bachetti - 1410.3590.pdf

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

An Ultraluminous X

ray Source Powered by An Accreting

Neutron Star

M. Bachetti

1,2

, F. A. Harrison

, D. J.

Walton

B. W.

Grefenstette

Chakrabarty

rst

Barret

1,2

Beloborodov

S. E.

Boggs

F. E.

Christensen

W. W.

Craig

A. C.

Fabian

C. J.

Hailey

Hornschemeier

Kaspi

S.R. Kulkarni

, T.

Maccarone

J. M.

Miller

Rana

Stern

S. P. Tendulkar

, J.

Tomsick

N. A. Webb

1,2

, W. W.

Zhang

Université de Toulouse, UPS

OMP, IRAP,

31400

Toulouse

France

CNRS;

Institut de Recherche en Astrophysique et

Plan

tologie;

9, Avenue du Colonel Roche

44346, 31028

Toulouse Cedex 4, France

Toulouse, France.

Cahill Center for Astrophysics, 1216 East California Boulevard, California Institute of Technology,

Pasade

na, California 91125, USA.

MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology,

Cambridge, MA 02139, USA

Physics Department, Columbia University. 538 W 120th Street, New York, NY 10027, USA

Space Sciences Labor

atory, U

niversity of California, Berke

ley, CA 94720, USA

DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, DK

2800

Lyngby, Denmark

Lawrence Livermore National Laboratory, Livermore, CA 94550, USA

Institute of

Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK

Columbia Astrophysics Laboratory, Columbia University, New York, NY 10027, USA

NASA Goddard Space Flight Center, Greenbelt, MD 20771, USA

Department of Physics, McGill Universi

ty, Montreal, Quebec, H3A 2T8, Canada

Department of Physics, Texas Tech University, Lubbock, TX 79409, USA

Department of Astronomy, University of Michigan, 500 Church Street, Ann Arbor, MI 48109

1042,

USA

Jet Propulsion Laboratory, California Institu

te of Techn

ogy, Pasadena, CA 91109, USA

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

Ultraluminous X

ray sources (ULX) are off

nuclear point sources in nearby

galaxies whose X

ray luminosity exceeds

the theoretical maximum for spherical

infall (the Eddington limit) onto stellar

mass black holes

1,2

. Their luminosity

ranges from

erg s

(0.5

–

10 keV)

erg s

Since higher masses

imply less extreme

ratios of the luminosity to the isotropic Eddington limit

theoretical models have focused on black hole rather than neutron star

systems

1,2

. The most challenging sources to explain are those at the luminous end

(

erg s

), which require black hole masses M

>50 M

¤

and/or

significant departures from the

standard thin disk accretion that powers bright

Galactic X

ray binaries. Here we report broadband X

ray observations of the

nuclear region of the galaxy M82, which contains two bright ULXs. The

observations reveal pulsations of average period 1.37 s w

ith a 2.5

day sinusoidal

modulation. The pulsations result from the rotation of a magnetized neutron

star, and the modulation arises from its binary orbit. The pulsed flux alone

corresponds to L

–

30 keV)

= 4.9 x 10

erg s

. The pulsating source

spatially coincident with a variable ULX

which can reach L

(0.

–

10 keV)

= 1.8

x 10

erg s

. This association implies a luminosity ~100 times the Eddington

limit for a 1.4 solar mass object, or more than ten times brighter than any known

accreting

pulsar. This finding implies that neutron stars may not be rare in the

ULX population, and it challenges physical models for the accretion of matter

onto magnetized compact objects.

The brightest accretion

powered X

ray pulsars, AO538

, SMC X

, and

GRO J1744

, are variable, with reported luminosities up to L

20 keV)

~ 10

erg s

, at the low end of the range that defines ULXs. Such luminosities, exceeding

the Eddington limit for a neutron star by a factor of about six, can be understood

resulting from accretion of material at moderately super

Eddington rates through a

disk that couples to the neutron star’s strong dipolar magnetic field (surface fields of

B~10

Gauss). At the magnetospheric (Alfvén) radius, material is funnelled along

he magnetic axis, radiation escapes from the column’s side, and radiation pressure is

ineffective at arresting mass transfer

9,10

. Explaining ULXs that have L

> 10

erg s

with a ~1 M

¤

compact object using typical accreting pulsar models is however

extre

mely challenging

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

The NuSTAR (Nuclear Spectroscopic Telescope Array) high energy X

ray

mission

observed the galaxy M82 (d

≈

3.6 Mpc) seven times

between 2014 Jan 23

and 2014 Mar 06

as part of a follow

up campaign of the supernova SN2014J. The

galaxy’s disk contains several ULXs, the most luminous being M82X

, which can

reach L

(0.3

10 keV) ~10

erg s

, and the second brightest being a transient,

M82X

2 (also referred to as

X42.3+59

), which has been observed to reach

4,14

(0.3

10 keV)

≈

1.8 x 10

erg s

. The two sources are separated by 5

′

, and so can

only be clearly resolved by the Chandra X

ray telescope. During the M82 monitoring

campaign, NuSTAR observed bright

emission from the nuclear region containing the

two ULXs. The

region shows moderate flux variability at the 20% level during the

first 22 days of observation. The flux then decreases by 60% during the final

observation ~20 days later. The peak flux

, F

–

30 keV)

= (2.33 +/

0.01) x 10

erg cm

(90% confidence; Figure 1) corresponds to a total 3

–

30 keV luminosity

assuming isotropic emission of

3

.

7

!

!

.

!"

!

!

.

!"

×

10

!"

erg s

A timing analysis revealed a narrow peak just above the noise in a power

density spectrum at a frequency of ~0.7 Hz. An accelerated epoch folding search

on overlapping 30 ksec intervals of data found coherent pulsations with a mean period

of 1.37 s modulated with a sinusoidal period of 2.53 days throughout the 10

day

inter

val starting at modified Julian day (MJD) 56691 (2014

Feb 03

), and also in the

last observation at MJD 56720 (Figure 1). The statistical significance of the

pulsations is ~13

during the most significant 30 ksec segments, and >30

for the

entire observa

tion. A refined analysis (see Methods) subsequently enabled the

detection of pulsations over a longer interval beginning on MJD 56686. The pulsed

flux is variable, ranging from 5

–

13% (3

–

30 keV), and 8

–

23% (10

–

30 keV); see

Figure 1 bottom panel.

While the pulsed flux increases with energy this may result

from a reduction in the contamination from other sources in the PSF rather than from

a true increase in pulsed fraction.

The maximum pulsed luminosity of the periodic

source, NuSTAR J095551+6940.

8, is

4

.

9

!

!

.

!"

!

!

.

!"

×

10

erg s

30 keV)

Analysis of the period modulation yields a near

circular orbit (upper

eccentricity limit of 0.003; see Methods) with a projected semi

major axis of

22.225(4) light

s (1

error). In addition to the orbital mod

ulation, a linear spin

up of

the pulsar is evident, with

푃

≈

2 x 10

s/s over the interval from MJD 56696 to 56701

when the pulse detection is most significant. Phase connecting the observations

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

enables detection of a changing spin

up rate over a longer

timespan (Figure 2 top

panel) as well as erratic variations likely related to local changes in the torque on the

neutron star applied by accreting matter

Chandra observed M82 from MJD 56690.8396 to 56692.618, during an epoch

when pulsations are detect

ed. Only two sources in the Chandra image, M82X

1 and

M82X

2 are sufficiently bright to be the counterpart of NuSTAR J095551+6940.8

(see Methods). We find the centroid of the pulsed emission (

=09

51.05

+69

′

47.9

′′

) to be consistent with the location of M82X

2 (Figure 3). Monitoring

by the

Swift

satellite establishes that the decrease in the nuclear region flux seen

during ObsID011 is due to fading of M82X

1. The persistence of pulsations during

this time further

secures the association of the pulsating source, NuSTAR

J095551+6940.8, with M82X

2. We derive a flux F

(0.5

–

10 keV) = 4.07 x 10

erg

, and an unabsorbed luminosity of L

(0.5

–

10 keV) = (6.6 +/

0.1) x 10

erg s

for M82 X

2 during the Chan

dra observation.

The detection of coherent pulsations, a binary orbit, and spin

up behaviour

indicative of an accretion torque unambiguously identify NuSTAR J095551+6940.8

as a magnetized neutron star accreting from a stellar companion. The highly circula

orbit suggests the action of strong tidal torques, which, combined with the high

luminosity, point to accretion via Roche lobe overflow. The orbital parameters give a

mass function

= 2.1 M

¤

, and the lack of eclipses and assumption of a Roche

lobe

fill

ing companion constrain the inclination to be i<60

. The corresponding minimum

companion mass assuming a 1.4M

¤

neutron star is M

>5.2M

¤

, with radius R

>7 R

¤

It is challenging to explain the high luminosity using standard models for

accreting magnetic neu

tron stars. Adding the Chandra

measured E<10 keV

luminosity to the E>10 keV pulsed flux (NuSTAR cannot directly spatially resolve

the ULX), NuSTAR J095551+6940.8 has a luminosity L

(0.5

–

30 keV)~10

erg s

Theoretically, the X

ray luminosity depends

strongly on the magnetic field and

geometry of the accretion channel, being largest for a thin, hollow funnel that can

result from the coupling of a disk onto the magnetic field

. A limiting luminosity

퐿

!

~

!

!

!

!

!

!

퐿

!""

, where l

is the arc length a

nd d

the thickness of the funnel, can be

reached if the magnetic field is high enough (B

Gauss) to contain the accreting

gas column

. Ratios of l

~40 are plausible, so that the limiting luminosity can

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

reach L

~10

erg s

, implying mass transfer

rates exceeding Eddington by many

times. Beyond this, additional factors increasing L

could result from increased

Edd

due to very high (B>10

G) fields, which can reduce the electron scattering opacity

and/or a heavy neutron star. Some geometric

beaming is also likely to be present.

This scenario is, however, difficult to reconcile with the measured rate of spin

–

up. The spin

up results from the torque applied by accreting material threading onto

the magnetic field

18,19

. NuSTAR J095551+6940.8

is likely in spin equilibrium given

the short spin

up timescale,

!

!

~

300

푦푟

. Near equilibrium, the magnetosphere radius,

, is comparable to the co

rotation radius (the radius where a Keplerian orbit co

rotates with the neutron star),

푟

=

!

!

!

!

!

!

!

!

/

!

=

2

.

1

×

10

!

!

!

.

!

!

푐푚

. With

this assumption we can convert the measured torque,

휏

=

2

휋퐼

휈

=

6

×

10

!"

퐼

!"

푔

푐푚

!

푠

!

!

(where

is the neutron star moment of inertia

/(10

g cm

) and

휈

is the measured frequency derivative) into a rate of matter

magnetically channeled onto the pulsar,

푀

!"#

=

5

×

10

!

!

푀

!

.

!

!

!

!

!

!

!

!

!

!

푀

⊙

푦푟

!

!

=

2

.

5

!

!

!

!

!

!

푀

!""

. From the spin

up we therefore find an accretion rate that is only a

few times high

er than Eddington, independent of any assumption about the pulsar

magnetic field. For an equilibrium spin period of 1.37 s and

푀

~

푀

!""

, the implied

magnetic field is B~10

Gauss, typical of accreting pulsars in HMXBs, and too low

to have an appreciab

le effect on L

Edd

. It is possible that the current

푀

is significantly

larger than the average for this system, so that

푟

!

<

푟

, increasing

푀

!"#

. For

푀

=

100

푀

!"#

푀

!"#

is increased tenfold, so that only moderate geometric beaming

is req

uired to explain the observed luminosity. A fan beam geometry

viewed at a

favorable angle could in this case produce the observed pulse profile (Figure 1) and

provide the requisite moderate collimation.

The discovery of an ultra

luminous pulsar has im

plications for understanding

the ULX population. The fraction of ULXs powered by neutron stars must now be

considered highly uncertain. M82 X

2 has been extensively studied

4,14

, however

pulsations have eluded detection due to the limited timing capabili

ties of sensitive X

ray instruments, the transient nature of the pulsations, and the large amplitude of the

orbital motion. Pulsars may indeed not be rare among the ULX population.

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

REFERENCES

Roberts, T. P. X

ray observations of ultraluminous X

ray s

ources.

Astrophysics and

Space Science

311

, 203

212

(2007).

Liu, J.

F., Bregman, J. N., Bai, Y., Justham, S. & Crowther, P. Puzzling accretion onto

a black hole in the ultraluminous X

ray source M 101 ULX

Nature

503

, 500

503

(2013).

Feng, H. &

Soria, R. Ultraluminous X

ray sources in the Chandra and XMM

Newton

era.

New Astronomy Reviews

, 166

183

(2011).

Feng, H., Rao, F. & Kaaret, P. Discovery of Millihertz X

Ray Oscillations in a

Transient Ultraluminous X

Ray Source in M82.

Astrophys. J.

Letters

710

, L137

L141

(2010).

Skinner, G. K.

et al.

Discovery of 69 MS periodic X

ray pulsations in A0538

66.

Nature

297

, 568

570

(1982).

Lucke, R., Yentis, D., Friedman, H., Fritz, G. & Shulman, S. Discovery of X

ray

pulsations in SMC X

Astrophys.

206

, L25

L28

(1976).

Kouveliotou, C.

et al.

A new type of transient high

energy source in the direction of

the Galactic Centre.

Nature

379

, 799

801

(1996).

Basko, M. M. & Sunyaev, R. A. The limiting luminosity of accreting neutron stars with

magnet

ic fields.

Mon. Not. R. Astron. Soc.

175

, 395

417

(1976).

Gnedin, Y. N. & Sunyaev, R. A. The Beaming of Radiation from an Accreting

Magnetic Neutron Star and the X

ray Pulsars.

Astron. Astrophys.

, 233

239

(1973).

Basko, M. M. & Sunyaev, R. A. Radia

tive transfer in a strong magnetic field and

accreting X

ray pulsars.

Astron. Astrophys.

, 311

321

(1975).

Harrison, F. A.

et al.

The Nuclear Spectroscopic Telescope Array (NuSTAR) High

energy X

Ray Mission.

Astrophys. J.

770

, 103

(2013).

Kaaret,

et al.

Chandra High

Resolution Camera observations of the luminous X

ray source in the starburst galaxy M82.

Mon. Not. R. Astron. Soc.

321

, L29

L32

(2001).

Kaaret, P., Simet, M. G. & Lang, C. C. A 62 Day X

Ray Periodicity and an X

Ray

Flare from the

Ultraluminous X

Ray Source in M82.

Astrophys. J.

646

, 174

183

(2006).

Kong, A. K. H., Yang, Y. J., Hsieh, P. Y., Mak, D. S. Y. & Pun, C. S. J. The

Ultraluminous X

Ray Sources Near the Center of M82.

Astrophys. J.

671

, 349

357

(2007).

Ransom, S. M.

.D. thesis, new search techniques for binary pulsars

Harvard

University

(2001).

Bildsten, L.

et al.

Observations of Accreting Pulsars.

Astrophys. J.

Supplement Series

113

, 367

408

(1997).

Canuto, V., Lodenquai, J. &

Ruderman, M. Thomson Scattering in a Strong Magnetic

Field.

Physical Review D

, 2303

2308

(1971).

Pringle, J. E. & Rees, M. J. Accretion Disc Models for Compact X

Ray Sources.

Astron. Astrophys.

, 1

(1972).

Ghosh, P. & Lamb, F. K. Accretion by

rotating magnetic neutron stars. III

Accretion

torques and period changes in pulsating X

ray sources.

Astrophys. J.

234

, 296

316

(1979).

Acknowledgements

This work was supported by NASA under grant no.

NNG08FD60C, and made use

of data from the Nuclear Spectroscopic Telescope Array (

NuSTAR

) mission, a project led by Caltech,

managed by the Jet Propulsion Laboratory and funded by NASA. We thank the

NuSTAR

erations,

software and calibration teams for support with execution and analysis of these observations.

This

work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester

MB wishes to thank the Centre National d’Études

Spatiales (CNES) and the Centre National de la

Recherche Scientifique (CNRS) for the support.

Author Contributions

M.B. reduction and timing analysis of the

NuSTAR

observations, interpretation

of results, manuscript preparation.

.A.

interpretation of r

esults, manuscript preparation. D.J.W.:

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

NuSTAR and Chandra spectroscopy, point source analysis. B.G.: NuSTAR image analysis. D.C.:

accretion torque analysis, interpretation. F.F. verification of timing analysis, interpretation, D.B., A.B.,

A.C.F., A.H., V

.M.K., T.M., J.T.: interpretation of results and manuscript review. S.B., F.C., W.W.C.,

C.J.H., D.S., S.P.T, N.W, W.W.Z.: manuscript review.

Author Information

Reprints and permissions information is available at www.nature.com/reprints.

The authors decl

are no competing financial interests. Readers are welcome to comment on the online

version of the paper. Correspondence and requests for materials should be addressed to M.B.

(matteo.bachetti@irap.omp.eu) and F.A.H. (

fiona@srl.caltech.edu

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

FIGURES

Figure 1

The X

ray lightcurve and pulsations from the region containing

NuSTAR J095551+6940.8

Panel a

: the background

subtracted 3

–

30 keV

lightcurve extracted from a 70

′

radius region around the position of

NuSTAR

J095551+6940.8

. Black and red indicate the count rate from each of the two

NuSTAR telescopes (1

errors).

Panel b

: detections of the pulse period (black

points) fit using the best sinusoidal ephemeris (grey dashed line). The mean period is

1.37

252266(12)

seconds

, with an orbital modulation period of

2.51784(6)

days. The

dashed vertical lines delineate the contemporaneous Chandra observation.

Panel c

shows the pulsed flux as a fraction of the emission from the 70

′

region.

The inserts

show

the pulse profile.

Chandra

011

008-009

007

006

004

ObsID 002

FPMA

FPMB

Couts / s / module

0.1

0.15

0.2

0.25

0.3

Period (ms) - 1372.5

−

0.5

03 - 10 keV

03 - 30 keV

10 - 30 keV

Pulsed flux (%)

MJD

56680

56690

56700

56710

56720

Δχ

−

Phase

012

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

Figure 2

The spin up behaviour of

NuSTAR J095551+6940.8

Panel a

: the

residual period after correcting for the sinusoidal orbital modulation given in

Extended Data Table 2. The period decreases consistently, but the spin up rate is

anging.

Panel b

: time of arrival residuals after correcting using the best

fit

sinusoidal orbital modulation and constant period derivative. There is a clear trend

independent of the choice of time binning (30, 40 or 50 ksec) that results from the

varia

ble spin up.

Panel c

: residuals after a smooth curve is fit to the TOA residuals.

Residual noise remains in the TOAs at the 100 ms level (1

uncertainties).

009

008

007

006

Best-fit model period

Period - 1372.5 (ms)

-0.1

-0.05

0.05

0.1

Orbital variations removed

Ephemeris:

PEPOCH (MJD) = 56696

F0 (Hz)= 0.72857393(5)

F1 (Hz/s) = 5.47(2)x10

-11

TOA Residual (s)

-4

-2

30 ks

40 ks

50 ks

Secular trends removed

TOA Residual (ms)

-200

-100

100

200

MJD

56685

56687.5

56690

56692.5

56695

56697.5

56700 56702.5

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

Figure 3

The counterpart of NuSTAR

J095551+6940.8

The

grayscale image

shows

′

x 45

′

Chandra image of the galaxy’s center

Green

diamonds

mark the

locations of M82 X

1 and X

NuSTAR 10

40 keV i

ntensity contours (dashed)

(

50% and 90% level

are shown

for the pulsed (

blue

) an

d the persistent (red)

emission. Solid error circles indicat

e the 3

statistical uncertainty on the centroid

locations (

see Methods).

The p

ulsed emission

centroid

is consistent with the location

of M82 X

and

the centroid of the persistent emission is between M82 X

1 and X

indicating that there is additional

persistent emission fr

2 as well as the

persistent emission from X

Pulsed Emission

Persistent Emission

170 pc

10"

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

METHODS

Observations and preliminary data reduction

NuSTAR

observed

the M82 field

times

between 2014 Jan 23 and 2014

Mar 06

(see

Extended Data Table 1

for details)

for

a total exposure of 1.91 Ms.

used

the

NuSTAR

data analysis software (NuSTARDAS) version 1.2.0 and

NuSTAR

CALDB version 20130509

with the standard

filter

s to obtain

good time intervals,

excluding the periods where the source was occulted by the Ear

th or was transiting

through the South At

lantic A

nomaly.

NuSTAR

records event arrival times with a

resolution of 10 μs. Clock drifts, mostly due to temperature, are recorded at each

ground station passage into a clock correction file that is updated month

ly. The final

time accuracy that can be reached by applying these clock corrections is ~2 ms. We

applied these corrections to obtain solar system barycenter corrected event times

using the general

purpose FTOOL barycorr and the NuSTAR clock correction file

(v030).

Chandra:

Chandra

observed the M82 field using the ACIS

S detector in

timed

exposure (TE)/

VFAINT mode between 2014

13 20:09:32

–

2014

04 14:50:00

for a total exposure of 47 ksec. We reduced the data with the standard pipeline in the

Chandra

Interactive Analysis of Observations software package (CIAO, version 4.6),

filtering the data for periods of high background to produce a cleaned event list.

extracted p

oint source spectra from circular regions of radius ~1

′

, depending on the

proxi

mity of other nearby sources, while the background was estimated from a larger

region of radius ~

′

, free of contaminating point sources and away from the plane of

the M82 galaxy. Spectra and instrumental responses were produced from the cleaned

events w

ith the CIAO SPECEXTRACT tool, and were corrected for the fraction of

the PSF falling outside the source region.

The primary goal of the

Chandra

observation was to constrain any faint soft X

ray

emission from the recent SN2014J

, and so the observation wa

s performed with the

maximum frame

time of 3.2s. Unfortunately, the two ULXs in M82 (X

1 and X

are sufficiently bright that the long frame integration time resulted in the

Chandra

spectra from these sources suffering from fairly severe pileup

(pileup

refers to the

scenario in which more than one photon is incident on a detector pixel within one

frame time, resulting in the spurious apparent detection of a single photon with the

combined energy of the individual incident photons). The detected counts

frame

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

is ~0.45 for both X

1 and X

2, which equates to a pileup fraction of ~20

30% based

on the

Chandra

ABC guide to pileup

(

http://cxc.harvard.edu/ciao/dow

nload/doc/pileup_

abc.pdf

). This unfortunately

prevents a straightforward estimation of the fluxes

of these two sources from the

Chandra

data alone. We will return to this issue below. None of the other point

sources are bright enough to suffer significantly from these effects.

There is a known flux calibration discrepancy of ~10% between

NuSTAR

and

Chandra

. We account for this discrepancy, and quote fluxes based on the

NuSTAR

zeropoint.

Swift

monitored the field of SN2014J regularly from 2014 Jan 23 through

2014 April. We reduced the data using the

Swift

mission automated data analysis

server

Timing Analysis

To determine the mean period and orbital parameters we divided the observations into

overlapping 30 ks

intervals

and ran a

accelerated epoch folding search

in each

interval. To do this we used the software PRESTO

originally design

ed for radio

observations of pulsars.

To adapt the

NuSTAR

data to this software we modified the

makebininf

script by Abdo and Ray, originally written to use PRESTO with data from

the

Fermi

satellite. To assess the quality of detection

, accounting for possi

ble

difference in statistics between radio and X

ray data

, we ran the same search with a

random distribution of initial guesses for the period, far from the observed pulse

period, and

looked at the distribution of

for the “best detections”. More than 99%

false detections were below

a PRESTO value of

, which we use to define

acceptable

detection. With this

criterion

detected pulsations over

~10 days of

observation

We cross

checked the detection with independent software using ISIS

The observed pulse period

exhibits sinusoidal variations resulting from the binary

orbital motion.

Assuming a circular orbit, the observed period p

obs

varies according to

obs

= p

(1 + X

sin

(

–

))), where p

is the period in the system of refer

ence

moving with the pulsar, X is the projected semi

major axis of the orbit in light

seconds,

orb

is the orbital angular velocity and T

is the time of longitude 90°

(or mid

eclipse) assuming the ascending node is at longitude 0.

Publisher: NPG; Journal: Nature: Nature; Article Type: Physics letter

Page

During ObsIDs

008

–

009, the interval over which we fit for the orbital parameters,

we find

an additional trend

the phases which require

period derivative

Ṗ

≈

-

2x10

s/s.

NuSTAR

’s relative timing accuracy

is currently known to ~

2 ms

over time

intervals comparable to these observations

. There is evidence for clock drifts of ~ 0.4

ms on the ~97 min orbital

timescale.

Taking this drift into account, the observed

period

could have a systematic error up to

~10

s. This is orders of magn

itude below

the observed trend (~0.1ms) that we associate with a period derivative.

ephemeris

determined above i

s not sufficiently precise to align the pulses

throughout any of the observations. In order to refine it, we calculated Times of

Arrival (TO

A) of the pulsation

in each 30 ks interval and

searched

for an ephemeris

that

connects

their phases

. To do this, we used the software Tempo2

. We found an

orbital solution that

aligns

the TOAs to better than 36 ms (r.m.s.) from MJD 56696 to

MJD 56701,

the interval with the most significant detections.

We looked

for signatures of eccentricity

using the ELL1 model in Tempo2, adequate

for low eccentricity orbits

. We used TOAs calculated

different timescales (from 10

ks to 40 ks) in order to account for

possible time

scale

related effects

We measured

values of the eccentricity that were always

consistent with 0

within

with a

maximum eccentricity

0.002. We use

this estimate to obtain a rough upper limit

on the eccentricity of 0.003. The

parameters

of this orbital

solution (determined for

ObsIDs 008

–

009) can be found in

Extended Data Table 2

Since the orbit is

circular

, we used the convention T

= T

asc

and so T

= T

asc

+ P

orb

/ 4.

We found that the above ephemeris was

not valid before

MJD

56696, with the

residuals from the best fit rapidly departing from 0.

Therefore, for the rest of the

ObsIds, we used PRESTO with the previously determined orbital solution,

and

searched

the

period

Ṗ

plane for