11institutetext:  INAF Istituto di Astrofisica e Planetologia Spaziali, Via
del Fosso del Cavaliere 100, 00133 Roma, Italy 11email<EMAIL_ADDRESS>22institutetext: Università degli Studi di Palermo, Dipartimento di Fisica e
Chimica, Emilio Segrè, via Archirafi 36 I-90123 Palermo, Italy
33institutetext: Department of Physics and Astronomy, FI-20014 University of
Turku, Finland
44institutetext: Dipartimento di Matematica e Fisica, Università degli Studi
Roma Tre, via della Vasca Navale 84, 00146 Roma, Italy 55institutetext: INAF
Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via P. Gobetti
101, I-40129 Bologna, Italy 66institutetext: Center for Astrophysics, Harvard
& Smithsonian, 60 Garden St, Cambridge, MA 02138, USA 77institutetext:
Astronomical Institute of the Czech Academy of Sciences, Boční II 1401/1,
14100 Praha 4, Czech Republic 88institutetext: Center for Astro, Particle and
Planetary Physics, New York University Abu Dhabi, PO Box 129188, Abu Dhabi,
UAE 99institutetext: INAF Osservatorio Astronomico di Brera, via E. Bianchi
46, 23807 Merate (LC), Italy 1010institutetext: Department of Physics,
University of Warwick, Coventry CV4 7AL, UK 1111institutetext: Astrophysics,
Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH
1212institutetext: INAF Istituto di Astrofisica Spaziale e Fisica Cosmica, Via
U. La Malfa 153, I-90146 Palermo, Italy 1313institutetext: Department of
Astronomy, University of Geneva, Ch. d’Ecogia 16, CH-1290 Versoix, Geneva,
Switzerland 1414institutetext: Faulkes Telescope Project, School of Physics
and Astronomy, Cardiff University, The Parade, Cardiff CF24 3AA, Wales, UK
1515institutetext: Astrophysics Research Institute, Liverpool John Moores
University, 146 Brownlow Hill, Liverpool L3 5RF, UK 1616institutetext: INAF
Osservatorio Astronomico di Cagliari, Via della Scienza 5, 09047 Selargius
(CA), Italy 1717institutetext: Guangxi Key Laboratory for Relativistic
Astrophysics, School of Physical Science and Technology, Guangxi University,
Nanning 530004, China 1818institutetext: NASA Marshall Space Flight Center,
Huntsville, AL 35812, USA 1919institutetext: Dipartimento di Fisica,
Università degli Studi di Cagliari, SP Monserrato-Sestu, KM 0.7, Monserrato,
I-09042 Italy 2020institutetext: INFN, Sezione di Cagliari, Cittadella
Universitaria, I-09042 Monserrato, CA, Italy 2121institutetext: INAF
Osservatorio Astronomico di Roma, Via Frascati 33, 00040 Monte Porzio Catone
(RM), Italy 2222institutetext: Instituto de Astrofísicade Andalucía – CSIC,
Glorieta de la Astronomía s/n, 18008 Granada, Spain 2323institutetext: Space
Science Data Center, Agenzia Spaziale Italiana, Via del Politecnico snc, 00133
Roma, Italy 2424institutetext: Istituto Nazionale di Fisica Nucleare, Sezione
di Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy 2525institutetext:
Dipartimento di Fisica, Università di Pisa, Largo B. Pontecorvo 3, 56127 Pisa,
Italy 2626institutetext: Istituto Nazionale di Fisica Nucleare, Sezione di
Torino, Via Pietro Giuria 1, 10125 Torino, Italy 2727institutetext:
Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria 1,
10125 Torino, Italy 2828institutetext: INAF Osservatorio Astrofisico di
Arcetri, Largo Enrico Fermi 5, 50125 Firenze, Italy 2929institutetext:
Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, Via
Sansone 1, 50019 Sesto Fiorentino (FI), Italy 3030institutetext: Istituto
Nazionale di Fisica Nucleare, Sezione di Firenze, Via Sansone 1, 50019 Sesto
Fiorentino (FI), Italy 3131institutetext: Agenzia Spaziale Italiana, Via del
Politecnico snc, 00133 Roma, Italy 3232institutetext: Science and Technology
Institute, Universities Space Research Association, Huntsville, AL 35805, USA
3333institutetext: Istituto Nazionale di Fisica Nucleare, Sezione di Roma “Tor
Vergata”, Via della Ricerca Scientifica 1, 00133 Roma, Italy
3434institutetext: Department of Physics and Kavli Institute for Particle
Astrophysics and Cosmology, Stanford University, Stanford, California 94305,
USA 3535institutetext: Institut für Astronomie und Astrophysik, Universität
Tübingen, Sand 1, D-72076 Tübingen, Germany 3636institutetext: RIKEN Cluster
for Pioneering Research, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
3737institutetext: California Institute of Technology, Pasadena, CA 91125, USA
3838institutetext: Yamagata University,1-4-12 Kojirakawa-machi, Yamagata-shi
990-8560, Japan 3939institutetext: Osaka University, 1-1 Yamadaoka, Suita,
Osaka 565-0871, Japan 4040institutetext: University of British Columbia,
Vancouver, BC V6T 1Z4, Canada 4141institutetext: International Center for
Hadron Astrophysics, Chiba University, Chiba 263-8522, Japan
4242institutetext: Institute for Astrophysical Research, Boston University,
725 Commonwealth Avenue, Boston, MA 02215, USA 4343institutetext: Department
of Astrophysics, St. Petersburg State University, Universitetsky pr. 28,
Petrodvoretz, 198504 St. Petersburg, Russia 4444institutetext: Department of
Physics and Astronomy and Space Science Center, University of New Hampshire,
Durham, NH 03824, USA 4545institutetext: Physics Department and McDonnell
Center for the Space Sciences, Washington University in St. Louis, St. Louis,
MO 63130, USA 4646institutetext: Finnish Centre for Astronomy with ESO, 20014
University of Turku, Finland 4747institutetext: Istituto Nazionale di Fisica
Nucleare, Sezione di Napoli, Strada Comunale Cinthia, 80126 Napoli, Italy
4848institutetext: Université de Strasbourg, CNRS, Observatoire Astronomique
de Strasbourg, UMR 7550, 67000 Strasbourg, France 4949institutetext: MIT Kavli
Institute for Astrophysics and Space Research, Massachusetts Institute of
Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
5050institutetext: Graduate School of Science, Division of Particle and
Astrophysical Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi
464-8602, Japan 5151institutetext: Hiroshima Astrophysical Science Center,
Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima, Hiroshima 739-8526,
Japan 5252institutetext: University of Maryland, Baltimore County, Baltimore,
MD 21250, USA 5353institutetext: NASA Goddard Space Flight Center, Greenbelt,
MD 20771, USA 5454institutetext: Center for Research and Exploration in Space
Science and Technology, NASA/GSFC, Greenbelt, MD 20771, USA 5555institutetext:
Department of Physics, University of Hong Kong, Pokfulam, Hong Kong
5656institutetext: Department of Astronomy and Astrophysics, Pennsylvania
State University, University Park, PA 16801, USA 5757institutetext: Université
Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France 5858institutetext:
Dipartimento di Fisica e Astronomia, Università degli Studi di Padova, Via
Marzolo 8, 35131 Padova, Italy 5959institutetext: Dipartimento di Fisica,
Università degli Studi di Roma “Tor Vergata”, Via della Ricerca Scientifica 1,
00133 Roma, Italy 6060institutetext: Department of Astronomy, University of
Maryland, College Park, Maryland 20742, USA 6161institutetext: Mullard Space
Science Laboratory, University College London, Holmbury St Mary, Dorking,
Surrey RH5 6NT, UK 6262institutetext: Anton Pannekoek Institute for Astronomy
& GRAPPA, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, The
Netherlands

# Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1

Sergio Fabiani Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Fiamma Capitanio
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Rosario Iaria Discovery of
a variable energy-dependent X-ray polarization in the accreting neutron star
GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Juri Poutanen Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1 Andrea Gnarini Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Francesco Ursini Discovery of a variable energy-dependent X-ray polarization
in the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Ruben Farinelli
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Anna Bobrikova Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1 James F. Steiner Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Jiri Svoboda Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1 Alessio Anitra Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Maria C. Baglio Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1Discovery of a
variable energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Francesco Carotenuto Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Melania Del Santo Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Carlo Ferrigno Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Fraser Lewis
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 David M. Russell Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Thomas D. Russell Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Jakob van den Eijnden Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Massimo Cocchi Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1 Alessandro Di Marco Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1Discovery of a
variable energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1 Fabio La Monaca Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Kuan Liu Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 John Rankin Discovery of a
variable energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Martin C. Weisskopf Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Fei Xie Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Stefano Bianchi
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Luciano Burderi Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1Discovery of a
variable energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Tiziana Di Salvo Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1Discovery of a
variable energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Elise Egron Discovery of a
variable energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Giulia Illiano Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1 Philip Kaaret Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Giorgio Matt Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Romana Mikušincová
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Fabio Muleri Discovery of
a variable energy-dependent X-ray polarization in the accreting neutron star
GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Alessandro Papitto Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Iván Agudo Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1 Lucio A. Antonelli Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1Discovery of a
variable energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Matteo Bachetti Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1 Luca Baldini Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Wayne H. Baumgartner Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Ronaldo Bellazzini Discovery of a variable energy-dependent X-ray polarization
in the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Stephen D. Bongiorno
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Raffaella Bonino Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1Discovery of a
variable energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1 Alessandro Brez Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Niccolò Bucciantini Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Simone Castellano Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Elisabetta Cavazzuti Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Chien-Ting Chen Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Stefano Ciprini Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Enrico Costa Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Alessandra De Rosa
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Ettore Del Monte Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1 Laura Di Gesu Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Niccolò Di Lalla Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Immacolata Donnarumma Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Victor Doroshenko Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Michal Dovčiak Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1 Steven R. Ehlert Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Teruaki Enoto Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Yuri Evangelista
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Riccardo Ferrazzoli
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Javier A. Garcia Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1 Shuichi Gunji Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Kiyoshi Hayashida Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Jeremy Heyl Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1 Wataru Iwakiri Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Svetlana G. Jorstad Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Vladimir Karas Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1 Fabian Kislat Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Takao Kitaguchi Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Jeffery J. Kolodziejczak Discovery of a
variable energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Henric Krawczynski Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Luca Latronico Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1 Ioannis Liodakis Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Simone Maldera Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Alberto Manfreda
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Frédéric Marin Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1 Andrea Marinucci Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Alan P. Marscher Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Herman L. Marshall Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Francesco Massaro Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Ikuyuki Mitsuishi Discovery of a variable energy-dependent X-ray polarization
in the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Tsunefumi Mizuno
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Michela Negro Discovery of
a variable energy-dependent X-ray polarization in the accreting neutron star
GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Chi-Yung Ng Discovery of a
variable energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Stephen L. O’Dell Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Nicola Omodei Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1 Chiara Oppedisano Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
George G. Pavlov Discovery of a variable energy-dependent X-ray polarization
in the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Abel L. Peirson
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Matteo Perri Discovery of
a variable energy-dependent X-ray polarization in the accreting neutron star
GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Melissa Pesce-Rollins Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Pierre-Olivier Petrucci Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Maura Pilia Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Andrea Possenti Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1 Simonetta Puccetti Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Brian D. Ramsey Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Ajay Ratheesh Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1 Oliver J. Roberts Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Roger W. Romani Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Carmelo Sgrò
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Patrick Slane Discovery of
a variable energy-dependent X-ray polarization in the accreting neutron star
GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Paolo Soffitta Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1 Gloria Spandre Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Douglas A. Swartz Discovery of a variable energy-dependent X-ray polarization
in the accreting neutron star GX 5$-$1Discovery of a variable energy-dependent
X-ray polarization in the accreting neutron star GX 5$-$1 Toru Tamagawa
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Fabrizio Tavecchio
Discovery of a variable energy-dependent X-ray polarization in the accreting
neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Roberto Taverna Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in
the accreting neutron star GX 5$-$1 Yuzuru Tawara Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Allyn F. Tennant Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Nicholas E. Thomas Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Francesco Tombesi Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Alessio Trois Discovery of
a variable energy-dependent X-ray polarization in the accreting neutron star
GX 5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Sergey S. Tsygankov Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Roberto Turolla Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1Discovery of a variable
energy-dependent X-ray polarization in the accreting neutron star GX 5$-$1
Jacco Vink Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1Discovery of a variable energy-dependent X-ray
polarization in the accreting neutron star GX 5$-$1 Kinwah Wu Discovery of a
variable energy-dependent X-ray polarization in the accreting neutron star GX
5$-$1Discovery of a variable energy-dependent X-ray polarization in the
accreting neutron star GX 5$-$1 Silvia Zane Discovery of a variable energy-
dependent X-ray polarization in the accreting neutron star GX 5$-$1Discovery
of a variable energy-dependent X-ray polarization in the accreting neutron
star GX 5$-$1

(Received ?; accepted ?)

We report on the coordinated observations of the neutron star low-mass X-ray
binary (NS-LMXB) GX 5$-$1 in X-rays (IXPE, NICER, NuSTAR and INTEGRAL),
optical (REM and LCO), near-infrared (REM), mid-infrared (VLT VISIR), and
radio (ATCA). This Z-source was observed by IXPE twice in March–April 2023
(Obs. 1 and 2). In the radio band, the source was detected, but only upper-
limits to the linear polarization were obtained at a $3\sigma$ level of 6.1%
at 5.5 GHz and 5.9% at 9 GHz in Obs. 1 and 12.5% at 5.5 GHz and 20% at 9 GHz
in Obs. 2. The mid-IR, near-IR and optical observations suggest the presence
of a compact jet which peaks in the mid- or far-IR. The X-ray polarization
degree was found to be $3.7\%\pm 0.4\%$ (at 90% confidence level) during Obs.
1 when the source was in the horizontal branch of the Z-track and $1.8\%\pm
0.4\%$ during Obs. 2 when the source was in the normal-flaring branch. These
results confirm the variation of polarization degree as a function of the
position of the source in the color-color diagram as for previously observed
Z-track sources (Cyg X-2 and XTE 1701$-$462). Evidence for a variation of the
polarization angle $\sim 20\degr$ with energy is found in both observations,
likely related to the different, non-orthogonal polarization angles of the
disk and Comptonization components which peak at different energies.

###### Key Words.:

accretion, accretion disks – neutron stars – X-rays: general – X-rays:
binaries – X-rays: individual: GX 5$-$1

##  1 Introduction

Persistent neutron star low-mass X-ray binaries (NS-LMXBs) are among the X-ray
astronomical objects that the Imaging X-ray Polarimetry Explorer (IXPE,
Weisskopf et al. 2023, 2022; Soffitta et al. 2021) is investigating. Four of
them were already observed by IXPE during its first year campaign, namely the
Z-source Cyg X-2, the peculiar Z-Atoll transient XTE J1701$-$462, and two
bright soft-state Atoll-sources, GS 1826$-$238 and GX 9$+$9\. The source
classification (Z or Atoll) is based on the tracks that they draw on the
color-color-diagram (CCD; see, e.g., Hasinger & van der Klis, 1989; van der
Klis, 1995). GS 1826$-$238 data are compatible with a null polarization with
an upper limit on the polarization degree (PD) of 1.3% (Capitanio et al.,
2023), while Cyg X-2 (Farinelli et al., 2023) and GX 9+9 (Chatterjee et al.,
2023; Ursini et al., 2023) have shown a statistically significant linear
polarization with the PD of $\sim$2% and $\sim$1.5%, respectively. Strong
variations in PD was reported for XTE J1701$-$462, observed twice, that showed
a high PD$\sim 4.5$% in the first observation and a PD compatible with a null
polarization in the second one (Cocchi et al., 2023).

Table 1: List of observations.

Telescope | Obsid | Obs. Start | Obs. Stop | Net Exposure (ks) | Notes
---|---|---|---|---|---
IXPE Obs. 1 |
IXPE | 02002799 | 2023-03-21, 04:16:14 | 2023-03-22, 05:02:52 | 48.6 | obs. segment 1
NICER | 6010230101/2 | 2023-03-21, 03:41:20 | 2023-03-22, 04:50:20 | 13.1 |
NuSTAR | 90902310002 | 2023-03-21, 16:41:48 | 2023-03-22, 08:04:34 | 12.6 |
INTEGRAL | 2070006/0001 | 2023-03-21, 03:58:07 | 2023-03-22, 04:28:46 | 40.1 |
REM | – | 2023-03-22, 05:25:24 | 2023-03-22, 07:33:05 | – | see Sect. 2.7 for exp. details
LCO | – | 2023-03-22, 16:33:07 | 2023-03-22, 16:38:07 | – | ”
No IXPE Obs. |
NICER | 6010230103/4 | 2023-03-24 18:19:20 | 2023-03-25 00:44:20 | 5.2 |
ATCA | – | 2023-03-24, 15:21:20 | 2023-03-25, 01:55:50 | – | see Sect. 2.5 for exp. details
VISIR | 110.2448 | 2023-03-28, 08:31:00 | 2023-03-28, 09:21:00 | – | see Sect. 2.6 for exp. details
LCO | – | 2023-03-29, 15:50:11 | 2023-03-31, 15:43:07 | – | see Sect. 2.7 for exp. details
VISIR | 110.2448 | 2023-03-31, 07:46:00 | 2023-03-31, 08:42:00 | – | see Sect. 2.6 for exp. details
IXPE Obs. 2 |
IXPE | 02002799 | 2023-04-13, 23:43:42 | 2023-04-15, 00:37:32 | 47.1 | obs. segment 2
NICER | 6010230105/6 | 2023-04-13 16:39:04 | 2023-04-15, 23:58:20 | 13.1 |
NuSTAR | 90902310004/6 | 2023-04-13, 15:57:07 | 2023-04-14, 23:23:24 | 15.7 |
INTEGRAL | multiple | 2023-04-13, 03:51:17 | 2023-04-15 08:53:00 | 85.0 |
REM | – | 2023-04-14, 03:16:55 | 2023-04-14, 06:31:56 | – | see Sect. 2.7 for exp. details
LCO | – | 2023-04-14, 05:35:19 | 2023-04-14, 23:23:55 | – | ”
ATCA | – | 2023-04-14, 11:32:00 | 2023-04-14, 17:57:40 | – | see Sect. 2.5 for exp. details

111 The three table sections comprise the observations related to IXPE Obs. 1,
Obs. 2, and observations in between performed with other observatories.

GX 5$-$1 is a Galactic Z-source (Kuulkers et al., 1994; Jonker et al., 2002)
located near the Galactic Center. It is a radio source with radio emission
most likely originating from a compact jet (Fender & Hendry, 2000). The radio
counterpart allowed an accurate localization that, despite optical obscuration
and crowded field near the Galactic Center, has led to the determination of a
likely infra-red companion candidate (Jonker et al., 2000). Until the early
1990’s GX 5$-$1 X-ray data were likely contaminated by the black hole LMXB GRS
1758$-$258, located only 40′ away. Sunyaev et al. (1991) and Gilfanov et al.
(1993) were able to resolve two sources, showing that GX 5$-$1 was $\sim$30–50
times brighter than GRS 1758$-$258 below 20 keV. GX 5$-$1 has not shown any
X-ray pulsations or X-ray bursts (Paizis et al., 2005).

An X-ray halo due to scattering of X-ray photons is clearly revealed in the
Chandra image (Smith et al., 2006; Clark, 2018). Such a halo arises due to the
presence of multiple clouds along the line of sight.

In X- and $\gamma$-rays, Paizis et al. (2005) studied one year of INTEGRAL
data, which covered all the Z-track of the source (mainly the horizontal
branch (HB) and normal branch (NB)). ISGRI and JEM-X average spectra showed a
clear hard X-ray emission above 20 keV, not detected previously and compatible
with thermal Comptonization of soft photons from a hot, optically thin plasma
in the vicinity of the NS. However, Paizis et al. (2005) were not able to
constrain the temperature of the Comptonizing plasma. They assessed the
compatibility of GX 5$-$1 energy spectrum with the so called ‘eastern’
(Mitsuda et al., 1984) and ‘western’ (White et al., 1986) models and found the
former being physically more meaningful, describing the spectral ‘flattening’
above $\sim 20$ keV as a Comptonized hard-tail emission. Paizis et al. (2006)
described the GX 5$-$1 energy spectrum in the 20–100 keV energy band observed
by INTEGRAL IBIS/ISGRI with a Comptonization component (comptt, Titarchuk
(1994)) plus a power law to account for the hard X-ray emission. Such a high-
energy tail was first detected by Asai et al. (1994) although a possible
contamination from the nearby black hole GRS 1758$-$258 could not be excluded
in this latter case.

Paizis et al. (2006) highlighted the presence of a correlation between the
X-ray spectral states and the radio emission. Steady radio emission is
associated with low/hard state (typical for Atoll sources; Fender & Hendry,
2000; Migliari & Fender, 2006). These sources brighten considerably during
intermediate states, often showing bright, transient flares (HB of Z-sources),
before quenching during the very soft states in the NB and FB branches of
Z-sources (Fender & Hendry, 2000; Di Salvo & Stella, 2002). Moreover, Paizis
et al. (2006) reported that the radio flux is positively correlated with the
flux of the hard tail in the 40–100 keV energy range. They suggested that this
correlation is related to the acceleration of electrons along open field lines
in the NS magnetosphere at the base of the jet seen in the radio. Berendsen et
al. (2000) reported upper limits to the radio linear polarization of 33% at
6.3 cm and 23% at 3.5 cm not sufficient to constrain the emission mechanism or
the optical depth of the jet.

Figure 1: Light curves of NuSTAR, NICER and IBIS/ISGRI during IXPE Obs. 1
(left panel) and Obs. 2. (right panel). On the top row of each panel the three
IXPE DU’s light curves are shown (DU1 blue, DU2 orange, and DU3 green). In the
left panel the NICER soft purple and dark red points correspond to ObsID
6010230101 and 6010230102. In the right panel the NuSTAR red and purple points
correspond to ObsID 90902310004 and 90902310006. The NICER gray points
correspond to ObsID 6010230106.

##  2 Observations and data reduction

###  2.1 IXPE

The X-ray polarimeter IXPE (Weisskopf et al., 2023, 2022; Soffitta et al.,
2021) observed GX 5$-$1 twice (Obsid 02002799) from March 21 to 22 and from
April 13 to 15, 2023 (see Table 1 and Fig. 1 for the light curves) with a
nominal integration time of 50 ks each. IXPE provides timing, imaging,
spectroscopic, and polarimetric data in the 2–8 keV band. Data reduction and
analysis were performed by means of the ixpeobssim software version 30.5.0
(Baldini et al., 2022) and the heasoft package version 6.31.1 (Nasa Heasarc,
2014). Data were filtered by using ixpeobssim tools xpselect and binned222The
default energy binning is 40 eV. with xpbin to produce images and $I$, $Q$,
and $U$ energy spectra for spectro-polarimetric analysis performed with xspec
version 12.13.0c (Arnaud, 1996). We used the latest version 12 of the IXPE
response matrices available at the ixpeobssim public
repository333https://github.com/lucabaldini/ixpeobssim (also available at the
HEASARC archive). A circular source extraction region of 60″ in radius was
selected from the image for each one of the three detector units (DUs). No
background subtraction was applied due to the high count rate of the source
($\sim$20–25 cts s-1 per DU) (see Di Marco et al., 2023). Only xspec allows
currently a ‘weighted analysis’ (Di Marco et al., 2022) in which a weight is
assigned to each photo-electron track recorded by the DUs depending on the
shape of the charge distribution.

The normalized Stokes parameters $q=Q/I$ and $u=U/I$, the PD and polarization
angle (PA) with their uncertainties can be calculated by using the model-
independent pcube binning algorithm of ixpeobssim. On the other hand, PD and
PA obtained with xspec require the definition of a spectro-polarimetric model.
Because the PD and PA are not independent, the appropriate way to report
results is by means of contour plots at certain confidence levels for the
joint measurements of both parameters. We report xspec (PD,PA) contour plots
as obtained by using the steppar command, while contour plots associated to
the ixpeobssim analysis are obtained from the statistics of the number of
counts (Weisskopf et al., 2010; Strohmayer & Kallman, 2013; Muleri, 2022).

The spectro-polarimetric analysis was carried out by taking into account the
current IXPE effective area instrument response function (arf) which may not
be as accurate as possible at energies above 6 keV where there is a
significant roll-off in the spectral response. Because the high-energy part of
the IXPE band is of special interest for our study, we estimate the IXPE
spectral systematic uncertainties to be as 3% in Obs. 1 and 2% in Obs. 2,
based on the comparison with NICER, NuSTAR and IBIS/ISGRI energy spectra. The
spectral models for both the IXPE observations are frozen based on the
spectral analysis of these other observatories. We used the xspec gain fit
tool for the IXPE data only, to shift the energies on which the response
matrix is defined and to match the effective area curve during the fit
procedure. The spectro-polarimetric fit of the IXPE data was carried out
freeing the three DU’s normalization constants, the gain slope, gain offset
and the polarimetric parameters.444The normalization constants, gain slope and
offset parameters are identical between $I$, $Q$ and $U$ spectra of the same
DU. The PA and PD parameters of those spectra are identical also for each DU.

###  2.2 NuSTAR

GX 5$-$1 was observed by NuSTAR (Harrison et al., 2013) on March 21 and twice
on April 13–14, 2023. All the relevant observation times, sequence IDs and
exposure times are provided in Table 1 and the corresponding light curves are
shown in Fig. 1. The unfiltered event files were processed with the NuSTAR
Data Analysis Software (nustardas v.2.1.2) to produce the cleaned and
calibrated level 2 data using the latest calibration files (CALDB v.20221130)
and the standard filtering criteria with the nupipeline task, where
statusexpr"STATUS==b0000xxx00xxxx000" was set due to the source flux exceeding
100 counts s-1. The spectra and light curves were extracted using the
nuproducts task, selecting a circular region of 60″ in radius centered on the
source.

###  2.3 NICER

NICER (Gendreau et al., 2016) observed GX 5$-$1 between March 21–25 and April
13–14, 2023. The observations identified with ID 6010230101, 6010230102, and
6010230106 were included in the spectro-polarimetric analysis, because they
are simultaneous with the IXPE observations. The calibrated and cleaned files
were extracted by using the standard nicerl2 command of the NICER Data
Analysis Software (nicerdas v.10) together with the latest calibration files
(CALDB v.20221001). The spectra and the light curves were then obtained with
the nicerl3-spect and nicerl3-lc tasks, while the background was computed
using the
SCORPEON555https://heasarc.gsfc.nasa.gov/docs/nicer/analysis_threads/scorpeon-
overview/ model. Light curves were obtained including 50 NICER FPMs available
during the ObsIDs included in the analysis (out of 52 available, excluding
noisy detectors ID. 14 and ID. 34). Thus, no discontinuities in the NICER
light curves are present (see Fig. 1).

During the contemporary observation with IXPE there were two significant
increases of count rate in the NICER data, up to the double of the typical
value. These events were coincident with two solar flares. The first one was a
C class peaking at about 60048.5389 MJD and and the second one was an M class
peaking at about MJD 60048.6806. We removed them manually from the GTIs (the C
class flare from MJD 60048.53535 to MJD 60048.60033 and the M class flare from
MJD 60048.67506 to MJD 60048.73744).

We noticed some relevant features in the energy spectrum below 4 keV, most
likely due to spectral features unaccounted for in the NICER ARF. Because of
the source’s high count rate, such features become apparent in the spectral
modeling. We therefore accounted for calibration artifacts owing to
imperfections in modeling the dead layer of the silicon detector at the Si-K
edge, and of the concentrator mirror surface roughness at the Au-M edges,
which affects the $\approx$2.2–3.5 keV
range.666https://heasarc.gsfc.nasa.gov/docs/nicer/analysis_threads/arf-rmf/ We
froze the energy of those edges at their best-fit value as reported in Table
18.

###  2.4 INTEGRAL IBIS/ISGRI

INTEGRAL IBIS/ISGRI (Winkler et al., 2003) observed the region of GX 5$-$1
from March 21 to 22 and from April 13 to 15, 2023, responding to a request by
the IXPE team. The data for this source are publicly available and were
reduced for the imager IBIS (Ubertini et al., 2003) and the ISGRI detector
(Lebrun et al., 2003). We used the MMODA777https://www.astro.unige.ch/mmoda/
platform that empowers the Off-Line Science Analysis (OSA) version 11.2
distributed by the ISDC (Courvoisier et al., 2003) with the most recent
calibration files that are continuously ingested in the Instrument
Characteristic repository. We first built a mosaicked image of all individual
pointings that constitute the standard dithering strategy of observation for
IBIS/ISGRI in the 28–40 keV energy range. These images were used to make the
catalog of detected sources with a signal-to-noise ratio larger than 7. Using
these catalog, we extracted light curves with 1000 s time bins and spectra in
256 standard channels for IBIS/ISGRI, these were grouped in 10 equally spaced
logarithmic channels between 28 and 150 keV. We also accounted for a
systematic uncertainty of the spectra at the 1.5% level. The equivalent on-
axis exposures of the IBIS/ISGRI spectra are 40 and 85 ks, respectively, after
correction for dead time and vignetting. Products are available at the
INTEGRAL Product
gallery.888https://www.astro.unige.ch/mmoda/gallery/astrophysical-
entity/gx-5-1

###  2.5 ATCA

The Australia Telescope Compact Array (ATCA) observed GX 5$-$1 on March 24 and
April 14, 2023. On March 24, the telescope observed with the array in its 750C
configuration.999https://www.narrabri.atnf.csiro.au/operations/array_configurations/configurations.html
Observations taken on April 14 were carried out with the array in a relatively
compact H214 configuration, in combination with an isolated antenna located 6
km from the array core, which was also included for our analysis. For both
observations, data were recorded simultaneously at central frequencies of 5.5
GHz and 9.0 GHz, with 2 GHz of bandwidth at each frequency.

We used PKS 1934$-$638 for bandpass and flux density calibration. PKS
1934$-$638 was also used to solve for the antenna leakages (D-terms) for the
polarization calibration. The nearby source B1817$-$254 was used for gain
calibration and to calibrate the PA using the Common Astronomy Software
Applications for radio astronomy (casa, version 5.1.2; CASA Team et al. 2022)
atcapolhelpers.py task qufromgain.101010 https://github.com/radio-astro
Calibration and imaging followed standard procedures within casa. When
imaging, we used a Briggs robust parameter of 0 to balance sensitivity and
resolution (Briggs, 1995), as well as suppress the effects from some bright,
diffuse emission within the field.

For our March 24 observations, fitting for a point source in the image plane,
we detect GX 5$-$1 at a flux density of $960\pm 19$ $\mu$Jy at 5.5 GHz and
$810\pm 11\,\mu$Jy at 9 GHz coincident with the previously reported radio the
X-ray position (e.g., Berendsen et al., 2000; Liu et al., 2007). These
detections correspond to a radio energy spectral index of $-0.37\pm 0.09$. The
Stokes $Q$ and $U$ values were measured at the position of the peak source
flux density (Stokes $I$). No significant linearly polarized (LP) emission was
detected at either frequency. Measuring the root mean square of the image
noise in a $50\arcsec\times 50\arcsec$ region over the source position (taken
as 1$\sigma)$, provides 3$\sigma$ upper limits on the polarized intensity
$\sqrt{Q^{2}+U^{2}}$ of $58\,\mu$Jy beam-1 at 5.5 GHz and $48\,\mu$Jy beam-1
at 9 GHz. These corresponds to a 3$\sigma$ upper limit on the PD of 6.1% at
5.5 GHz and 5.9% at 9 GHz. Stacking the two frequencies to maximize the
sensitivity also yields a non-detection of linearly polarized emission, with a
3$\sigma$ upper-limit of 4.2% (centered at 7.25 GHz).

On April 14, following the same calibration and imaging procedure, we measured
the flux density of GX 5$-$1 to be $750\pm 50\,\mu$Jy and $620\pm 40\,\mu$Jy
at 5.5 and 9 GHz, respectively. These detections correspond to a radio
spectral index of $-0.4\pm 0.1$. We note that due to the more compact array
configuration for this epoch, and the presence of diffuse emission in the
field, we imaged with a strictly uniform weighting scheme (setting the Briggs
robust parameter to $-2$), reducing the impact of diffuse emission in the
field on our resultant images. The compact configuration coupled with a
shorter exposure time did result in a higher noise level in the images. At 5.5
GHz, we do not detect any linearly polarized emission, with a 3$\sigma$ upper-
limit on the PD of 12.5%. Similarly, at 9 GHz we measure a 3$\sigma$ upper-
limit on the PD of 20%. Stacking the two frequencies places an 3$\sigma$
upper-limit on the PD of 8% at 7.25 GHz. We do note that during the final
$\sim$30 min of the observation, some linear polarization was detected from
close to the source position, but only at 9 GHz. Due to the non-detection at
5.5 GHz and the short and sudden nature of this emission, we attribute it to
radio frequency interference and not an astrophysical event.

###  2.6 VLT VISIR

Mid-IR observations of the field of GX 5$-$1 were made with the European
Southern Observatory’s Very Large Telescope (VLT) on March 28 and 31 2023
under the program 110.2448 (PI: D. Russell). The VLT Imager and Spectrometer
for the mid-Infrared (VISIR; Lagage et al., 2004) instrument on the VLT was
used in small-field imaging mode. Four filters ($M$-band, $J8.9$, $B10.7$ and
$B11.7$) were used, with central wavelengths of 4.67, 8.70, 10.64, and 11.51
$\mu$m, respectively. For each observation, the integration time on source was
composed of a number of nodding cycles; chopping and nodding between source
and sky. The total observing time was usually almost twice the integration
time.

Observations of standard stars were made on the same nights as the target, in
the same filters (photometric standards HD137744, HD169916, HD130157 and
HD145897 were observed, all at airmass 1.0–1.1). Conditions were clear on both
nights. All data (target and standard stars) were reduced using the VISIR
pipeline in the gasgano environment.
111111https://www.eso.org/sci/software/gasgano.html Raw images from the
chop/nod cycle were recombined. Photometry was performed on the combined
images using PHOT in IRAF.121212IRAF is distributed by the National Optical
Astronomy Observatory, which is operated by the Association of Universities
for Research in Astronomy, Inc., under cooperative agreement with the National
Science Foundation For the B10.7 filter, two standard stars were observed on
each night, just before and after each observation of GX 5$-$1, to check for
stability. We found that the counts/flux ratio values from these standards
agree to a level of 6.4%, which we adopt as the systematic error of all flux
measurements. The estimated counts/flux ratio in each filter was used to
convert count rates (or upper limits) of GX 5$-$1 to flux densities.

On 2023-03-28 (MJD 60031.37), the B10.7 filter was used only, and we derive a
3$\sigma$ flux density upper limit of 3.27 mJy at 10.64 $\mu$m (the airmass
was 1.05–1.10). On 2023-03-31 (MJD 60034.34), GX 5$-$1 was detected in
$M$-band and $J8.9$, with flux densities of $4.2\pm 1.4$ mJy at 4.67 $\mu$m
and $10.0\pm 2.3$ mJy at 8.70 $\mu$m, respectively (at airmass 1.07–1.17). The
significance of the detection was 5.9$\sigma$ in both filters. The errors on
the fluxes incorporate the statistical error on each detection, and the
systematic error from the standard stars, in quadrature. The source was not
detected in the $B10.7$ and $B11.7$ filters on 2023-03-31, with flux upper
limits that were less constraining than on 2023-03-28.

GX 5$-$1 lies in a crowded region of the Galactic plane, with several stars
detected within 5″ of the source. The near-IR counterpart was confirmed
through photometry and spectroscopy (named as star 513; Jonker et al., 2000;
Bandyopadhyay et al., 2003), and its coordinates agree with the radio and
X-ray position. We are confident that the source we detect with VISIR is
indeed GX 5$-$1, because star 503 from Jonker et al. (2000) and Bandyopadhyay
et al. (2003) is also detected (at a low significance of 3.1–3.3$\sigma$) at
the correct coordinates. This star is estimated from Fig. 1 of Jonker et al.
(2000) to lie 4$\aas@@fstack{\prime\prime}$3 to the south-east of GX 5$-$1\.
In the $J8.9$ VISIR image the detected source is measured to be
4$\aas@@fstack{\prime\prime}$28 to the south-east of the position of the
detected GX 5$-$1, as expected. The flux density of star 503 is $1.4\pm 0.5$
mJy in $M$-band and $4.5\pm 2.2$ mJy in $J8.9$.

Figure 2: Polarization of GX 5$-$1 measured by IXPE in the 2–8 keV energy
range during Obs. 1 and Obs. 2 obtained with xspec and ixpeobssim. Contours
are computed for two parameters of interest at 50%, 90%, and 99.9% confidence
levels.

###  2.7 REM and LCO

Optical (SDSS $griz$ filters) and near infrared (NIR; 2MASS $H$-band)
observations of GX 5$-$1 were acquired with the robotic 60 cm Rapid Eye Mount
(REM; Zerbi et al. 2001; Covino et al. 2004) telescope on March 22 and on
April 14, 2023 (see Table 1). Strictly simultaneous observations were obtained
in all bands; on March 22, a series of 150 30-s exposures were acquired in
H-band (dithering was applied), and 20 300-s exposures in each of the optical
bands; on April 14, a series of 225 30-s exposures were acquired in H-band
(dithering was applied), and 30 300-s exposures in each of the optical bands.

Optical observations were also acquired with the 1 m and 2 m telescopes of the
Las Cumbres Observatory (LCO) network, using the $i^{\prime}$ and $Y$ filters.
Observations with the 2 m telescope (Siding Spring - Faulkes Telescope South)
were performed on 2023-03-22T16:33:07, 2023-03-29T15:50:11,
2023-03-30T15:46:39 and 2023-03-31T15:43:07 (300s integration in all epochs
and bands), and with the 1 m telescopes (at the locations of Cerro Tololo,
Siding Spring and Sutherland) on 2023-03-21T07:09:39, 2023-03-22T01:01:36,
2023-03-22T08:11:35, 2023-04-14T05:35:19, T08:11:37, T15:11:30, T23:23:55
(300s integration in all epochs and bands).

The optical images were bias- and flat-field corrected using standard
procedures; the contribution of the sky in the NIR images was evaluated by
performing a median of the dithered images five-by-five, and was then
subtracted from each image. In all bands and epochs, all reduced images were
then aligned and averaged in order to increase the signal-to-noise. Aperture
photometry was performed using PHOT in IRAF. Flux-calibration was performed
against a group of 6 stars with magnitudes tabulated in the 2MASS
catalog131313https://irsa.ipac.caltech.edu/Missions/2mass.html and 6 stars
from the PanSTARRS catalog.141414https://catalogs.mast.stsci.edu/panstarrs/

Due to the very high extinction of the source ($N_{\rm H}=4.93\times
10^{22}\,\rm cm^{-2}$ and $4.88\times 10^{22}\,\rm cm^{-2}$, which
translates151515See Sect. 3.5 and Foight et al. (2016a). into $A_{V}=17.2$ mag
and 17 mag in Obs. 1 and Obs. 2, respectively) and to the combination of the
low spatial resolution of our images and the crowded field of the source, GX
5$-$1 is not detected in any of the optical and NIR images acquired. A blend
of our target with at least one of the nearby stars can be detected at very
low significance in the averaged $H$-band image, at a position consistent with
the proposed optical and NIR counterpart of the source (Jonker et al. 2000,
star 513). However, this detection is not significant enough to extract a flux
for the blend.

Figure 3: Stokes parameters as a function of energy for IXPE Obs. 1 and Obs. 2
(left panels) and for the combined data set (right panels) obtained with
ixpeobssim. The normalized Stokes $q$ parameter is compatible with a constant
value in each one of the IXPE observations, whereas the Stokes $u$ parameter
is not (see Table 17). This behavior of the Stokes parameters is consistent
with a variation of the PA (see Fig. 4). Table 2: Polarization in the 2–8 keV
band (see Fig. 2) and in 4 energy bins estimated with ixpeobssim for Obs. 1
and Obs. 2.

Energy (keV) | Parameters | Obs. 1 | Obs. 2
---|---|---|---
2–8 | PD ($\%$) | $4.3\pm 0.3$ | $2.0\pm 0.3$
PA (deg) | $-9.7\pm 2.0$ | $-9.2\pm 4.0$
2–3 | PD ($\%$) | $4.0\pm 0.5$ | $2.0\pm 0.4$
PA (deg) | $0.2\pm 3.4$ | $6.0\pm 6.2$
3–4 | PD ($\%$) | $3.8\pm 0.4$ | $1.7\pm 0.3$
PA (deg) | $-14.4\pm 3.8$ | $-3.5\pm 6.5$
4–5 | PD ($\%$) | $4.4\pm 0.5$ | $2.5\pm 0.5$
PA (deg) | $-9.8\pm 3.5$ | $-19.2\pm 6.0$
5–8 | PD ($\%$) | $5.4\pm 0.7$ | $2.6\pm 0.7$
PA (deg) | $-14.0\pm 3.7$ | $-21.0\pm 7.9$
161616The errors are at 68% confidence level.

We estimate the following $3\sigma$ upper limits (only the most constraining
ones per epoch are quoted): $H=13.84$, $Y=19.08$, $z=18.28$,
$i^{\prime}=21.79$ (LCO), $r^{\prime}=20.22$, $g^{\prime}=20.45$ for Obs 1,
$H=14.00$, $Y=18.86$, $z=18.35$, $i^{\prime}=21.22$, $r=20.46$, $g=20.50$ for
Obs 2. These upper limits are consistent with the $H$-band magnitude of the
proposed NIR counterpart reported by Jonker et al. (2000) (Star 513;
$H=14.1\pm 0.2$).

##  3 Results

###  3.1 Polarimetric model-independent analysis

The model-independent analysis of the X-ray polarization with ixpeobssim (see
Table 16) in the 2–8 keV energy band gives the PD of $4.3\%\pm 0.3\%$ and
$2.0\%\pm 0.3\%$ in Obs. 1 and Obs. 2, respectively (with 1$\sigma$ errors).
The corresponding PAs are $-9\aas@@fstack{\circ}7\pm 2\aas@@fstack{\circ}0$
and $-9\aas@@fstack{\circ}2\pm 4\aas@@fstack{\circ}0$. We see a significantly
larger PD in Obs. 1 compared to Obs. 2. However, the PA is compatible with
being constant during the two observations. Contour plots of the ixpeobssim
analysis in the 2–8 keV energy range are reported in Fig. 2 (dashed lines).

Table 3: Results of the Stokes parameters fit with a constant value for Obs.
1, Obs. 2, and the combined data set.

Stokes | Best-fit | Obs. 1 | Obs. 2 | Obs. 1 + Obs. 2
---|---|---|---|---
parameter | parameters |  |  |
| constant (%) | $3.86\pm 0.25$ | $1.86\pm 0.24$ | $2.83\pm 0.17$
$q$ | $\chi^{2}_{\nu}$ | 1.31 | 0.15 | 1.26
|  $\alpha$ (%) | 26.8 | 93.0 | 28.7
| constant (%) | $-1.32\pm 0.25$ | $-0.74\pm 0.24$ | $-0.89\pm 0.17$
$u$ | $\chi^{2}_{\nu}$ | 4.26 | 4.00 | 7.16
|  $\alpha$ (%) | 0.52 | 0.74 | 0.01
171717The reduced $\chi^{2}$ of the fit is $\chi^{2}_{\nu}$. The significance
level of the $\chi^{2}$ value is $\alpha$. The number of degrees of freedom is
3.

The behavior of polarization as a function of energy is reported in Table 16.
The energy dependence of the PD is essentially the same in the two
observation, whereas the PA varies from positive to negative values. A proper
assessment of this behavior requires the use of Stokes parameters. The left
panels of Fig. 3 show the Stokes parameters as a function of energy of both
the observations separately. For each observation, the Stokes $q$ parameters
are consistent with being constant in energy, albeit at different values
between the first and second observations. On the other hand, the Stokes $u$
parameters are not compatible with a constant (see Obs. 1 and Obs. 2 columns
of Table 17). This requires the variation of the PA.

On the basis of the assumption that the geometry and the physical process
producing polarization are the same in the two observations, we also
calculated the Stokes parameters of the IXPE observations combined (Obs. 1 and
Obs. 2) to improve the statistics. While the resulting normalized Stokes
parameter $q$ still remains compatible with a constant value, the Stokes $u$
is even more far from being a constant with the reduced $\chi^{2}$ values for
$\nu=3$ degrees of freedom being $\chi^{2}_{\nu}=1.26$ and
$\chi^{2}_{\nu}=7.16$ for $q$ and $u$, respectively. As anticipated by the
separate analysis of the two observations, this behavior of $q$ and $u$
implies a variation of the PA. Such a variation by about 20° is highlighted in
Fig. 4. In the top panel the contour plots on the PD–PA plane for the IXPE
whole observation are shown. Polarization in the 2–3 keV energy bin is not
compatible with that in the 5–8 keV bin with a probability of $\sim 98.7\%$.
In the bottom panel the variation of the PA with energy is shown together with
the fit by a constant giving a value of $-9\aas@@fstack{\circ}1\pm
1\aas@@fstack{\circ}6$ with $\chi^{2}_{\nu}=6.44$ for $\nu=3$ corresponding to
a significance level $\alpha=0.02\%$.

Figure 4: Polarization contour plot (top panel) and PA (bottom panel) as a
function of energy of the combined IXPE data set (Obs. 1 and Obs. 2).  Figure
5: NuSTAR CCD and HID of GX 5$-$1 contemporary to IXPE observation. During
IXPE Obs. 1 the source was in the HB, while during Obs. 2 it was in the NB-FB.
Black, red and purple colors refer to the observing days March 21, April 13
and 14, 2023, respectively.

###  3.2 X-ray spectral analysis

The NICER, NuSTAR and IBIS/ISGRI light curves contemporary to IXPE
observations are shown in Fig. 1. The time-resolved CCD and hardness-intensity
diagram (HID) for all the observations with IXPE, NICER and NuSTAR show GX
5$-$1 moving along the complete Z-track from March 21 to April 14. NuSTAR CCD
and HID, obtained from the GTIs contemporary to the IXPE observations (see
Fig. 5), highlight clearly the Z shape, disentangling also the NB with respect
to the FB, due to the wide energy band from 3 to 20 keV used to construct the
CCD colors. During IXPE Obs. 1, the source was in the HB, whereas it was in
the NB-FB during Obs. 2 which we have checked also by constructing CCD and HID
from the IXPE data of both observations. From March 24 to 25 (about 3 days
after the end of Obs. 1), when ATCA was observing, NICER detected GX 5$-$1
moving from the HB-NB corner towards the NB.

Table 4: Best-fit parameters of GX 5$-$1 spectral model from NICER, NuSTAR and
IBIS/ISGRI data simultaneous to IXPE observation.

Components | Parameters | Obs. 1 | Obs. 2
---|---|---|---
edge |  $E$ (keV) | 1.82148 (frozen)
| $\tau$ | $0.172^{+0.028}_{-0.016}$ | $0.152\pm 0.017$
edge |  $E$ (keV) | 1.95197 (frozen)
| $\tau$ | $0.051\pm 0.016$ | $0.484\pm 0.016$
edge |  $E$ (keV) | 2.28003 (frozen)
| $\tau$ | $0.037\pm 0.014$ | $0.025\pm 0.014$
edge |  $E$ (keV) | 2.44444 (frozen)
| $\tau$ | $0.050\pm 0.013$ | $0.038\pm 0.013$
edge |  $E$ (keV) | 3.16139 (frozen)
| $\tau$ | $0.020^{+0.007}_{-0.008}$ | $0.012\pm 0.007$
Continuum paramters
tbabs |  $N_{\rm H}$ ($10^{22}$ cm-2) | $4.93^{+0.12}_{-0.06}$ | $4.88\pm 0.04$
diskbb |  $kT$ (keV) | $0.95\pm 0.07$ | $1.20\pm 0.03$
|  $R_{\rm in}\sqrt{\cos{\theta}}$ (km)aa$a$Radii are estimated assuming the distance to the source of 7.6 kpc (see Sect. 3.5). | $25^{+2}_{-3}$ | $19.6^{+0.9}_{-0.8}$
thcomp | $\Gamma$ | $2.35^{+0.13}_{-0.49}$ | $<2.1$
|  $kT_{\rm e}$ (keV) | $2.99^{+0.02}_{-0.10}$ | $3.08^{+0.37}_{-0.11}$
| $f$ | $0.99^{+0.01}_{-0.36}$ | $0.032^{+0.08}_{-0.005}$
bbodyrad |  $kT_{\rm bb}$ (keV) | $1.27^{+0.26}_{-0.11}$ | $1.68^{+0.03}_{-0.04}$
|  $R_{\rm bb}$ (km)aa$a$Radii are estimated assuming the distance to the source of 7.6 kpc (see Sect. 3.5). | $19^{+1}_{-6}$ | $9.3^{+0.6}_{-0.5}$
expabs |  $E_{\rm cut}$ (keV) |  [= $kT_{\rm bb}$] | –
powerlaw | $\Gamma$ | $2.62^{+0.49}_{-0.92}$ | –
| norm | $0.45^{+2.3}_{-0.43}$ | –
Cross-calibration constants
const | $C_{\rm NICER}$ | $1.107\pm 0.003$ | $1.034\pm 0.004$
| $C_{NuSTAR,\rm FPMA}$ | 1 (frozen)
| $C_{NuSTAR,\rm FPMB}$ | $1.0136\pm 0.0013$ | $0.9908\pm 0.0014$
| $C_{\rm IBIS/ISGRI}$ | $0.66\pm 0.08$ | $1.29\pm 0.03$
|  $\chi^{2}$/d.o.f. | 421/451 | 338/365
|  $\tau_{\tt thcomp}$bb$b$The optical depth $\tau_{\tt thcomp}$ comes from Eq. (14) in Zdziarski et al. (2020). | $8.7^{+2.5}_{-0.7}$ | $>10.0$
|  $f_{2-8\,\rm keV}$cc$c$The unabsorbed flux is measured in units 10-8 erg cm-2 s-1. | 2.3 | 2.4
|  $f_{2-5\,\rm keV}$cc$c$The unabsorbed flux is measured in units 10-8 erg cm-2 s-1. | 1.5 | 1.7
|  $f_{5-8\,\rm keV}$cc$c$The unabsorbed flux is measured in units 10-8 erg cm-2 s-1. | 0.8 | 0.7
|  $f_{\rm({\tt thcomp*bbodyrad})}$ / $f_{2-8\,\rm keV}$ |  61$\%$ |  33$\%$
181818The errors are at 90% confidence level. The edges reported on the top
section of the table are referred only to the NICER energy spectrum.

We fit the NICER, NuSTAR and IBIS/ISGRI data of Obs. 1 and Obs. 2 presenting
results in Fig. 6 and Table 18. The better fits we obtained are based on the
following spectral models for Obs. 1 and Obs. 2:

tbabs*(diskbb+expabs*powerlaw+thcomp*bbodyrad),

tbabs*(diskbb+thcomp*bbodyrad),

respectively.

Figure 6: Deconvolved NICER (1.5–10 keV), NuSTAR (3.5–45 keV for Obs. 1 and
3.5–35 keV for Obs. 2) and IBIS/ISGRI (28–50 keV) spectra simultaneous with
both IXPE observations as obtained from the best-fit model reported in Table
18 and residuals between data and model in units of $\sigma$.

We included the normalizing cross-calibration multiplicative factors for the
NICER, IBIS/ISGRI and NuSTAR FPMA (frozen at unity) and FPMB telescopes. A
tbabs (Wilms et al., 2000) multiplicative model component was used to take
into account the low-energy absorption due to the interstellar medium. We used
the abundances and cross-section tables according to Wilms et al. (2000) and
Verner et al. (1996) (wilm, vern in xspec). We modeled the GX 5$-$1 energy
spectra of both the observations with a multi-color disk and a harder
boundary/spreading layer (BL, or SL) emission (e.g., Popham & Sunyaev, 2001;
Revnivtsev et al., 2013). In both observations, the convolution model
component thcomp (Zdziarski et al., 2020) is used to represent Comptonized
emission from the BL/SL (e.g. Di Salvo et al., 2002; Farinelli et al., 2009)
modeled with the bbodyrad component. The $f$ parameter of thcomp represents
the fraction of Comptonized seed photons. In Obs. 1, this parameter is $>0.63$
with the best-fit value equal to 0.99. Effectively, all photons from the BL/SL
bbodyrad are Comptonized. In Obs. 2, only a fraction between 2.7% and 11.2%
(best-fit 3.2%) of seed photons are Comptonized. It is worth noting that a
higher Comptonization fraction corresponds to a higher PD observed from the
source. During Obs. 1, when the source is on the HB, the energy spectrum is
harder, and a high-energy excess was seen (it was absent in Obs. 2). This
excess is modeled with an additional hard tail represented by a power-law
component with a low-energy exponential roll-off. The e-folding energy for the
absorption of the exponential roll-off is set equal to the bbodyrad $kT_{\rm
bb}$ energy of the SL/BL. This parameter link comes from the assumption that
the power-law emission originates from the seed distribution of the SL/BL
blackbody. The BL and the inner disk are hotter in Obs. 2 than in Obs. 1,
while the BL sphere-equivalent radius and inner disk radius are larger in Obs.
1. In contrast to Obs. 1, the additional power-law component is not needed to
model the spectrum of Obs. 2.

The softer disk component dominates up to $\sim 3.5$ keV in Obs. 1 and up to
$\sim 5.5$ keV in Obs. 2 (see Fig. 6). In the 2–8 keV band, the energy flux in
the Comptonized component (including the contribution of the exponentially
absorbed power-law component) accounts for $\sim 61\%$ of the total in Obs. 1.
In Obs. 2, the energy flux of the Comptonized component drops to $\sim 33\%$
of the total in the same energy band.

###  3.3 X-ray spectro-polarimetric analysis

The results of the spectro-polarimetric analysis, including IXPE, once the
spectral model used to fit the data from the other observatories is frozen, is
reported in Table 19. The PD obtained with a polconst multiplicative model
component applied to the whole spectral model of GX 5$-$1 in Obs. 1 and Obs. 2
is $3.7\%\pm 0.4\%$ and $1.8\%\pm 0.4\%$, respectively. The PA is around
$-9\degr$, in both the observations. The polarization contour plot in the 2–8
keV energy band obtained with xspec (polconst model applied to the spectral
model) is shown in Fig. 2. These contours are nearly identical to those
obtained using ixpeobssim.

Table 5: Best-fit parameters of polarization analysis with xspec.

DU | Parameters | Obs. 1 | Obs. 2
---|---|---|---
DU1 | $N_{\rm DU1}$ | $0.796\pm 0.006$ | $0.798\pm 0.004$
| gain slope | $0.953^{+0.003}_{-0.03}$ | $0.961\pm 0.003$
| gain offset (keV) | $0.13\pm 0.02$ | $0.102\pm 0.015$
DU2 | $N_{\rm DU2}$ | $0.772\pm 0.006$ | $0.769\pm 0.004$
| gain slope | $0.952\pm 0.003$ | $0.960\pm 0.003$
| gain offset (keV) | $0.15\pm 0.02$ | $0.131\pm 0.014$
DU3 | $N_{\rm DU3}$ | $0.734\pm 0.005$ | $0.736\pm 0.004$
| gain slope | $0.976\pm 0.004$ | $0.966\pm 0.003$
| gain offset (keV) | $0.10\pm 0.02$ | $0.114\pm 0.015$
Components | Parameters | Obs. 1 | Obs. 2
polconst*(diskbb+[expabs*powerlaw]aa$a$expabs*powerlaw component was included
only in Obs. 1.+thcomp*bbodyrad)
|  PD ($\%$) | $3.7\pm 0.4$ | $1.8\pm 0.4$
| PA (deg) | $-9\pm 3$ | $-9\pm 6$
|  $\chi^{2}$/d.o.f. | 1806/1799 | 1733/1711
polconst1*diskbb+polconst2*([expabs*powerlaw]aa$a$expabs*powerlaw component
was included only in Obs. 1.+thcomp*bbodyrad)
polconst1 |  PD ($\%$) | $2.3\pm 0.9$ | $1.8\pm 0.9$
| PA (deg) | $21\pm 11$ | $14\pm 15$
polconst2 |  PD ($\%$) | $5.7\pm 1.4$ | $4.3\pm 2.0$
| PA (deg) | $-16\pm 20$ | $-32\pm 14$
|  $\chi^{2}$/d.o.f. | 1792/1806 | 1726/1718
191919The errors are at 90% confidence level. See Table 18 for the
corresponding spectral analysis. Polarization is computed in the 2–8 keV
energy range.

The spectro-polarimetric analysis with xspec allows us to assign a
polarization to the different spectral components. The result of such an
analysis is reported in Table 19 and Fig. 7. For Obs. 1, we assigned the same
polarization for the expabs*powerlaw and thcomp*bbodyrad components, assuming
that the power law is just a continuation of the BL/SL component, with the
power-law low energy rollover $E_{\rm cut}$ being equal to the temperature of
the BL/SL bbodyrad $kT_{\rm bb}$.

The Comptonization component is well constrained at a 99.9% confidence level
only in Obs. 1, while the disk component is not constrained at 99% in either
observation (see Fig. 7). Moreover, in both the observations the polarization
of each component has similar PAs, suggesting that the geometry responsible
for the polarization is similar. Figure 8 shows the fit of the $Q$ and $U$
Stokes parameters as a function of energy with the two polconst components for
both the observations. The contribution to the total flux of the polarized
component is different (higher in Obs. 1) probably due to a dilution effect by
unpolarized radiation connected with a low covering fraction of the
Comptonization component (see Table 18). Unfortunately, even if the source was
active in the radio band during the observation campaign, it is impossible to
compare the direction of the PA with the direction of the jet, because the
radio observations reported in this paper do not have the spatial resolution
to resolve it. Moreover, literature does not report any information about jet
direction.

Figure 7: Polarization contour plots from the spectro-polarimetric analysis in
the 2–8 keV energy range of Obs. 1 (top panel) and Obs. 2 (bottom panel). The
polconst polarimetric model is applied separately to the diskbb component of
both IXPE observations and to the (expabs*powerlaw+thcomp*bbodyrad) components
as a whole. The expabs*powerlaw component (labeled as pl. in the plot legend)
is included only in Obs. 1. Contour plots are computed for 4 parameters of
interest, taking into account the fact that the polarization of the disk and
Comptonization components are correlated in the simultaneous fit.

Figure 8: Fit of the IXPE Stokes parameters $Q$ and $U$ as a function of
energy with the model comprising two polconst components applied to the disk
(dotted lines) and to the Comptonization (dashed lines) for Obs. 1 (left
column) and Obs. 2 (right column).

The variation of the PA of the total emission, reported in Sect. 3.1, obtained
with ixpeobssim model independent analysis

can be explained by the different PAs of the disk and Comptonized spectral
components which are not aligned, nor being 90° apart. Indeed, the PA of the
total emission varies from being positive at lower energies (dominated by the
diskbb component) to negative values at higher energies dominated by the
Comptonization component with a positive PA.

When assessing polarization as a function of time, no significant variations
are seen. This implies that polarization is not sensitive to the flux
variation present in the light curves (see Fig. 1).

###  3.4 Spectral energy distribution

Thanks to the multi energy observation campaign it was possible to produce a
broadband (radio–X-ray) spectral energy distribution (SED) of GX 5$-$1 for
both the observations (see Fig. 9). Optical and infrared fluxes have been de-
reddened using the hydrogen column density reported in this work ($N_{\rm
H}=4.93\times 10^{22}$ cm-2 and $4.88\times 10^{22}\,\rm cm^{-2}$ in Obs. 1
and 2, respectively), which was converted into an estimate of the $V$-band
extinction $A_{V}$ using the relation reported in Foight et al. (2016b),
resulting in $A_{V}=17.18\pm 0.77$ mag and $17.00\pm 0.72$ mag for the two
observations, respectively. The different absorption coefficients at optical
and near-IR wavelengths have then been evaluated using the relations reported
in Cardelli et al. (1989) and Nishiyama et al. (2008), respectively. For the
mid-IR, the coefficients reported in Weingartner & Draine (2001) have instead
been used.

Figure 9: Broad-band radio to X-ray SED of GX 5$-$1 during the two
observations. For Obs. 2, no mid-IR flux is reported as observations were not
performed with VISIR at that time (see Sect. 2.6 for details). The flux
densities at mid-IR, near-IR and optical frequencies have been de-reddened as
described in Sect. 3.4. The errors are at 68% confidence level.

GX 5$-$1 is detected at radio and mid-IR wavelengths, with upper limits in the
near-IR and optical. As mentioned in Sect. 2.7, this is due to the large value
of dust extinction of $A_{V}\approx 17$. This implies an extinction of $\sim$7
mag at 1 $\mu$m ($Y$-band) and $\sim$3 mag at 1.6 $\mu$m ($H$-band). The radio
spectral index of $-0.4\pm 0.1$ is too steep for the radio emission to arise
from a steady, compact jet (for which we expect a spectral index from $\sim 0$
to +0.5). As such, it is likely due to optically thin jet ejections, or a
combination of compact jet and optically thin ejections. In the mid-IR, we
report the first detection of this source. The de-reddened flux densities are
comparable to the near-IR values reported in the literature (Naylor et al.,
1991; Jonker et al., 2000; Bandyopadhyay et al., 2003); however, the de-
reddened near-IR fluxes depend sensitively on the value of the interstellar
extinction. We note that different values of the neutral hydrogen column
densities are reported in the literature, ranging from $N_{\rm H}=2.54\times
10^{22}$ cm-2 to $6.20\times 10^{22}$ cm-2 (Christian & Swank, 1997; Zeegers
et al., 2017; Homan et al., 2018; Clark, 2018; Bhulla et al., 2019). Yang et
al. (2022) has derived $N_{\rm H}=(4.52\pm 0.01)\times 10^{22}$ cm-2 by
measuring the Si K edge due to scattering by dust using the Chandra gratings.
This value is in agreement with our measurements because $N_{\rm H}$ is
slightly overestimated when fitting the continuum with the absorption model
tbabs (Corrales et al., 2016). In this work, we observed GX 5$-$1 over a
significantly larger energy range, and we are confident to have properly
constrained the absorption in the interstellar medium. However, if there is a
component of the neutral hydrogen column which is intrinsic to the LMXB, this
could cause varying measurements and introduce uncertainty into the relation
between $N_{\rm H}$ and the extinction $A_{V}$. Moreover, older works using
Anders & Grevesse (1989) solar abundances rather than Wilms et al. (2000)
interstellar abundances, could be affected by model systematic.

The mid-IR flux measured with the VLT VISIR is higher than the extrapolation
of the ATCA spectral index from radio to mid-IR. The mid-IR emission is
therefore unlikely to be due to optically thin synchrotron from discrete jet
ejections that were seen in the radio, but it could be optically thin
synchrotron emission from the compact jet (from above the jet spectral break;
Russell et al. 2013). We find evidence of strong mid-IR variability between
the two epochs, with the 9–11 $\mu$m flux density changing from $<3.27$ mJy on
2023-03-28, to $9.95\pm 2.31$ mJy on 2023-03-31. While this variation by a
factor of $\geq 3$ ($\geq 2.5$ magnitudes) is quite high for a LMXB accretion
disk on these timescales, high amplitude (spanning several magnitudes)
infrared variability has been reported from a number of bright, persistent NS-
LMXBs, including GX 17+2, Cir X-1, 4U 1705$-$440 and GX 13+1 (e.g. Glass,
1994; Callanan et al., 2002; Bandyopadhyay et al., 2002; Homan et al., 2009;
Corbet et al., 2010; Harrison et al., 2011). This variability has been
generally interpreted as indicative of highly variable synchrotron emission
from a compact jet. Variable near-IR polarization has also been reported from
the bright, persistent NS-LMXBs Sco X-1 and Cyg X-2, as well as the NS-LMXB
transient SAX J1808.4$-$3658 (Shahbaz et al., 2008; Russell & Fender, 2008;
Baglio et al., 2020). The de-reddened mid-IR 4.7–8.7 $\mu$m spectral index on
2023-03-31 is $-2.3$ to $-0.4$ (adopting $A_{V}=17.18\pm 0.77$), which is
consistent with optically thin synchrotron emission from relativistic
particles, or a steeper particle distribution with a thermal (Maxwellian)
component, as has been seen at infrared wavelengths from jets in some black
hole LMXBs (e.g., Russell et al., 2010; Shahbaz et al., 2013). Thus, this
emission could originate from a compact jet which peaks in the mid- or far-IR,
although follow-up observations characterizing the IR spectrum and variability
would be beneficial to confirm the nature of the IR emission. If the compact
jet is present, its spectrum from radio to mid-IR must be inverted, with index
$>0.33$ (and fainter than the observed radio emission). The radio to IR
spectrum is similar in some ways to the NS-LMXBs 4U 1728$-$34 and 4U 0614+091
(Migliari et al., 2010; Díaz Trigo et al., 2017).

Figure 10: Fit of the infrared extinction $A_{K_{s}}$ between 5 and 15 kpc
from Marshall et al. (2006) with a linear function (the best-fit line and the
lines taking into account the associated errors are in blue). The red
horizontal lines represent the estimate with the corresponding upper and lower
limits of $A_{K_{s}}$ from Eq. (3). The distance to the source is thus
$d=7.6\pm 1.1$ kpc.

###  3.5 Measurement of the distance to the source

In order to derive some spectral model parameters (namely $R_{\rm
in}\sqrt{\cos\theta}$ of diskbb and $R_{\rm bb}$ of bbodyrad), an estimate of
the distance to the source is needed. Such an estimate can be obtained from
the equivalent hydrogen column density $N_{\rm H}$ which we get from our
analysis. We find that $N_{\rm H}=(4.93^{+0.12}_{-0.06})\times 10^{22}$ cm-2
and $(4.88^{+0.03}_{-0.04})\times 10^{22}$ cm-2 for the first and the second
observations, respectively. Because the two values are the same at the 90%
confidence levels, we use the average value and its largest uncertainty range,
that is $(4.91^{+0.14}_{-0.07})\times 10^{22}$ cm-2, in the following
discussion. To estimate the distance to the source we adopt the approach
proposed by Gambino et al. (2016). We use the model of the infrared Galactic
interstellar extinction discussed by Marshall et al. (2006). Because the
Galactic coordinates of GX 5$-$1 are $l=5\aas@@fstack{\circ}08$ and
$b=-1\aas@@fstack{\circ}02$ we adopt the map that relates the infrared
extinction $A_{K_{s}}$ with the source distance $d$ valid for $l=5\degr$ and
$b=-1\degr$ (see black dots with the error bars in Fig. 10).

Because the visual extinction $A_{V}$ is related to $N_{\rm H}$ as (Foight et
al., 2016a)

$N_{\rm H}=(2.87\pm 0.12)\times 10^{21}\;A_{V},$ (1)

and the relation between $A_{V}$ and the extinction in the $K_{s}$ band is
(Nishiyama et al., 2008)

$A_{K_{s}}=(0.062\pm 0.005)\;A_{V},$ (2)

we obtain

$A_{K_{s}}=\frac{(0.062\pm 0.005)}{(2.87\pm 0.12)\times 10^{21}}\;N_{\rm
H}\;{\rm mag}=1.06\pm 0.10\ \mbox{mag}.$ (3)

We fit the $A_{K_{s}}$ values between 5 and 15 kpc with a linear function (the
best-fit line and the lines taking into account the associated errors are in
blue color in Fig. 10). We infer that the distance to the source is $d=7.6\pm
1.1$ kpc. This distance is in agreement with the previously reported values
(Penninx, 1989; Smith et al., 2006).

##  4 Discussion

As shown in Sect. 3, the two multiwavelength observations of GX 5$-$1 allowed
us to catch the source when it was covering the complete Z-track on its
CCD/HID (see Fig. 5). In particular, during the first observation, GX 5$-$1
was on the HB of the track, while in the second it moved across to the NB and
FB. Very interestingly, we found the same behavior in the peculiar transient
XTE J1701$-$462 (Cocchi et al., 2023), in which the PD was correlated with the
source position on the Z-track, being higher in the HB and decreasing by a
factor about two in the NB. Long et al. (2022) hypothesized the same behavior
also for Sco X-1. There are at least three regions which may potentially
contribute to the polarization: the BL/SL, the accretion disk, and the
reflection of the BL/SL photons from the disk atmosphere or a wind.

Table 6: Best-fit parameters with reflection included in the energy spectrum
model of GX 5$-$1 from NICER, NuSTAR and INTEGRAL data simultaneous to IXPE
observation.

Components | Parameters | Obs1 | Obs2
---|---|---|---
edge |  $E$ (keV) | $1.820\pm 0.013$ | $1.818\pm 0.013$
| $\tau$ | $0.15\pm 0.02$ | $0.15\pm 0.02$
edge |  $E$ (keV) | 1.95197 (fixed)
| $\tau$ | $0.05\pm 0.02$ | $0.05\pm 0.02$
edge |  $E$ (keV) | 2.28003 (fixed)
| $\tau$ | $0.034\pm 0.014$ | $0.027\pm 0.013$
edge |  $E$ (keV) | 2.44444 (fixed)
| $\tau$ | $0.049\pm 0.013$ | $0.038\pm 0.013$
edge |  $E$ (keV) | 3.16139 (fixed)
| $\tau$ | $0.021\pm 0.007$ | $0.011\pm 0.007$
tbabs |  $N_{\rm H}$ ($10^{22}$ cm-2) | $4.80\pm 0.05$ | $4.87\pm 0.05$
diskbb |  $kT$ (keV) | $1.21\pm 0.05$ | $1.20\pm 0.03$
|  $R_{\rm in}\sqrt{\cos{\theta}}$ (km)aa$a$Radii are estimated assuming the distance to the source of 7.6 kpc (see Sect. 3.5). | $16\pm 1$ | $19^{+1}_{-0.9}$
comptb |  $kT_{0}$ (keV) | $1.93\pm 0.13$ | $1.71\pm 0.04$
| $\alpha$ | $2.9^{+1.7}_{-0.8}$ | $<1.16$
|  $kT_{\rm e}$ (keV) | $3.6^{+1.9}_{-0.4}$ | $3.24^{+0.38}_{-0.10}$
| $\log A$ | 8 (fixed) | $-1.54^{+0.54}_{-0.06}$
| $N_{\rm comptb}$ | $0.148\pm 0.003$ | $0.123\pm 0.006$
expabs |  $E_{\rm cut}$ (keV) |  [= $kT_{0}$] | –
powerlaw | $\Gamma$ |  $2.4$ (fixed) | –
| norm | $0.17\pm 0.05$ | –
rdblur | betor |  $-2.5$ (fixed)
|  $R_{\rm in}$ ($R_{\rm g}$) | 7 (fixed)
|  $R_{\rm out}$ ($R_{\rm g}$) | 1000 (fixed)
| incl. (deg) |  $60$ (fixed)
rfxconv | rel-refl | 0.3 (fixed)
| $\log\xi$ | 3.8 (fixed)
|  $\chi^{2}$/d.o.f. | 268/295 | 247/260
202020The errors are at 90% confidence level.

The spectro-polarimetric analysis of the IXPE data (Table 19) shows that the
disk polarization is about 2% in both observations, which is compatible with
the classical results of a high optical depth scattering atmosphere at an
inclination of 60° (Chandrasekhar, 1960). The higher PD value of the hard
component on the other hand, cannot be explained by repeated Compton
scattering in high optical depth environment, neither for a boundary layer
coplanar with the disk (which otherwise would resemble a Chandrasekhar-like
slab) nor for a spreading layer around the neutron star, for which a maximum
PD of $\la 2$% is expected.

Disk reflection is probably the most natural way to explain a PD of order of
4%–5%, as shown by Lapidus & Sunyaev (1985). It is important to note that we
do not find a strong reflection signature in the spectral analysis, and it
deserves mentioning that the reflection contribution to the spectrum may be
low and sometimes may be embedded in the continuum but, nevertheless, make a
large contribution to the net polarization signal (Schnittman & Krolik, 2009).
This may be particularly true if the primary spectrum is not a hard power law,
but a blackbody-like spectrum with a rollover below 30 keV. Note that a
similar argument has been used also for Cyg X-2 (Farinelli et al., 2023) and
GX 9+9 (Ursini et al., 2023) to explain the high PD attributed to the
Comptonization spectrum in a two-fold spectro-polarimetric approach.

The PD of the reflected radiation is not easy to predict because it depends on
geometrical and physical factors (e.g., the disk ionization parameter)
however, it is not likely to exceed $\sim$20% (Matt, 1993; Poutanen et al.,
1996; Schnittman & Krolik, 2009). We tested the hypothesis as to whether there
is a reflection component in the GX 5$-$1 energy spectrum by making some
assumptions: (1) highly ionized disk due to the absence of a broad emission
line in the Fe-K region of the spectrum, (2) inclination $i=60\degr$ since GX
5$-$1 is a Cyg-like Z-source (Homan et al., 2018), (3) keep the reflection
amplitude $f=\Omega/2\pi$ at a typical value for the NS-LMXBs (namely 30%,
see, e.g., Di Salvo et al., 2015; Matranga et al., 2017). We applied the
following spectral models:

Obs. 1:

constant*tbabs(diskbb + expabs*powerlaw + rdblur*rfxconv*comptb + comptb),

Obs. 2:

constant*tbabs(diskbb + rdblur*rfxconv*comptb + comptb).

The comptb (Farinelli et al., 2008) model component was included in place of
the thcomp to prevent a double convolution of the BL/SL blackbody. Details on
rfxconv and rdblur model components can be found in Kolehmainen et al. (2011)
and Fabian et al. (1989), respectively. The sum rdblur*rfxconv*comptb + comptb
accounts for the reflected radiation (the first term) plus the incident
radiation (the second term).

This modeling of the reflection component contribute $\sim$22% of the flux in
Obs. 1 and $\sim$12% in Obs. 2. Such a contribution to the total emission can
easily account for the polarization detected (see Table 20 for details of the
fit parameters of the energy spectrum). The fraction of Comptonized photons in
Obs. 2 is significantly smaller with respect to Obs. 1, as obtained also in
Sect. 3 by applying only the Comptonization model thcomp. The parameter $\log
A=-1.54^{+0.54}_{-0.06}$ in comptb corresponds to a $2.8^{+6.3}_{-0.4}\%$ of
photons upscattered in energy (consistent with $3.2^{+8.0}_{-0.5}\%$ obtained
when reflection is not taken into account as in Sect. 3). This confirms the
presence of a blackbody component observed through an almost vanished
Comptonization medium in Obs. 2, even if reflection is included. However, the
fraction of Comptonized photons, albeit small ($\sim$3%), is still sufficient
to manifest its presence at high energy. Indeed, if we would neglect this
small fraction of Comptonized photons by substituting comptb with a blackbody
component, such as bbodyrad, we obtain an unacceptable fit result
($\chi^{2}_{\nu}=3.6$, with a significant excess at high energy due to this
small fraction of Comptonized photons).

Another possible mechanism for producing polarization is related to scattering
in the wind above the accretion disk: as was shown in Sunyaev & Titarchuk
(1985), the emission scattered once in a plane (e.g. equatorial wind) can be
polarized up to 27% for an inclination $i=60\degr$. This polarization degree
is only weakly dependent on the opening angle of the wind. Assuming that 20%
of the source emission is scattered, we can obtain the observed PD. Recently,
a similar model was shown to explain well the presence of a constant polarized
component in the X-ray pulsars RX J0440.9+4431 / LS V +44 17 (Doroshenko et
al., 2023). Although it is well known that strong winds can be indeed present
in the soft states of X-ray binaries (e.g., Neilsen & Lee, 2009; Ponti et al.,
2012, 2014), it is worth noting that we do not see wind absorption features in
the energy spectrum of GX 5$-$1, implying that, if present, the wind should be
completely ionized.

Both IXPE observations show similar behavior of the PD values: they are
smaller in the 2–4 keV band and increase slightly with energy. The reduction
of the PD at lower energies can be explained by the energy dependence of the
disk emission: in the low energy band we have a marginally polarized disk
emission dominating the spectrum, while at higher energies, the emission of
the SL and/or the scattered/reflected component is more visible. Another
feature of the observed emission that needs to be addressed is the variation
of the PA with energy. In the spectro-polarimetric analysis the disk and the
Comptonization components have non-orthogonal PAs, thus the variation of the
polarization plane of the total emission with energy can be interpreted as the
energy-dependent contribution of these two components to the total emission.
The same applies if, for instance, the SL emission is scattered in the wind
and the disk emission is polarized with a different and non-orthogonal angle.
The PA of the combined emission will be energy dependent. It is well known
that the disk emission exhibits the rotation of the polarization plane with
energy (Connors et al., 1980; Dovčiak et al., 2008; Loktev et al., 2022).
Simulations of the SL emission also show a change of the PA with energy but
predict a PD at most 1.5% (Bobrikova A., in prep.). Thus, a single component
explanation of the PA variation cannot be considered compatible with the high
measured PD. Further modeling will be needed to satisfactory address the
explanations presented above.

##  5 Summary

IXPE observed the NS-LMXB GX 5$-$1 twice in the period March–April 2023.
Contemporary observations in the X-ray energy band were put in place with
NICER, NuSTAR, and INTEGRAL. Multi-wavelength coverage was ensured by ATCA in
the radio, VLT VISIR in mid-IR, REM in optical, and NIR and LCO in optical.

During the observations GX 5$-$1 moved across the entire Z-track. NuSTAR
disentangled clearly the NB with respect to the FB thanks to its extended
energy band. The presence of a hard tail, reported in previous analyses, was
clearly detected in Obs. 1, but not in Obs. 2, when the source had a softer
energy spectrum. The X-ray PD was $\sim$4% during Obs. 1 when the source was
in the HB and $\sim$2% during Obs. 2 with the source in the NB-FB. This result
is in agreement with findings from the other Z-sources observed by IXPE
(namely Cyg X-2 and XTE J1701$-$462).

The source manifested an unexpected variation of the PA as a function of
energy by $\sim$ 20°. The magnitude of the variation combined with the
magnitude of the PD require further modeling. However, it is likely related to
the different PAs of the disk and Comptonization components which are non-
orthogonal and, moreover, have the emission peaks at different energies.

In the radio band, the source was detected, but only upper-limits to the
polarization were obtained ($\sim$6% at 5.5 GHz and 9 GHz in Obs. 1 and 12.5%
at 5.5 GHz and 20% at 9 GHz in Obs. 2). The mid-IR counterpart was detected in
M and the J8.9 bands. This emission could originate from a compact jet which
peaks in the mid- or far-IR. Follow-up observations characterizing the IR
spectrum and its variability would be beneficial. Due to the very high
extinction toward the source and to the crowded field, the source was not
detected in any of the optical and NIR images acquired.

###### Acknowledgements.

The Imaging X-ray Polarimetry Explorer (IXPE) is a joint US and Italian
mission. The US contribution is supported by the National Aeronautics and
Space Administration (NASA) and led and managed by its Marshall Space Flight
Center (MSFC), with industry partner Ball Aerospace (contract NNM15AA18C). The
Italian contribution is supported by the Italian Space Agency (Agenzia
Spaziale Italiana, ASI) through contract ASI-OHBI-2017-12-I.0, agreements ASI-
INAF-2017-12-H0 and ASI-INFN-2017.13-H0, and its Space Science Data Center
(SSDC) with agreements ASI-INAF-2022-14-HH.0 and ASI-INFN 2021-43-HH.0, and by
the Istituto Nazionale di Astrofisica (INAF) and the Istituto Nazionale di
Fisica Nucleare (INFN) in Italy. This research used data products provided by
the IXPE Team (MSFC, SSDC, INAF, and INFN) and distributed with additional
software tools by the High-Energy Astrophysics Science Archive Research Center
(HEASARC), at NASA Goddard Space Flight Center (GSFC). ATCA is part of the
Australia Telescope National Facility (https://ror.org/05qajvd42) which is
funded by the Australian Government for operation as a National Facility
managed by CSIRO. We acknowledge the Gomeroi people as the Traditional Owners
of the ATCA Observatory site. Partly based on observations with INTEGRAL, an
ESA project with instruments and science data centre funded by ESA member
states (especially the PI countries: Denmark, France, Germany, Italy,
Switzerland, Spain), and with the participation of the Russian Federation and
the USA. Data have been reduced using the Multi-Messenger Online Data Analysis
platform provided by the ISDC (University of Geneva), EPFL, APC, and KAU. J.P.
acknowledges support from the Academy of Finland grant 333112. A.B. is
supported by the Finnish Cultural Foundation grant 00220175. T.D.R. thanks
Jamie Stevens and James Miller-Jones for the helpful discussions regarding the
radio observations. J.S. and M.D. acknowledge the support from the GACR
project 21-06825X.

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