversion11.3.2,tofitspectrawithmodels.
thermalradiationfromAEAqrissignificantlylowerthan The source was detected with the XIS in the 0.5 – 10
the estimated gravitational potential of its WD, whose keV band at an intensity of 0.37 c s−1 and 0.28 c s−1 per
mass is about 0.8 – 0.9 times the solar mass (Casares sensor, in 2005 and 2006, respectively. In the XIS analy-
etal. 1996;Welshetal. 1995). Furthermore,itsUVtoX- sis,weexcludedalltelemetry-saturateddataportions,and
rayluminosity(1031 ergs−1)isthreeordersofmagnitude data takenin “low” data-ratemode. We further removed
lower than that in a simple accretioncase (Eracleous and those intervals when the source elevation above Earth’s
Horne 1996) with a rate of 1017 g s−1. Therefore, the limb was below 5◦, Earth’s day-night boundary was less
accreting matter may be inhibited fromreachingthe WD than 25◦, or the spacecraft was in, and 436 s after, leav-
surfacebythefastWDrotation(Itohetal. 2006). Wynn ing the South Atlantic Anomaly (SAA). We then accu-
et al. (1997) argue that only 1 % of the accreting gas in mulated nominal-grade events within 6 mm (4.′3) of the
AEAqrreachestheWDsurface,whiletherestisexpelled image centroid. The XIS background events were taken
No. ] Suzaku Discovery of Hard X-ray Pulsations from AE Aquarii 3
fromasource-freeregionofthecorrespondingsensor. The ing for ∼ 2500 s. In the PIN data, however, no corre-
derived background,exhibiting a rate of ∼0.02 c s−1 per sponding flux increases are found, primarily because of
sensor in 0.5–10 keV, is generally negligible except in the insufficient count statistics. Even if PIN counts increased
highest end of the XIS bandpass. byafactorof3in2500s(maximum∼38cper25ks),the
In calculating XIS ancillary response files, we took into associatedstatisticalerrors,∼36c,wouldbecomparable.
accountefficiency reductioncausedby the window option
andbyun-controlledfluctuationsoftheopticalaxisofthe
XRT (Serlemitsos et al. 2007). In the first observation,
the effective areasofXIS-0, 1,2,and 3were thus reduced
to 92.3%, 93.1%, 93.4%, and 93.7% of their nominal val-
ues, respectively, while those during the second observa-
tion were 93.7%, 93.2%, 92.8%, and 93.8% respectively.
TheHXDdatawerescreenedusingthesamecriteriaas
used on the XIS data. In addition, we discarded data ac-
quired during time intervals when the geomagnetic cutoff
rigidity was lower than 8 GV. After these filtering steps,
the final event list of HXD-PIN was obtained using only
those events that survived the standard anti-coincidence
function of the HXD (DET TYPE=1). The non X-ray
background (NXB) of HXD-PIN was synthesized by ap-
propriately combining night-Earthdata sets acquired un-
der different conditions (Kokubun et al. 2007), using Fig. 1. Background-subtracted light curves of AE Aqr dur-
METHOD=‘PINUDLC’ and version of METHODV=1.2 ingthetwoobservations,obtainedwiththeXIS(0.5–2keV
(Watanabe et al. 2007). and2–10keV)andtheHXD(13–30keV).TheHXDdata
After selecting event lists, the first observation yielded arecorrectedfordeadtime. TheXISandHXD-PINdataare
binnedinto250s.
netexposuresofabout 70.3and53.1ks with the XIS and
the HXD, respectively. Those in the second observation
3.2. XIS Period Determination
were 48.6 with the XIS, and 42.4 ks with the HXD.
After applying the standard barycentric corrections to
3. Timing Analyses thephotonarrivaltimes(Teradaetal. 2008),wesearched
the XIS light curves extracted from the source region for
3.1. Light Curves
periodic intensity variations synchronized with the WD
Background-subtracted light curves of AE Aqr, ob- rotation. Indoingso,wedidnotsubtractthebackground,
tained with the XIS and the HXD, are shown in fig- because the background events occupy only 5.0% of the
ure 1. From this figure, it is not obvious whether the total count rate of the XIS, and no periodicity around
source is detected with HXD-PIN. More quantitatively, P was found in the background data. The standard
sp
the background-subtracted 13–30 keV PIN counts inte- epoch-foldinganalysisofthe0.5–10keVXISdatarevealed
grated over 1 ks become 14.0±14.5±4.0 c ks−1 and highly significant source pulsations on both occasions, at
18.0±20.9±6.0 c ks−1, in 2005 and 2006, respectively; a barycentric period of P =33.0769 s. After Larsson
XIS
where the first uncertainties are statistical 90% errors, (1996), 68% errors associated with these period determi-
while the second ones are systematic errors in the PIN nationsareestimatedtobe 0.0063s and0.0104s,in2005
NXB subtraction estimated from the reproducibility of and 2006, respectively. Within these errors, the derived
counts during the satellite pointing at Earth. For ref- period is consistent with the values of P measured in
sp
erence, the PIN NXB counts in the same energy range the optical (Patterson 1979;de Jager et al. 1994), in X-
were 198 and 202 c ks−1 in 2005 and 2006, respectively. rayswithGinga,ASCA(Choietal. 1999),XMM-Newton
Therefore, the source detection with HXD-PIN becomes (Itoh et al. 2006), and Chandra (Mauche 2006), and in
significant both in the 2005 and 2006 observations when TeVγ-rays(Meintjes et al. 1992). Therefore,we identity
integratedoverthe fullexposureof∼50ks. However,the P with the rotational period of the WD in AE Aqr;
XIS
detection becomes marginal when we consider contribu- that is, P =P .
XIS sp
tion from the cosmic X-ray background (CXB) which is Figure 2 (top) shows 0.5–10 keV XIS periodograms,
estimated to be 18.0 c ks−1 in the 13–30 keV PIN band, used in determining P . Strictly speaking, the above
XIS
basedonitscanonicalsurfacebrightness(Boldt 1987)and period determinations utilized the full length of the 2005
the angularresponseofthe PINdiodes to uniformillumi- and 2006 data sets, while the periodograms in this fig-
nation. Aiming at a higher detection sensitivity, below ure were obtained with the 2005 data divided into the
we searchthe data for periodic modulations synchronized first and second halves (hereafter 2005a and 2005b, re-
with the WD rotation, before carrying out spectral anal- spectively), each having a 90.2 ks gross duration, and a
yses. net exposure of 26.4 and 34.6 ks, respectively. The very
In both observations, the XIS data reveal severalflares similar shapes of the three (2005a, 2005b, and 2006) XIS
involving two- to three-fold intensity increases, each last- periodogramsindicatethattheperiodicmodulationinthe
4 Y. Terada et al. [Vol. ,
of the folded pulse profiles is conducted in subsection 3.4.
Fig. 2. Periodogramscalculatedfromthebackground-inclu-
siveXISdata(red) andtheHXD-PINdata (blue). Thever-
tical axis shows reduced χ2, calculated against a hypothesis
that the folded data profile is constant. The period step is Fig. 3. Energy-resolved light curves folded on the
2.5×10−5 s, using 7 and 64 bins per cycle for the XIS and XIS-determined period of 33.0769 s. The non X-ray
HXD, respectively. The vertical green lines indicate various backgroundsaresubtractedfromtheXISdata,butnotfrom
expected periods; the spin period PSP (thick dashed); Ppro theHXD-PINdata. Theenergies fromtoptobottom panels
and Pret (thin dashed); and the beat periods between PSP are0.5–1keV, 1–2keV,2–4keV, 4–6keV,and 6–10
and 1 day (dotted). (left) Results from the first half of the keV for the XIS, while10 – 40 keV or 13 – 40 keV with the
2005data, wherethePINenergybandis10–30keV.(mid- HXD for the 2005 and 2006 observations, respectively. The
dle)Thesameasleftpanel,butforthesecondhalfofthe2005 vertical axis shows the count rate ineach energy band, with
observation. (right)Resultsfromtheentire2006observation, the maximum scale set to 1.3 times the averaged count rate
wherethePINenergybandrefersto13–30keV. of that band. Phase 0.0 corresponds to BJD 2453673.5000,
and the date of the pulse peak in the 0.5-2 keV band (at
XIS band is quite stable. Although we could in princi- a spin phase of 0.035) occurs on BJD 2453673.5000134 ±
0.0000011.
ple determine the period with a much higher accuracy
by coherently combining the 2005 and 2006 datasets, the
3.3. HXD Period Search
periods on individual occasions are too uncertain to ex-
trapolatethemforone yearwithoutpulse-countambigui- After the same barycentric corrections, we folded
ties. Instead,weincoherentlycombinedthe2005and2006 background-inclusivePINdataontheperiodofP . The
XIS
periodograms, which reduced the period error to 0.0001s 2005datawereanalyzedinanenergyrangeof10–30keV,
(Larsson 1996). We hence quote the XIS-determined pe- while those of 2006 in 13–30 keV, because thermal noise
riod as PXIS=33.0769±0.0001s. arosearoundthePINlowerthresholdlevelinthisobserva-
In energies below 2 keV, the pulse-peak phase tion. Since the PIN data have much poorer signal statis-
comes at BJD (Barycentric Julian Ephemeris Day) tics, we tentatively divided the period into seven phase
2453673.5000134±0.0000011,fromthecombineddataset bins. Then, as shown in figure 3 (bottom) in blue, a sta-
of2005and2006foldedonthe periodofPXIS. Whenthis tistically significant modulation with a spiky profile was
epoch and the above determined PXIS are employed, our found from the 2005 data with a reduced chi-squared of
measurement predicts the pulse peak to occur at BJD χ2 =2.5 for ν=6, whereas the 2006 data was consistent
ν
2453613.2767025 during the Chandra observation con- with being constant (χ2 =0.62).
ν
ducted on 2005August31. This agrees,within 0.0000033 Now that the PIN signals exhibit a hint of periodic
days, or 0.29 s with that actually measured on that occa- modulation at the period of P at least in the first ob-
XIS
sion by Mauche (2006), namely BDJ 2453613.2767058± servation, we proceed to more systematic epoch-folding
0.0000039. analyses on the background-inclusive 10–30 keV (or 13–
TheXISlightcurves,foldedonthespinperiodPXIS,are 30 keV) PIN light curves. The reason for not subtract-
presented in figure 3 in several energy bands. Thus, the ing the background is that the actual background would
modulationatlowerenergieshasasinusoidalprofile,with not vary significantly in 30 s (Kokubun et al. 2007), and
an amplitude of ∼±16% of the mean intensity. Toward that the synthetic PIN background models have larger
higher energies, the folded pulse profiles become more uncertainties when used on time scales of ∼1 s, as would
structured;this maybe responsiblefor the fine structures be needed here. Specifically, we calculated HXD peri-
seen in the XIS periodograms(figure 2). Further analysis odograms over a trial period range of 33.04 to 33.12 s,
No. ] Suzaku Discovery of Hard X-ray Pulsations from AE Aquarii 5
with a typical period step of 2.5×10−5 s or even finer.
The bin number per cycle was varied in the range be-
tween 7 and 13. Furthermore, to avoid false quantization
effects due to finite phase bin numbers, we calculated, at
each trial period, chi-squares by changing the time origin
withinasinglephasebin,andthenselectedthemaximum
value to construct the periodogram. Typical results from
these studies are shown in figure 2 in blue, in comparison
with those from the XIS data. Thus, the three (2005a,
2005b, and 2006) PIN periodograms all exhibit multiple
peaks reachingχ2 =3−4. Therefore, the PIN signals are
ν
inferredtobesignificantlyvariableontimesscalesof∼33
s, possibly involving rather rapid variations as suggested
by the narrow widths of these peaks.
The most important finding from these studies is that
the2005bPINperiodogramexhibitsitshighestpeakwith
χ2=4.2(forν=6)ataperiodofP =33.0764±0.0005
ν HXD
s, which agrees well with P , and hence P within re-
sp XIS
spective errors. The probability of this peak arising by
chance is lower than 7×10−7. Although the results pre-
sented here were obtained using a particular 7 phase bins
per cycle, the results do not change if different numbers
of bins (e.g., 8, 11, or 13) are utilized. The reason why
the PIN profile in figure 3 exhibited χ2 =2.5 instead of
ν
the peakvalue(χ2=4.2)isthatitwascalculatedatP
ν XIS
ratherthanP . The peak atP doesnot disappear
HXD HXD
evenifwedividethe2005bdataintotwohalveseachcom-
prising 32 PIN detectors. Furthermore, side lobes seen at
33.060sand33.092sinthe2005bplotcanbeinterpreted
asduetobeatbetweenP andtheSuzakusamplingwin-
sp
dow. ThesefactssuggestthattheperiodicsignalatP
HXD
in the 2005b PIN data is real, and is intrinsic to the WD
rotation. ThenarrowerpeakinthePINperiodogramcom-
paredtothatoftheXIS,isconsistentwiththefoldedPIN
profile having sharp structures, as already suggested by
figure 3. In contrast,the PIN signal modulation at P is
sp
not significant either in the 2005a or the 2006 data.
3.4. Pulse Profiles
We have so far obtained promising evidence that the
PIN signals are indeed modulated at P . Of course, the
sp
peak in the 2005bperiodogram(figure 2) could be an ac-
cidentalcoincidencecausedbysomenon-periodichardX-
ray variations, considering the presence of multiple peaks Fig. 4. Soft and hard X-ray profiles of AE Aqr, folded on
in the other PIN periodograms. However,in figure 3, the theHXD-determinedperiodPHXD. Phase0.0correspondsto
BJD2453673.5000. SeethetextfortherelativeXISvs. HXD
XIS profiles become similarly structured toward higher
timing alignment. (Top and middle) Background-inclusive
energies. Therefore, we expect that the hard X-ray pe- 0.5–4 keV (green) and 4 – 10 keV (in red) XIS profiles ac-
riodicity can be reinforced by comparing the folded PIN quiredin2005 and 2006, respectively. The 0.4–4 keV profile
profiles with those from the XIS in harder energies. is arbitrarilyscaled to approximately agrees with the 4 – 10
keV profile. (Bottom) The background-inclusive 10–30 keV
We sorted the XIS data into two bands (0.5–4 keV and
HXD-PIN data, taken in the entire 2005 observation in blue
4–10 keV), and folded them both at the period of P .
HXD andthesecondhalfof2005ingreen.
For reference, we also folded the 2005 HXD-PIN data in
10–30 keV at the same period, with the same bin size as
bottom,the2005PINsignalmodulationbecomesstronger
for the XIS data, namely 29 bins per cycle. The folded
whenwelimitthedatatothesecondhalf(2005b)inagree-
profilesderivedinthethreeenergybandsarepresentedin
ment with the inference from the periodogram (figure 2);
figure 4. As already suggested by figure 3, the PIN pro-
the modulation amplitude of the spike changes from 0.03
files indeed exhibit several sharp spikes, among which at
± 0.01 c s−1 to 0.05 ± 0.01 c s−1. Importantly, a similar
leasttwo,oneatapulse phaseofφ∼0.9andthe otherat
spikeisalsoobservedatφ∼0.95inthe4–10keVXISpro-
φ∼0.1, are statistically significant. As shown in figure 4
6 Y. Terada et al. [Vol. ,
file in 2005 (figure 4), superposed on the approximately 3.5. Other issues
sinusoidalintensitymodulationwhichdominatesthespin-
While we have so far concentrated on the signal mod-
folded profiles in lowerenergies. As seen in figure 4 (mid-
ulation at the spin period P , the signals could also
dle), the sharp features in the 4 – 10 keV XIS profile is sp
be modulated at beat periods between the rotational
found also from the 2006 data, but with a reduced am-
and orbital periods, namely at so-called prograde period
plitude, in agreement with the negative detection of the
P =(P−1−P−1)−1 = 33.1075 s, or retrograde period
periodic signal in the 2006 PIN data (section 3.3). pro sp orb
P =(P−1+P−1)−1 = 33.0460 s. If, for instance, the
In figure 4, the major sharp spike shows a slight phase ret sp orb
difference by φ∼0.05 between the XIS (4–10 keV) and WD is rotating in the same sense as its binary motion,
andtheX-rayemissionregionisstationarywhenobserved
PIN data sets. This could be either real or instrumental,
from a frame ofreference co-rotatingwith the binary,the
because the relative timing between the XIS and HXD is
accurateonlytowithin∼±0.5seventhoughtheabsolute signals would be modulated at Ppro rather than at Psp.
Indeed,the2005aPINperiodogram(figure2left)exhibits
timing of the HXD has been verified to an accuracy of
the highest peak at 33.1080±0.0003 s, which is close to
360 µs (Terada et al. 2008). In order to study at which
P . All the XIS periodograms(figure 2)also showsome
energy this spike appears, and to examine whether the pro
enhancements at ∼P . However, the peak in the 2005a
majorspikeexhibitsanyenergy-dependentphaseshift,we pro
PINperiodogramisslightly(butsignificantly)offsetfrom
cross-correlatedtheenergy-sortedXISprofilesofthe2005
the exact P . Moreover,the 2005bPIN data exhibit no
observation(figure3left)againstthepulsetemplatefrom pro
significant modulation at P , nor at P . Therefore,we
thePINdata(i.e.,figure4bottom). Theresults,shownin pro ret
concludethatthe hardX-rayperiodicityatthe beatperi-
figure5,revealsaphasediscontinuityatabout4keV.This
ods are less convincing, and defer further examination to
means that the XIS profile below 4 keV is dominated by
a future publication.
the sinusoidal modulation, and the separate spike starts
Since the WD in AE Aqr has a projected orbital semi-
appearingabove4keV.Sincethecross-correlationpeakis
thus found consistently at φ∼−0.06 over the 4 – 10 keV major axis of ∼ 2 l-s around the binary center of gravity,
the X-ray pulse arrivaltimes are expected to vary by this
energybandoftheXIS,theapparentphasedifference(by
φ∼0.05)seeninfigure4betweentheXIS(4–10keV)and amount depending on the orbital phase. In fact, Mauche
(2006) successfully detected this effect, and determined
PIN profiles is likely to be instrumental rather than real.
the orbital modulation amplitude as A = 2.17±0.48 l-
Basedontheclosesimilaritybetweenthe4–10keVXIS
s; this is ±8% of the pulsation period. While this may
foldedprofileandthosefromHXD-PIN,weconcludethat
be negligible when the pulse profile is sinusoidal, the or-
the periodicity in the PIN signal (at least in 2005b) is in
bitaleffectscouldhavesignificanteffectswhenithassharp
fact due to the WD rotation, and hence AE Aqr emits,
structures,asis infactthe casewiththe 2005bPINdata.
at least occasionally, and at least in the 4-30 keV band,
Therefore,we attempted tocorrectthe arrivaltimes, t, of
a periodic hard X-ray emission component whose folded
individual X-ray events by subtracting the expected or-
profile consists of a few sharp pulses.
bital modulation,
2
0.
t−t
∆t=Acos 2π 0 −ξ , (2)
(cid:20) (cid:18)P (cid:19)(cid:21)
orb
1
0.
where t is the time of the superior conjunction of the
0
e WD, and ξ (0≤ξ≤1) is any possible phase shift.
s
ha Employing the nominal orbital parameters by de Jager
a P 0 etal. (1994),namelyξ=0.0,t =BJD2445172.2784,and
elt 0
D A=2.04s,whereAisconsistentwithinerrors(2.04±0.13
s) with the value 2.17±0.48s by Mauche (2006), we ap-
1
−0. plied the correction of equation (2) to the 4–10 keV XIS
data. Then, the periodogram peak at P became in-
XIS
deedhigher,withχ2/ν increasingfrom7.8to 9.2in2005,
2
−0.0.5 1 2 5 10 and from 6.5 to 8.0 in 2006. When the same correction
Energy (keV) is applied to the PIN data, the 2005b periodogram peak
at P has also increased from 4.2 to 4.3, although no
Fig. 5. EnergydependenceofthephaseoftheXISpulsepro- HXD
files from the 2005 observation, relative to the 10 – 30 keV major effects were observed in the other two PIN peri-
PIN profile. The vertical axis shows the phase at which the odograms. This reinforces our inference that the hard
cross correlation value of each profile to the PIN profile be- X-raypulsationin the 2005bdata is due to the WD rota-
comes maximum. The folded XIS profiles refer to figure 3
tion. WhenweallowedAandξ tovary,the4–10keVXIS
(left),whilethatofHXD-PINthe2005datainfigure4(bot-
data preferredA=1.5±0.5andξ=−0.1±0.1,whichare
tom).
notmuchdifferentfromthenominalephemeris. Although
errors are large, the 2005b PIN data also favor these pa-
rameter regions.
No. ] Suzaku Discovery of Hard X-ray Pulsations from AE Aquarii 7
Fig. 6. Background-subtracted spectra of AE Aqr obtained with Suzaku in2005 and 2006 (leftand right, respectively) presented
withoutremovingtheinstrumentalresponses;errorbarsarestatistical only. Thelightgreencurvesshowthetypical uncertaintyof
thePINnonX-raybackground, andthedarkgreencurvesindicatestheexpected cosmicX-raybackground(Boldt 1987).
4. Spectral Analyses been shown with ASCA and XMM-Newton (Choi et al.
1999; Itoh et al. 2006) to be reproduced by an optically
To study the origin of the pulsating hard X-ray com- thin thermal plasma emission model with a few different
ponentrevealedinthe timing analyses(section3), wean- temperature components. Thus,to reproducethe Suzaku
alyzed the pulse phase-averaged spectra taken with the spectra in the 0.5 – 25 keV band, we adopted a multi-
XIS andthe HXD. In this analyses,we discardedhalf the temperatureVMEKALmodel(Meweetal. 1995;Liedahl
PIN data acquired in 2006, under the reduced voltage of et al. 1995)which are constrainedto have common metal
400V, because the PIN response under this non-standard abundances but allowed to have separate temperatures.
operation condition is not yet fully calibrated. These components were subjected to a common photo-
The background-subtracted X-ray spectra of AE Aqr electric absorption with a free neutral column density.
obtained in this way are shown in figure 6. In agreement Theoverallmodelnormalizationwasconstrainedtobethe
with the inference made in section 3.1, the signal detec- samebetweenthe XISandPIN.Inthefitting, weignored
tion with the HXD is significant both in 2005 and 2006, thesystematicerrorsinthePINNXBestimation,because
up to ∼ 25 keV. This statement remains valid even if we thePINfluxwasconsistentwiththepulsefluxinthespin
consider the systematic errors in the PIN NXB subtrac- profile as already described. As summarized in table 1
tion,whichisestimatedtobe∼3%inthepresentcaseas (noted as “2005+2006”),the spectra were roughly repro-
judged from the reproducibility of the Earth occultation duced by three VMEKAL components, and the derived
data. However, as shown in figure 6, the PIN detection abundances are consistent with those by XMM-Newton
becomes marginal when we consider the CXB contribu- (Itoh et al. 2006). However, the fit was unacceptable
tion. Therefore, we further subtracted the CXB from the with large reduced chi-squared values of 1.79, and was
spectra,andsummedtheresultovertwoobservations. As not improved even if we added another VMEKAL com-
plotted in figure 7a, we obtained positive PIN signals at ponent. Inaddition,the modelfellanorderofmagnitude
a level of ∼2×10−4 c s−1 kev−1 around 20 keV. Thus short of the PIN data.
the source has been detected up to ∼25 keV. There, the The large value of reduced chi-squared from the three-
greenlineinthefigurerepresentsthephase-averaged13– temperature VMEKAL fit (table 1) is mainly caused by
30 keV count rate of the spiky signals,∼1.5×10−4 c s−1 disagreements between the model and the data around
keV−1, obtained as a difference between the pulse-peak 1 keV, where the Fe-L line complex is present. Thus, we
phase (φ = -0.1 – 0.1) and the other phase in figure 4 ignoredthedatabelow1.5keVandfittedthe1.5–25keV
(bottom). The good agreement in figure 7a, between the data with two VMEKAL components, whose abundances
spectralandtimingresultsfromHXD-PIN,indicatesthat werefixedtothevaluesbyItohetal. (2006)forsimplicity.
the emission in the PIN range is pulsating nearly 100%. Asshowninfigure7bandlistedintable2,thefitbecame
The phase averaged X-ray spectra of AE Aqr has muchimprovedwithreasonabletemperaturesof2.90+0.20
−0.16
8 Y. Terada et al. [Vol. ,
Table 1. BestfitparametersofthemultitemperatureVMEKALModeltothephaseaveragedspectra.
XMM-Newton 2001∗ 2005 2006 2005+2006
N (1020cm−2) 3.59+1.47 <1.28 <2.04 <1.92
H −1.20
kT (keV) 4.60+0.60 3.17+0.25 3.19+0.65 3.04+0.14
1 −0.47 −0.15 −0.35 −0.22
kT (keV) 1.21+0.13 0.93+0.05 0.87+0.07 0.86±0.06
2 −0.08 −0.08 −0.13
kT (keV) 0.59±0.02 0.53+0.02 0.50+0.04 0.50+0.04
3 −0.03 −0.07 −0.05
kT (keV) 0.14+0.05 – – –
4 −0.02
N (Abundance†) 3.51+0.92 3.51 fix 3.51 fix 3.51 fix
−0.81
O (Abundance†) 0.74+0.17 0.66+0.09 0.57±0.16 0.64+0.09
−0.23 −0.10 −0.05
Ne (Abundance†) 0.43+0.28 0.66±0.17 0.49+0.26 0.68+0.14
−0.25 −0.18 −0.16
Mg (Abundance†) 0.70+0.15 0.76+0.10 0.68+0.22 0.77±0.12
−0.14 −0.13 −0.18
Si (Abundance†) 0.81+0.14 0.65+0.09 0.43+0.13 0.58+0.09
−0.12 −0.11 −0.12 −0.10
S (Abundance†) 0.73+0.20 0.89±0.15 0.70±0.19 0.80±0.15
−0.18
Ar (Abundance†) <0.89 0.67+0.45 0.31+0.66 0.55+0.47
−0.43 −0.41 −0.46
Ca (Abundance†) <1.11 0.37+0.53 0.83±0.80 0.68+0.59
−0.37 −0.60
Fe (Abundance†) 0.47+0.07 0.40+0.04 0.33±0.07 0.39+0.04
−0.06 −0.05 −0.02
Ni (Abundance†) 1.27+0.57 1.36+0.37 0.89+0.54 1.14+0.31
−0.50 −0.39 −0.42 −0.34
Flux‡(10−12 erg s−1 cm−2) 11.6 6.83+0.33 6.22+0.38 6.65+0.20
−0.26 −0.24 −0.29
χ2(dof) 1.22(992) 1.94(152) 1.45(152) 1.79(152)
ν
∗ FromItohetal. (2006).
† Solarabundances byAndersandGrevesse (1989).
‡ Inthe0.5–10keVband.
keVand0.53+0.14 keV.However,themodelstilldisagrees 25keV,however,showsanexcessemissionoverthemodel.
−0.13
with the PIN data points. This excess can be fitted by a power-law model with a
To reproduce the PIN flux, we added an additional photon index of 1.1±0.6,or another thermal model with
power-law component to the two VMEKAL model, and the temperature of 54+26 keV. In the 13–30 keV range,
−47
obtained an acceptable result as shown in figure 7c and the spectrally measured excess, 3.2+9.7 c s−1, is consis-
−2.5
table2. TheF-statisticofthisimprovementis15.5,which tent within large errors with that contained in the sharp
means that the probability of this improvement being peaks in the spin-folded hard X-ray light curves.
causedbychanceis2.0×10−6. Thus,addinganothercom- The 4–30 keV flux of the additional hard component
ponent is justified. The power-law modeling is, however, from the spectral analysesis obtained as L ∼1.7+4.9×
HX −0.1
not unique, and another VMEKAL model instead of the 10−12ergcm−2 s−1,whichgivesaluminosityof5.3+15.3×
power-law model also provides a significantly improved −0.3
1029 erg s−1 at the distance of 102 pc (Friedjung 1997).
fit at a temperature of 54+26 keV (table 2), with the F-
−47 This correspondsto ∼0.01%of the spin-down luminosity
test value of 11.1 or the chance probability of 3.5×10−6. of 6×1033 erg s−1 (de Jager 1994;de Jageret al. 1994).
The derived temperature is essentially considered a lower
Note, however, that the hard X-ray pulsation has a duty
limit, i.e., >7 keV. Since a thermal component of such a ratio of only ∼0.1. If the hard X-ray emission is highly
temperatureis notrareamongaccretingWDs, wecannot
anisotropicwithouta constantbias,andifthe emissionis
distinguish, from the spectral analysis alone, whether the
beamed away from us in the other pulse phases, the true
additionalhardX-raycomponentdetectedwiththe HXD
hard X-ray luminosity would be higher, amounting up to
is thermal or non-thermal. 5×1030ergs−1whichis0.1%ofthespin-downluminosity.
In any case, the ratio of the hard X-ray emission to the
5. Discussion
spin-down luminosity of AE Aqr comes in the range of
5.1. Summary of the Observation 0.01–0.1%, which is the same as those measured in the
2–10 keV range from NS pulsars (Becker and Truemper
UsingSuzaku,weobservedAEAqrin2005and2006. In
1997; Possenti et al. 2002).
the first observation, the HXD detected periodic signals
synchronized with the rotation of the WD (section 3.3) 5.2. The Nature of the Hard X-ray Component
whose profile has a sharp peak (section 3.4) with a dura-
The observed hard X-ray emission pulsates at the WD
tion of ∼0.1 in phase. The same sharp feature was also
rotation period, but not at the prograde or retrograde
foundinthespin-foldedXISlightcurvesinenergiesabove
beat periods. In order to reinforce this result, we further
4 keV. The phase-averaged spectra from the XIS above
folded the 4–10 keV XIS data at the prograde and retro-
1.5keVcanbeexplainedwiththetwoopticallythinther-
grade beat periods, but the results were consistent with
mal plasma models with temperatures of 2.90+0.20 keV
−0.16 theabsenceofanyperiodicmodulation,eitherinthe2005
and 0.53+−00..1143 keV (section 4). The PIN spectrum up to or 2006data sets. This implies that the hard X-rayemis-
No. ] Suzaku Discovery of Hard X-ray Pulsations from AE Aquarii 9
Table 2. BestFitParametersofthemultitemperatureVMEKAL† with/withoutPowerLawmodeltothephaseaveragedspectra
inthe1.5–25keVband.
Model∗ N † kT ‡ Flux§ kT ‡ Flux§ Photon Index or kT ‡ Flux§ χ2 (dof)
H 1 2 3 ν
i <0.165 2.90+0.20 3.77+0.30 0.53+0.14 3.18+4.61 – – 1.27 (84)
−0.16 −0.18 −0.13 −0.97
ii 0.66+0.36 2.04+0.09 1.96+0.32 0.27+0.05 0.74+1.64 1.12+0.63 0.59+1.80 0.95 (82)
−0.38 −0.21 −0.37 −0.05 −0.56 −0.62 −0.05
iii 0.67+0.17 2.01+0.17 2.13+0.03 0.26+0.07 3.82+6.86 54.4+25.7 0.66+11.9 0.95 (82)
−0.20 −0.23 −0.64 −0.04 −2.83 −47.2 −0.20
∗ Abundances are fixed to the XMM-Newton values (Itoh et al. 2006). Model (i) is double VMEKAL, (ii) is double
VMEKALwithpowerlaw,and(iii)istripleVMEKALmode.
† Columndensityin1020 cm−2.
‡ TemperatureinkeV.
§ Fluxin10−12 ergs−1 cm−2 in0.5–10keV.
sion region is fixed in the frame which is co-rotating with ing the XMM-Newton RGS data of AE Aqr, concluded
the WD, while excludes a possibility that the emission that a plasma with the electron density n ∼1011 cm−3
e
region is fixed to the binary frame. is spread over a scale of (2−3)×1010 cm in this binary
Although approximately in phase with the soft X-ray system. Since this plasma density exceeds the Godreich-
spin modulation, the hard X-ray pulses exhibit a spiky Juliandensity(GoldreichandJulian 1969)whichiscalcu-
profile with a duty ratio of only ∼ 0.1 in phase, un- latedas∼5×104 cm−3 inthe presentcase(Ikhsanovand
like the sinusoidal profile in the XIS band below 4 keV. Biermann 2006), the induced potential would be short-
Furthermore, the spin phase of the major spike exhibits circuited, and hence an efficient acceleration would not
an energy dependence with a discontinuity at ∼ 4 keV takeplace. However,boththeoretical(Wynnetal. 1997)
(figure5). ThesoftandhardX-raycomponentsarethere- and observational works suggest that the propeller effect
fore likely to originate from distinct emission sites. If in- producesalow-densitycavityaroundtheWD,byinhibit-
terpreted as hot thermal emission, the hard component, ing the accretion plasma from getting closer to the WD
with its very high temperature, should be emitted from than∼1010 cm(Wynn et al. 1997). The electric acceler-
the bottom of the gravitational potential, i.e., the WD ation may be possible in such regions.
surface, while the softer component from some outer re- Eveniftheplasmadensityissufficientlylow,anefficient
gions (Itoh et al. 2006). However, it would be highly electric-field acceleration also requires evacuation of neu-
difficulttoproducethe observedsharppulse profilesfrom tral matter from the acceleration region; otherwise, the
the WD surface (e.g., magnetic poles) via any thermal electrons would suffer too heavy ionization losses to be
process. Indeed, such X-ray pulsations, appearing only accelerated efficiently. The mean-free-path of an electron
in the hard X-ray band with very sharp profiles, have with energy E , due to ionization loss, is given by
e
never been observed from other accreting magnetic WDs
1 1 πe2 −2
(Teradaetal. 2004),inwhichthethermalemissionmech- λ ∼
e
anism is considered to dominate. We thus consider that nplnΛ(cid:18)8ǫ0Ee(cid:19)
the hardcomponentismorenaturallyinterpretedasnon- n −1 E 2
thermal emission, as evidenced by its successful power- ∼107 p e cm, (3)
lawmodeling. Ifso,apopulationofnon-thermalparticles (cid:16)1010cm−3(cid:17) (cid:18)1keV(cid:19)
must be accelerated in the AE Aqr system, at least oc- where np is the density of protons,lnΛ is a Coulomblog-
casionally,producingthe hardX-raypulsesdetectedwith arithm (typically ∼ 10 – 20), e is the elementary charge,
Suzaku. In the following two subsections, we discuss pos- andǫ0 isthe vacuumdielectricconstant(seee.g.,Rybichi
sible particle acceleration mechanisms, and hard X-ray & Lightman 1979). If aninitialelectronenergyisEe∼ 1
emission mechanisms from the accelerated electrons. keV assuming a thermal plasma in the system, the en-
ergy gain of the electron accelerated along the length
5.3. Possible Acceleration Mechanism
of λ can be roughly estimated to be E ∼ V ·λ ∼
e acc llc e
As mentioned in section 1, the fast rotating WD in the −1
1010 np eV, with V ∼1014 V and l ∼1011
AE Aqr system is expected to produce an induced elec- (cid:16)1010cm−3(cid:17) lc
tricpotentialreachingV ≃1014–15V.Therefore,itismost cm. Thus, the energy gain Eacc exceeds the initial en-
natural to assume that the non-thermal particles are ac- ergy Ee when the surrounding density is np<1017 cm−3.
celeration by this electric potential. Therefore, in the AE Aqr system with ∼1011 cm−3 (Itoh
Althoughthe suggestedaccelerationmechanismis very etal. 2006),theionizationlossdoesnotaffecttheelectron
similar to that in rotation-powered pulsars, the present acceleration.
WD system differs from pulsars in an important physical 5.4. The Hard X-ray Emission Mechanism
condition. While a rotation-powered pulsar is expected
to reside in a low-density environment, AE Aqr is an ac- In general,there are the following four elementary pro-
creting binary system. In particular, the radius of the cesses that can produce hard X-ray emission from ac-
light cylinder, l ∼P /2π∼5 l-s, is comparable to the celerated electrons: non-thermal bremsstrahlung, inverse
lc sp
binary size of ∼6 l-s. In fact, Itoh et al. (2006), analyz- Comptonscattering,synchrotronemission,andcurvature
10 Y. Terada et al. [Vol. ,
emanating hard X-ray spectrum is expected to have a
photon index of ∼1, when the target is thick and hence
the electrons have a flattened energy distribution due to
Coulomb losses (Uchiyama et al. 2002). This is in good
agreement with the observed photon index, 1.12+0.63.
−0.62
Candidates of the dense matter, co-rotating with the
WD, includes the surface of the WD and the accretion
stream toward the magnetic poles. However, to produce
the sharp hard X-ray pulses, the electrons must be in the
form of collimated beams (e.g., along the magnetic field
lines), and furthermore, must be moderately relativistic
(≥ 200 keV) so that the bremsstrahlung emissivity is
sufficientlyanisotropic(KochandMotz 1959)toproduce
the spike in the hard X-ray light curve. It is not obvious
whether these conditions can be fulfilled. Furthermore,
a still larger difficulty is in energetics: in the 10 – 100
keV range, an electron loses ∼104 times larger energies
in ionization (or Coulomb) loss than in radiation. Then,
the particle acceleration requires an energy input which
is more than an order of magnitude higher than the
spin-down luminosity. We therefore conclude that the
bremsstrahlung interpretation is difficult.
In the inverse-Comptonscenario, the seed photons can
beeithertheUVphotonsfromtheWDortheopticalpho-
tons from the companion star whose spectral type is K3–
K5 (Welsh et al. 1995). Then, the electrons are required
to have a Lorentz factor of γ∼102, or an energy of ∼100
MeV. The estimated 4–30 keV luminosity (after account-
ing for the duty ratio; section 5.1) translates to a hard-
photonnumberfluxof2.6×1037s−1. Thisisareasonably
smallfraction(∼10−7)ofthe opticalphotonnumber flux
tobeexpectedfromaK4star(≃5×1044s−1neartheWD
surface). However,the inverse-Comptonprocess is rather
inefficient; an electron with a Lorentz factor γ ≃102 is
expectedtolosehalfits energyinT ≃ 1 mec2 ∼4×106
1/2 γσTcus
s,wherem istheelectronmass,σ istheThomsoncross
e T
section, and u ≃0.1 erg cm−3 is the visible photon den-
s
sity at the position of the WD. Therefore, the electron is
expectedtoleavethe systemafterdepositing only∼10−6
ofitsenergy. Theenergyinputneededtosustainthepar-
Fig. 7. Model fits to the phase-average Suzaku spectra, ticle acceleration would be then ∼106LHX, making the
summed over the two observations (2005 and 2006). Red inverse Compton scenario highly unlikely.
and blue crosses show the XIS and PIN data, respectively, As the third possibility, we consider synchrotronradia-
from which the NXB and CXB have been subtracted. (a)
tionbyrelativisticelectrons. Foramagneticfieldstrength
Afitwithathree-temperature VMEKALmodelinthe0.5–
of B = B ×105 G, an electron is required to have a
25 keV band, with the parameters listed in table 1 (labeled 5
as2005+2006). Thehorizontalgreenlineindicatesthe13–30 Lorentz factor γ ∼ 104B5−1 to emit ∼ 30 keV photons.
keVPINX-raycountrateobtainedfromthefoldedpulsepro- This value of γ is lower than the maximum possible en-
file (figure 4 bottom), as a difference between φ= -0.1 – 0.1 ergy expected from the induced voltage (section 1) by
andφ=0.1–0.9. (b)Afitwithatwo-temperatureVMEKAL
∼4 orders of magnitude. Furthermore, the synchrotron
model,inthe1.5–25keVband. Thebest-fitparametersare
emission is highly efficient, with a very short lifetime of
listedintable2. (c)Thesameaspanel(b), butapower-law
withphotonindexof1.12(cyan) isadded. ∼ 8×10−6B−2( γ )−1 s (e.g, Reynolds 1998; Vink &
5 104
Laming 2003). Considering further that the synchrotron
radiation. Considering the observational results, we ex- emission is highly anisotropic, we presume that this sce-
amine these processes. nario is quite likely, if the electrons are accelerated along
If the hard X-rays are due to non-thermal the field lines, and then at some stage, acquire cross-field
bremsstrahlung in thick materials, electrons have to velocity and start emitting synchrotron photons. The
be accelerated only to an energy of ∼ 100 keV to emit observed photon index Γ∼1.1 predicts a very flat elec-
X-rays with an energy of several tens of keV. The tron spectrum with a spectral index of ∼1.2. This does