# Velocity independent constraints on spin-dependent DM-nucleon interactions
from IceCube and PICO.

M. G. Aartsen  Dept. of Physics and Astronomy, University of Canterbury,
Private Bag 4800, Christchurch, New Zealand  M. Ackermann  DESY, D-15738
Zeuthen, Germany  J. Adams  Dept. of Physics and Astronomy, University of
Canterbury, Private Bag 4800, Christchurch, New Zealand  J. A. Aguilar
Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
M. Ahlers  Niels Bohr Institute, University of Copenhagen, DK-2100 Copenhagen,
Denmark  M. Ahrens  Oskar Klein Centre and Dept. of Physics, Stockholm
University, SE-10691 Stockholm, Sweden  C. Alispach  Département de physique
nucléaire et corpusculaire, Université de Genève, CH-1211 Genève, Switzerland
K. Andeen  Department of Physics, Marquette University, Milwaukee, WI, 53201,
USA  T. Anderson  Dept. of Physics, Pennsylvania State University, University
Park, PA 16802, USA  I. Ansseau  Université Libre de Bruxelles, Science
Faculty CP230, B-1050 Brussels, Belgium  G. Anton  Erlangen Centre for
Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg,
D-91058 Erlangen, Germany  C. Argüelles  Dept. of Physics, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  J. Auffenberg  III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  S.
Axani  Dept. of Physics, Massachusetts Institute of Technology, Cambridge, MA
02139, USA  P. Backes  III. Physikalisches Institut, RWTH Aachen University,
D-52056 Aachen, Germany  H. Bagherpour  Dept. of Physics and Astronomy,
University of Canterbury, Private Bag 4800, Christchurch, New Zealand  X. Bai
Physics Department, South Dakota School of Mines and Technology, Rapid City,
SD 57701, USA  A. Balagopal V  Karlsruhe Institute of Technology, Institut für
Kernphysik, D-76021 Karlsruhe, Germany  A. Barbano  Département de physique
nucléaire et corpusculaire, Université de Genève, CH-1211 Genève, Switzerland
S. W. Barwick  Dept. of Physics and Astronomy, University of California,
Irvine, CA 92697, USA  B. Bastian  DESY, D-15738 Zeuthen, Germany  V. Baum
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz,
Germany  S. Baur  Université Libre de Bruxelles, Science Faculty CP230, B-1050
Brussels, Belgium  R. Bay  Dept. of Physics, University of California,
Berkeley, CA 94720, USA  J. J. Beatty  Dept. of Physics and Center for
Cosmology and Astro-Particle Physics, Ohio State University, Columbus, OH
43210, USA  Dept. of Astronomy, Ohio State University, Columbus, OH 43210, USA
K.-H. Becker  Dept. of Physics, University of Wuppertal, D-42119 Wuppertal,
Germany  J. Becker Tjus  Fakultät für Physik & Astronomie, Ruhr-Universität
Bochum, D-44780 Bochum, Germany  S. BenZvi  Dept. of Physics and Astronomy,
University of Rochester, Rochester, NY 14627, USA  D. Berley  Dept. of
Physics, University of Maryland, College Park, MD 20742, USA  E. Bernardini
DESY, D-15738 Zeuthen, Germany  D. Z. Besson  Dept. of Physics and Astronomy,
University of Kansas, Lawrence, KS 66045, USA  G. Binder  Lawrence Berkeley
National Laboratory, Berkeley, CA 94720, USA  Dept. of Physics, University of
California, Berkeley, CA 94720, USA  D. Bindig  Dept. of Physics, University
of Wuppertal, D-42119 Wuppertal, Germany  E. Blaufuss  Dept. of Physics,
University of Maryland, College Park, MD 20742, USA  S. Blot  DESY, D-15738
Zeuthen, Germany  C. Bohm  Oskar Klein Centre and Dept. of Physics, Stockholm
University, SE-10691 Stockholm, Sweden  M. Börner  Dept. of Physics, TU
Dortmund University, D-44221 Dortmund, Germany  S. Böser  Institute of
Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany  O.
Botner  Dept. of Physics and Astronomy, Uppsala University, Box 516, S-75120
Uppsala, Sweden  J. Böttcher  III. Physikalisches Institut, RWTH Aachen
University, D-52056 Aachen, Germany  E. Bourbeau  Niels Bohr Institute,
University of Copenhagen, DK-2100 Copenhagen, Denmark  J. Bourbeau  Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin, Madison, WI 53706, USA  F. Bradascio  DESY, D-15738 Zeuthen,
Germany  J. Braun  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA  S. Bron
Département de physique nucléaire et corpusculaire, Université de Genève,
CH-1211 Genève, Switzerland  J. Brostean-Kaiser  DESY, D-15738 Zeuthen,
Germany  A. Burgman  Dept. of Physics and Astronomy, Uppsala University, Box
516, S-75120 Uppsala, Sweden  J. Buscher  III. Physikalisches Institut, RWTH
Aachen University, D-52056 Aachen, Germany  R. S. Busse  Institut für
Kernphysik, Westfälische Wilhelms-Universität Münster, D-48149 Münster,
Germany  T. Carver  Département de physique nucléaire et corpusculaire,
Université de Genève, CH-1211 Genève, Switzerland  C. Chen  School of Physics
and Center for Relativistic Astrophysics, Georgia Institute of Technology,
Atlanta, GA 30332, USA  E. Cheung  Dept. of Physics, University of Maryland,
College Park, MD 20742, USA  D. Chirkin  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin, Madison, WI
53706, USA  S. Choi  Dept. of Physics, Sungkyunkwan University, Suwon 16419,
Korea  L. Classen  Institut für Kernphysik, Westfälische Wilhelms-Universität
Münster, D-48149 Münster, Germany  A. Coleman  Bartol Research Institute and
Dept. of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA
G. H. Collin  Dept. of Physics, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  J. M. Conrad  Dept. of Physics, Massachusetts
Institute of Technology, Cambridge, MA 02139, USA  P. Coppin  Vrije
Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium  P. Correa
Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium  D. F.
Cowen  Dept. of Physics, Pennsylvania State University, University Park, PA
16802, USA  Dept. of Astronomy and Astrophysics, Pennsylvania State
University, University Park, PA 16802, USA  R. Cross  Dept. of Physics and
Astronomy, University of Rochester, Rochester, NY 14627, USA  P. Dave  School
of Physics and Center for Relativistic Astrophysics, Georgia Institute of
Technology, Atlanta, GA 30332, USA  C. De Clercq  Vrije Universiteit Brussel
(VUB), Dienst ELEM, B-1050 Brussels, Belgium  J. J. DeLaunay  Dept. of
Physics, Pennsylvania State University, University Park, PA 16802, USA  H.
Dembinski  Bartol Research Institute and Dept. of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA  K. Deoskar  Oskar Klein Centre
and Dept. of Physics, Stockholm University, SE-10691 Stockholm, Sweden  S. De
Ridder  Dept. of Physics and Astronomy, University of Gent, B-9000 Gent,
Belgium  P. Desiati  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA  K. D. de
Vries  Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium
G. de Wasseige  Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050
Brussels, Belgium  M. de With  Institut für Physik, Humboldt-Universität zu
Berlin, D-12489 Berlin, Germany  T. DeYoung  Dept. of Physics and Astronomy,
Michigan State University, East Lansing, MI 48824, USA  A. Diaz  Dept. of
Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA  J.
C. Díaz-Vélez  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin, Madison, WI 53706, USA  H. Dujmovic  Dept. of
Physics, Sungkyunkwan University, Suwon 16419, Korea  M. Dunkman  Dept. of
Physics, Pennsylvania State University, University Park, PA 16802, USA  E.
Dvorak  Physics Department, South Dakota School of Mines and Technology, Rapid
City, SD 57701, USA  B. Eberhardt  Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA
T. Ehrhardt  Institute of Physics, University of Mainz, Staudinger Weg 7,
D-55099 Mainz, Germany  P. Eller  Dept. of Physics, Pennsylvania State
University, University Park, PA 16802, USA  R. Engel  Karlsruhe Institute of
Technology, Institut für Kernphysik, D-76021 Karlsruhe, Germany  P. A. Evenson
Bartol Research Institute and Dept. of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA  S. Fahey  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin, Madison, WI
53706, USA  A. R. Fazely  Dept. of Physics, Southern University, Baton Rouge,
LA 70813, USA  J. Felde  Dept. of Physics, University of Maryland, College
Park, MD 20742, USA  K. Filimonov  Dept. of Physics, University of California,
Berkeley, CA 94720, USA  C. Finley  Oskar Klein Centre and Dept. of Physics,
Stockholm University, SE-10691 Stockholm, Sweden  A. Franckowiak  DESY,
D-15738 Zeuthen, Germany  E. Friedman  Dept. of Physics, University of
Maryland, College Park, MD 20742, USA  A. Fritz  Institute of Physics,
University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany  T. K. Gaisser
Bartol Research Institute and Dept. of Physics and Astronomy, University of
Delaware, Newark, DE 19716, USA  J. Gallagher  Dept. of Astronomy, University
of Wisconsin, Madison, WI 53706, USA  E. Ganster  III. Physikalisches
Institut, RWTH Aachen University, D-52056 Aachen, Germany  S. Garrappa  DESY,
D-15738 Zeuthen, Germany  L. Gerhardt  Lawrence Berkeley National Laboratory,
Berkeley, CA 94720, USA  K. Ghorbani  Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA
T. Glauch  Physik-department, Technische Universität München, D-85748
Garching, Germany  T. Glüsenkamp  Erlangen Centre for Astroparticle Physics,
Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany
A. Goldschmidt  Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
J. G. Gonzalez  Bartol Research Institute and Dept. of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA  D. Grant  Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  Z. Griffith
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, WI 53706, USA  S. Griswold  Dept. of Physics
and Astronomy, University of Rochester, Rochester, NY 14627, USA  M. Günder
III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
M. Gündüz  Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780
Bochum, Germany  C. Haack  III. Physikalisches Institut, RWTH Aachen
University, D-52056 Aachen, Germany  A. Hallgren  Dept. of Physics and
Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden  L. Halve
III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany
F. Halzen  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin, Madison, WI 53706, USA  K. Hanson  Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin, Madison, WI 53706, USA  A. Haungs  Karlsruhe Institute of
Technology, Institut für Kernphysik, D-76021 Karlsruhe, Germany  D. Hebecker
Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany
D. Heereman  Université Libre de Bruxelles, Science Faculty CP230, B-1050
Brussels, Belgium  P. Heix  III. Physikalisches Institut, RWTH Aachen
University, D-52056 Aachen, Germany  K. Helbing  Dept. of Physics, University
of Wuppertal, D-42119 Wuppertal, Germany  R. Hellauer  Dept. of Physics,
University of Maryland, College Park, MD 20742, USA  F. Henningsen  Physik-
department, Technische Universität München, D-85748 Garching, Germany  S.
Hickford  Dept. of Physics, University of Wuppertal, D-42119 Wuppertal,
Germany  J. Hignight  Dept. of Physics, University of Alberta, Edmonton,
Alberta, Canada T6G 2E1  G. C. Hill  Department of Physics, University of
Adelaide, Adelaide, 5005, Australia  K. D. Hoffman  Dept. of Physics,
University of Maryland, College Park, MD 20742, USA  R. Hoffmann  Dept. of
Physics, University of Wuppertal, D-42119 Wuppertal, Germany  T. Hoinka  Dept.
of Physics, TU Dortmund University, D-44221 Dortmund, Germany  B. Hokanson-
Fasig  Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, WI 53706, USA  K. Hoshina  Dept. of Physics
and Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin,
Madison, WI 53706, USA  F. Huang  Dept. of Physics, Pennsylvania State
University, University Park, PA 16802, USA  M. Huber  Physik-department,
Technische Universität München, D-85748 Garching, Germany  T. Huber  Karlsruhe
Institute of Technology, Institut für Kernphysik, D-76021 Karlsruhe, Germany
DESY, D-15738 Zeuthen, Germany  K. Hultqvist  Oskar Klein Centre and Dept. of
Physics, Stockholm University, SE-10691 Stockholm, Sweden  M. Hünnefeld  Dept.
of Physics, TU Dortmund University, D-44221 Dortmund, Germany  R. Hussain
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, WI 53706, USA  S. In  Dept. of Physics,
Sungkyunkwan University, Suwon 16419, Korea  N. Iovine  Université Libre de
Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium  A. Ishihara  Dept.
of Physics and Institute for Global Prominent Research, Chiba University,
Chiba 263-8522, Japan  G. S. Japaridze  CTSPS, Clark-Atlanta University,
Atlanta, GA 30314, USA  M. Jeong  Dept. of Physics, Sungkyunkwan University,
Suwon 16419, Korea  K. Jero  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA  B. J. P.
Jones  Dept. of Physics, University of Texas at Arlington, 502 Yates St.,
Science Hall Rm 108, Box 19059, Arlington, TX 76019, USA  F. Jonske  III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  R.
Joppe  III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen,
Germany  D. Kang  Karlsruhe Institute of Technology, Institut für Kernphysik,
D-76021 Karlsruhe, Germany  W. Kang  Dept. of Physics, Sungkyunkwan
University, Suwon 16419, Korea  A. Kappes  Institut für Kernphysik,
Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany  D.
Kappesser  Institute of Physics, University of Mainz, Staudinger Weg 7,
D-55099 Mainz, Germany  T. Karg  DESY, D-15738 Zeuthen, Germany  M. Karl
Physik-department, Technische Universität München, D-85748 Garching, Germany
A. Karle  Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, WI 53706, USA  U. Katz  Erlangen Centre for
Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg,
D-91058 Erlangen, Germany  M. Kauer  Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA
J. L. Kelley  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin, Madison, WI 53706, USA  A. Kheirandish  Dept.
of Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin, Madison, WI 53706, USA  J. Kim  Dept. of Physics, Sungkyunkwan
University, Suwon 16419, Korea  T. Kintscher  DESY, D-15738 Zeuthen, Germany
J. Kiryluk  Dept. of Physics and Astronomy, Stony Brook University, Stony
Brook, NY 11794-3800, USA  T. Kittler  Erlangen Centre for Astroparticle
Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen,
Germany  S. R. Klein  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  Dept. of Physics, University of California, Berkeley, CA 94720,
USA  R. Koirala  Bartol Research Institute and Dept. of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA  H. Kolanoski  Institut für
Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany  L. Köpke
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz,
Germany  C. Kopper  Dept. of Physics and Astronomy, Michigan State University,
East Lansing, MI 48824, USA  S. Kopper  Dept. of Physics and Astronomy,
University of Alabama, Tuscaloosa, AL 35487, USA  D. J. Koskinen  Niels Bohr
Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark  M. Kowalski
Institut für Physik, Humboldt-Universität zu Berlin, D-12489 Berlin, Germany
DESY, D-15738 Zeuthen, Germany  K. Krings  Physik-department, Technische
Universität München, D-85748 Garching, Germany  G. Krückl  Institute of
Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany  N.
Kulacz  Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G
2E1  N. Kurahashi  Dept. of Physics, Drexel University, 3141 Chestnut Street,
Philadelphia, PA 19104, USA  A. Kyriacou  Department of Physics, University of
Adelaide, Adelaide, 5005, Australia  M. Labare  Dept. of Physics and
Astronomy, University of Gent, B-9000 Gent, Belgium  J. L. Lanfranchi  Dept.
of Physics, Pennsylvania State University, University Park, PA 16802, USA  M.
J. Larson  Dept. of Physics, University of Maryland, College Park, MD 20742,
USA  F. Lauber  Dept. of Physics, University of Wuppertal, D-42119 Wuppertal,
Germany  J. P. Lazar  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA  K.
Leonard  Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, WI 53706, USA  A. Leszczynska  Karlsruhe
Institute of Technology, Institut für Kernphysik, D-76021 Karlsruhe, Germany
M. Leuermann  III. Physikalisches Institut, RWTH Aachen University, D-52056
Aachen, Germany  Q. R. Liu  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA  E.
Lohfink  Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099
Mainz, Germany  C. J. Lozano Mariscal  Institut für Kernphysik, Westfälische
Wilhelms-Universität Münster, D-48149 Münster, Germany  L. Lu  Dept. of
Physics and Institute for Global Prominent Research, Chiba University, Chiba
263-8522, Japan  F. Lucarelli  Département de physique nucléaire et
corpusculaire, Université de Genève, CH-1211 Genève, Switzerland  J. Lünemann
Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels, Belgium  W.
Luszczak  Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, WI 53706, USA  Y. Lyu  Lawrence Berkeley
National Laboratory, Berkeley, CA 94720, USA  W. Y. Ma  DESY, D-15738 Zeuthen,
Germany  J. Madsen  Dept. of Physics, University of Wisconsin, River Falls, WI
54022, USA  G. Maggi  Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050
Brussels, Belgium  K. B. M. Mahn  Dept. of Physics and Astronomy, Michigan
State University, East Lansing, MI 48824, USA  Y. Makino  Dept. of Physics and
Institute for Global Prominent Research, Chiba University, Chiba 263-8522,
Japan  P. Mallik  III. Physikalisches Institut, RWTH Aachen University,
D-52056 Aachen, Germany  K. Mallot  Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA
S. Mancina  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin, Madison, WI 53706, USA  I. C. Mariş
Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
R. Maruyama  Dept. of Physics, Yale University, New Haven, CT 06520, USA  K.
Mase  Dept. of Physics and Institute for Global Prominent Research, Chiba
University, Chiba 263-8522, Japan  R. Maunu  Dept. of Physics, University of
Maryland, College Park, MD 20742, USA  F. McNally  Department of Physics,
Mercer University, Macon, GA 31207-0001  K. Meagher  Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin,
Madison, WI 53706, USA  M. Medici  Niels Bohr Institute, University of
Copenhagen, DK-2100 Copenhagen, Denmark  A. Medina  Dept. of Physics and
Center for Cosmology and Astro-Particle Physics, Ohio State University,
Columbus, OH 43210, USA  M. Meier  Dept. of Physics, TU Dortmund University,
D-44221 Dortmund, Germany  S. Meighen-Berger  Physik-department, Technische
Universität München, D-85748 Garching, Germany  T. Menne  Dept. of Physics, TU
Dortmund University, D-44221 Dortmund, Germany  G. Merino  Dept. of Physics
and Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin,
Madison, WI 53706, USA  T. Meures  Université Libre de Bruxelles, Science
Faculty CP230, B-1050 Brussels, Belgium  J. Micallef  Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  G. Momenté
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz,
Germany  T. Montaruli  Département de physique nucléaire et corpusculaire,
Université de Genève, CH-1211 Genève, Switzerland  R. W. Moore  Dept. of
Physics, University of Alberta, Edmonton, Alberta, Canada T6G 2E1  R. Morse
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, WI 53706, USA  M. Moulai  Dept. of Physics,
Massachusetts Institute of Technology, Cambridge, MA 02139, USA  P. Muth  III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  R.
Nagai  Dept. of Physics and Institute for Global Prominent Research, Chiba
University, Chiba 263-8522, Japan  U. Naumann  Dept. of Physics, University of
Wuppertal, D-42119 Wuppertal, Germany  G. Neer  Dept. of Physics and
Astronomy, Michigan State University, East Lansing, MI 48824, USA  H.
Niederhausen  Physik-department, Technische Universität München, D-85748
Garching, Germany  S. C. Nowicki  Dept. of Physics and Astronomy, Michigan
State University, East Lansing, MI 48824, USA  D. R. Nygren  Lawrence Berkeley
National Laboratory, Berkeley, CA 94720, USA  A. Obertacke Pollmann  Dept. of
Physics, University of Wuppertal, D-42119 Wuppertal, Germany  M. Oehler
Karlsruhe Institute of Technology, Institut für Kernphysik, D-76021 Karlsruhe,
Germany  A. Olivas  Dept. of Physics, University of Maryland, College Park, MD
20742, USA  A. O’Murchadha  Université Libre de Bruxelles, Science Faculty
CP230, B-1050 Brussels, Belgium  E. O’Sullivan  Oskar Klein Centre and Dept.
of Physics, Stockholm University, SE-10691 Stockholm, Sweden  T. Palczewski
Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  Dept. of
Physics, University of California, Berkeley, CA 94720, USA  H. Pandya  Bartol
Research Institute and Dept. of Physics and Astronomy, University of Delaware,
Newark, DE 19716, USA  D. V. Pankova  Dept. of Physics, Pennsylvania State
University, University Park, PA 16802, USA  N. Park  Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin,
Madison, WI 53706, USA  P. Peiffer  Institute of Physics, University of Mainz,
Staudinger Weg 7, D-55099 Mainz, Germany  C. Pérez de los Heros  Dept. of
Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
S. Philippen  III. Physikalisches Institut, RWTH Aachen University, D-52056
Aachen, Germany  D. Pieloth  Dept. of Physics, TU Dortmund University, D-44221
Dortmund, Germany  E. Pinat  Université Libre de Bruxelles, Science Faculty
CP230, B-1050 Brussels, Belgium  A. Pizzuto  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin, Madison, WI
53706, USA  M. Plum  Department of Physics, Marquette University, Milwaukee,
WI, 53201, USA  A. Porcelli  Dept. of Physics and Astronomy, University of
Gent, B-9000 Gent, Belgium  P. B. Price  Dept. of Physics, University of
California, Berkeley, CA 94720, USA  G. T. Przybylski  Lawrence Berkeley
National Laboratory, Berkeley, CA 94720, USA  C. Raab  Université Libre de
Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium  A. Raissi  Dept.
of Physics and Astronomy, University of Canterbury, Private Bag 4800,
Christchurch, New Zealand  M. Rameez  Niels Bohr Institute, University of
Copenhagen, DK-2100 Copenhagen, Denmark  L. Rauch  DESY, D-15738 Zeuthen,
Germany  K. Rawlins  Dept. of Physics and Astronomy, University of Alaska
Anchorage, 3211 Providence Dr., Anchorage, AK 99508, USA  I. C. Rea  Physik-
department, Technische Universität München, D-85748 Garching, Germany  R.
Reimann  III. Physikalisches Institut, RWTH Aachen University, D-52056 Aachen,
Germany  B. Relethford  Dept. of Physics, Drexel University, 3141 Chestnut
Street, Philadelphia, PA 19104, USA  M. Renschler  Karlsruhe Institute of
Technology, Institut für Kernphysik, D-76021 Karlsruhe, Germany  G. Renzi
Université Libre de Bruxelles, Science Faculty CP230, B-1050 Brussels, Belgium
E. Resconi  Physik-department, Technische Universität München, D-85748
Garching, Germany  W. Rhode  Dept. of Physics, TU Dortmund University, D-44221
Dortmund, Germany  M. Richman  Dept. of Physics, Drexel University, 3141
Chestnut Street, Philadelphia, PA 19104, USA  S. Robertson  Lawrence Berkeley
National Laboratory, Berkeley, CA 94720, USA  M. Rongen  III. Physikalisches
Institut, RWTH Aachen University, D-52056 Aachen, Germany  C. Rott  Dept. of
Physics, Sungkyunkwan University, Suwon 16419, Korea  T. Ruhe  Dept. of
Physics, TU Dortmund University, D-44221 Dortmund, Germany  D. Ryckbosch
Dept. of Physics and Astronomy, University of Gent, B-9000 Gent, Belgium  D.
Rysewyk  Dept. of Physics and Astronomy, Michigan State University, East
Lansing, MI 48824, USA  I. Safa  Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA
S. E. Sanchez Herrera  Dept. of Physics and Astronomy, Michigan State
University, East Lansing, MI 48824, USA  A. Sandrock  Dept. of Physics, TU
Dortmund University, D-44221 Dortmund, Germany  J. Sandroos  Institute of
Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz, Germany  M.
Santander  Dept. of Physics and Astronomy, University of Alabama, Tuscaloosa,
AL 35487, USA  S. Sarkar  Dept. of Physics, University of Oxford, Parks Road,
Oxford OX1 3PU, UK  S. Sarkar  Dept. of Physics, University of Alberta,
Edmonton, Alberta, Canada T6G 2E1  K. Satalecka  DESY, D-15738 Zeuthen,
Germany  M. Schaufel  III. Physikalisches Institut, RWTH Aachen University,
D-52056 Aachen, Germany  H. Schieler  Karlsruhe Institute of Technology,
Institut für Kernphysik, D-76021 Karlsruhe, Germany  P. Schlunder  Dept. of
Physics, TU Dortmund University, D-44221 Dortmund, Germany  T. Schmidt  Dept.
of Physics, University of Maryland, College Park, MD 20742, USA  A. Schneider
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, WI 53706, USA  J. Schneider  Erlangen Centre
for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg,
D-91058 Erlangen, Germany  F. G. Schröder  Bartol Research Institute and Dept.
of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA
Karlsruhe Institute of Technology, Institut für Kernphysik, D-76021 Karlsruhe,
Germany  L. Schumacher  III. Physikalisches Institut, RWTH Aachen University,
D-52056 Aachen, Germany  S. Sclafani  Dept. of Physics, Drexel University,
3141 Chestnut Street, Philadelphia, PA 19104, USA  D. Seckel  Bartol Research
Institute and Dept. of Physics and Astronomy, University of Delaware, Newark,
DE 19716, USA  S. Seunarine  Dept. of Physics, University of Wisconsin, River
Falls, WI 54022, USA  S. Shefali  III. Physikalisches Institut, RWTH Aachen
University, D-52056 Aachen, Germany  M. Silva  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin, Madison, WI
53706, USA  R. Snihur  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA  J.
Soedingrekso  Dept. of Physics, TU Dortmund University, D-44221 Dortmund,
Germany  D. Soldin  Bartol Research Institute and Dept. of Physics and
Astronomy, University of Delaware, Newark, DE 19716, USA  M. Song  Dept. of
Physics, University of Maryland, College Park, MD 20742, USA  G. M. Spiczak
Dept. of Physics, University of Wisconsin, River Falls, WI 54022, USA  C.
Spiering  DESY, D-15738 Zeuthen, Germany  J. Stachurska  DESY, D-15738
Zeuthen, Germany  M. Stamatikos  Dept. of Physics and Center for Cosmology and
Astro-Particle Physics, Ohio State University, Columbus, OH 43210, USA  T.
Stanev  Bartol Research Institute and Dept. of Physics and Astronomy,
University of Delaware, Newark, DE 19716, USA  R. Stein  DESY, D-15738
Zeuthen, Germany  P. Steinmüller  Karlsruhe Institute of Technology, Institut
für Kernphysik, D-76021 Karlsruhe, Germany  J. Stettner  III. Physikalisches
Institut, RWTH Aachen University, D-52056 Aachen, Germany  A. Steuer
Institute of Physics, University of Mainz, Staudinger Weg 7, D-55099 Mainz,
Germany  T. Stezelberger  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  R. G. Stokstad  Lawrence Berkeley National Laboratory, Berkeley,
CA 94720, USA  A. Stößl  Dept. of Physics and Institute for Global Prominent
Research, Chiba University, Chiba 263-8522, Japan  N. L. Strotjohann  DESY,
D-15738 Zeuthen, Germany  T. Stürwald  III. Physikalisches Institut, RWTH
Aachen University, D-52056 Aachen, Germany  T. Stuttard  Niels Bohr Institute,
University of Copenhagen, DK-2100 Copenhagen, Denmark  G. W. Sullivan  Dept.
of Physics, University of Maryland, College Park, MD 20742, USA  I. Taboada
School of Physics and Center for Relativistic Astrophysics, Georgia Institute
of Technology, Atlanta, GA 30332, USA  F. Tenholt  Fakultät für Physik &
Astronomie, Ruhr-Universität Bochum, D-44780 Bochum, Germany  S. Ter-Antonyan
Dept. of Physics, Southern University, Baton Rouge, LA 70813, USA  A. Terliuk
DESY, D-15738 Zeuthen, Germany  S. Tilav  Bartol Research Institute and Dept.
of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA  L.
Tomankova  Fakultät für Physik & Astronomie, Ruhr-Universität Bochum, D-44780
Bochum, Germany  C. Tönnis  Dept. of Physics, Sungkyunkwan University, Suwon
16419, Korea  S. Toscano  Université Libre de Bruxelles, Science Faculty
CP230, B-1050 Brussels, Belgium  D. Tosi  Dept. of Physics and Wisconsin
IceCube Particle Astrophysics Center, University of Wisconsin, Madison, WI
53706, USA  A. Trettin  DESY, D-15738 Zeuthen, Germany  M. Tselengidou
Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität
Erlangen-Nürnberg, D-91058 Erlangen, Germany  C. F. Tung  School of Physics
and Center for Relativistic Astrophysics, Georgia Institute of Technology,
Atlanta, GA 30332, USA  A. Turcati  Physik-department, Technische Universität
München, D-85748 Garching, Germany  R. Turcotte  Karlsruhe Institute of
Technology, Institut für Kernphysik, D-76021 Karlsruhe, Germany  C. F. Turley
Dept. of Physics, Pennsylvania State University, University Park, PA 16802,
USA  B. Ty  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin, Madison, WI 53706, USA  E. Unger  Dept. of
Physics and Astronomy, Uppsala University, Box 516, S-75120 Uppsala, Sweden
M. A. Unland Elorrieta  Institut für Kernphysik, Westfälische Wilhelms-
Universität Münster, D-48149 Münster, Germany  M. Usner  DESY, D-15738
Zeuthen, Germany  J. Vandenbroucke  Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA
W. Van Driessche  Dept. of Physics and Astronomy, University of Gent, B-9000
Gent, Belgium  D. van Eijk  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA  N. van
Eijndhoven  Vrije Universiteit Brussel (VUB), Dienst ELEM, B-1050 Brussels,
Belgium  S. Vanheule  Dept. of Physics and Astronomy, University of Gent,
B-9000 Gent, Belgium  J. van Santen  DESY, D-15738 Zeuthen, Germany  M.
Vraeghe  Dept. of Physics and Astronomy, University of Gent, B-9000 Gent,
Belgium  C. Walck  Oskar Klein Centre and Dept. of Physics, Stockholm
University, SE-10691 Stockholm, Sweden  A. Wallace  Department of Physics,
University of Adelaide, Adelaide, 5005, Australia  M. Wallraff  III.
Physikalisches Institut, RWTH Aachen University, D-52056 Aachen, Germany  N.
Wandkowsky  Dept. of Physics and Wisconsin IceCube Particle Astrophysics
Center, University of Wisconsin, Madison, WI 53706, USA  T. B. Watson  Dept.
of Physics, University of Texas at Arlington, 502 Yates St., Science Hall Rm
108, Box 19059, Arlington, TX 76019, USA  C. Weaver  Dept. of Physics,
University of Alberta, Edmonton, Alberta, Canada T6G 2E1  A. Weindl  Karlsruhe
Institute of Technology, Institut für Kernphysik, D-76021 Karlsruhe, Germany
M. J. Weiss  Dept. of Physics, Pennsylvania State University, University Park,
PA 16802, USA  J. Weldert  Institute of Physics, University of Mainz,
Staudinger Weg 7, D-55099 Mainz, Germany  C. Wendt  Dept. of Physics and
Wisconsin IceCube Particle Astrophysics Center, University of Wisconsin,
Madison, WI 53706, USA  J. Werthebach  Dept. of Physics and Wisconsin IceCube
Particle Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA
B. J. Whelan  Department of Physics, University of Adelaide, Adelaide, 5005,
Australia  N. Whitehorn  Department of Physics and Astronomy, UCLA, Los
Angeles, CA 90095, USA  K. Wiebe  Institute of Physics, University of Mainz,
Staudinger Weg 7, D-55099 Mainz, Germany  C. H. Wiebusch  III. Physikalisches
Institut, RWTH Aachen University, D-52056 Aachen, Germany  L. Wille  Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin, Madison, WI 53706, USA  D. R. Williams  Dept. of Physics and
Astronomy, University of Alabama, Tuscaloosa, AL 35487, USA  L. Wills  Dept.
of Physics, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104,
USA  M. Wolf  Physik-department, Technische Universität München, D-85748
Garching, Germany  J. Wood  Dept. of Physics and Wisconsin IceCube Particle
Astrophysics Center, University of Wisconsin, Madison, WI 53706, USA  T. R.
Wood  Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G
2E1  K. Woschnagg  Dept. of Physics, University of California, Berkeley, CA
94720, USA  G. Wrede  Erlangen Centre for Astroparticle Physics, Friedrich-
Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany  D. L. Xu
Dept. of Physics and Wisconsin IceCube Particle Astrophysics Center,
University of Wisconsin, Madison, WI 53706, USA  X. W. Xu  Dept. of Physics,
Southern University, Baton Rouge, LA 70813, USA  Y. Xu  Dept. of Physics and
Astronomy, Stony Brook University, Stony Brook, NY 11794-3800, USA  J. P.
Yanez  Dept. of Physics, University of Alberta, Edmonton, Alberta, Canada T6G
2E1  G. Yodh  Dept. of Physics and Astronomy, University of California,
Irvine, CA 92697, USA  S. Yoshida  Dept. of Physics and Institute for Global
Prominent Research, Chiba University, Chiba 263-8522, Japan  T. Yuan  Dept. of
Physics and Wisconsin IceCube Particle Astrophysics Center, University of
Wisconsin, Madison, WI 53706, USA  M. Zöcklein  III. Physikalisches Institut,
RWTH Aachen University, D-52056 Aachen, Germany  C. Amole  Department of
Physics, Queen’s University, Kingston, K7L 3N6, Canada  M. Ardid  Departament
de Física Aplicada, IGIC - Universitat Politècnica de València, Gandia 46730
Spain  I. J. Arnquist  Pacific Northwest National Laboratory, Richland,
Washington 99354, USA  D. M. Asner  [  Pacific Northwest National Laboratory,
Richland, Washington 99354, USA  D. Baxter  Department of Physics and
Astronomy, Northwestern University, Evanston, Illinois 60208, USA  Enrico
Fermi Institute, KICP and Department of Physics, University of Chicago,
Chicago, Illinois 60637, USA  E. Behnke  Department of Physics, Indiana
University South Bend, South Bend, Indiana 46634, USA  M. Bressler  Department
of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA  B.
Broerman  Department of Physics, Queen’s University, Kingston, K7L 3N6, Canada
G. Cao  Department of Physics, Queen’s University, Kingston, K7L 3N6, Canada
C. J. Chen  Department of Physics and Astronomy, Northwestern University,
Evanston, Illinois 60208, USA  U. Chowdhury  [  Department of Physics, Queen’s
University, Kingston, K7L 3N6, Canada  K. Clark  Department of Physics,
Queen’s University, Kingston, K7L 3N6, Canada  J. I. Collar  Enrico Fermi
Institute, KICP and Department of Physics, University of Chicago, Chicago,
Illinois 60637, USA  P. S. Cooper  Fermi National Accelerator Laboratory,
Batavia, Illinois 60510, USA  M. Crisler  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  Pacific Northwest National
Laboratory, Richland, Washington 99354, USA  G. Crowder  Department of
Physics, Queen’s University, Kingston, K7L 3N6, Canada  N.A. Cruz-Venegas
Instituto de Física, Universidad Nacional Autónoma de México, México D. F.
01000, México  C. E. Dahl  Department of Physics and Astronomy, Northwestern
University, Evanston, Illinois 60208, USA  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  M. Das  Astroparticle Physics and
Cosmology Division, Saha Institute of Nuclear Physics, Kolkata, India  S.
Fallows  Department of Physics, University of Alberta, Edmonton, T6G 2E1,
Canada  J. Farine  Department of Physics, Laurentian University, Sudbury, P3E
2C6, Canada  I. Felis  Departament de Física Aplicada, IGIC - Universitat
Politècnica de València, Gandia 46730 Spain  R. Filgas  Institute of
Experimental and Applied Physics, Czech Technical University in Prague,
Prague, Cz-12800, Czech Republic  F. Girard  Department of Physics, Laurentian
University, Sudbury, P3E 2C6, Canada  Département de Physique, Université de
Montréal, Montréal, H3C 3J7, Canada  G. Giroux  Department of Physics, Queen’s
University, Kingston, K7L 3N6, Canada  J. Hall  SNOLAB, Lively, Ontario, P3Y
1N2, Canada  C. Hardy  Department of Physics, Queen’s University, Kingston,
K7L 3N6, Canada  O. Harris  Northeastern Illinois University, Chicago,
Illinois 60625, USA  E. W. Hoppe  Pacific Northwest National Laboratory,
Richland, Washington 99354, USA  M. Jin  Department of Physics and Astronomy,
Northwestern University, Evanston, Illinois 60208, USA  L. Klopfenstein
Department of Physics, Indiana University South Bend, South Bend, Indiana
46634, USA  C. B. Krauss  Department of Physics, University of Alberta,
Edmonton, T6G 2E1, Canada  M. Laurin  Département de Physique, Université de
Montréal, Montréal, H3C 3J7, Canada  I. Lawson  Department of Physics,
Laurentian University, Sudbury, P3E 2C6, Canada  SNOLAB, Lively, Ontario, P3Y
1N2, Canada  A. Leblanc  Department of Physics, Laurentian University,
Sudbury, P3E 2C6, Canada  I. Levine  Department of Physics, Indiana University
South Bend, South Bend, Indiana 46634, USA  W. H. Lippincott  Fermi National
Accelerator Laboratory, Batavia, Illinois 60510, USA  F. Mamedov  Institute of
Experimental and Applied Physics, Czech Technical University in Prague,
Prague, Cz-12800, Czech Republic  D. Maurya  Bio-Inspired Materials and
Devices Laboratory (BMDL), Center for Energy Harvesting Material and Systems
(CEHMS), Virginia Tech, Blacksburg, Virginia 24061, USA  P. Mitra  Department
of Physics, University of Alberta, Edmonton, T6G 2E1, Canada  C. Moore
Department of Physics, Queen’s University, Kingston, K7L 3N6, Canada  T. Nania
Department of Physics, Indiana University South Bend, South Bend, Indiana
46634, USA  R. Neilson  Department of Physics, Drexel University,
Philadelphia, Pennsylvania 19104, USA  A. J. Noble  Department of Physics,
Queen’s University, Kingston, K7L 3N6, Canada  P. Oedekerk  Department of
Physics, Indiana University South Bend, South Bend, Indiana 46634, USA  A.
Ortega  Enrico Fermi Institute, KICP and Department of Physics, University of
Chicago, Chicago, Illinois 60637, USA  M.-C. Piro  Department of Physics,
University of Alberta, Edmonton, T6G 2E1, Canada  A. Plante  Département de
Physique, Université de Montréal, Montréal, H3C 3J7, Canada  R. Podviyanuk
Department of Physics, Laurentian University, Sudbury, P3E 2C6, Canada  S.
Priya  Bio-Inspired Materials and Devices Laboratory (BMDL), Center for Energy
Harvesting Material and Systems (CEHMS), Virginia Tech, Blacksburg, Virginia
24061, USA  A. E. Robinson  Département de Physique, Université de Montréal,
Montréal, H3C 3J7, Canada  S. Sahoo  Astroparticle Physics and Cosmology
Division, Saha Institute of Nuclear Physics, Kolkata, India  O. Scallon
Department of Physics, Laurentian University, Sudbury, P3E 2C6, Canada  S.
Seth  Astroparticle Physics and Cosmology Division, Saha Institute of Nuclear
Physics, Kolkata, India  A. Sonnenschein  Fermi National Accelerator
Laboratory, Batavia, Illinois 60510, USA  N. Starinski  Département de
Physique, Université de Montréal, Montréal, H3C 3J7, Canada  I. Štekl
Institute of Experimental and Applied Physics, Czech Technical University in
Prague, Prague, Cz-12800, Czech Republic  T. Sullivan  Department of Physics,
Queen’s University, Kingston, K7L 3N6, Canada  F. Tardif  Département de
Physique, Université de Montréal, Montréal, H3C 3J7, Canada  E. Vázquez-
Jáuregui  Instituto de Física, Universidad Nacional Autónoma de México, México
D. F. 01000, México  Department of Physics, Laurentian University, Sudbury,
P3E 2C6, Canada  N. Walkowski  Department of Physics, Indiana University South
Bend, South Bend, Indiana 46634, USA  U. Wichoski  Department of Physics,
Laurentian University, Sudbury, P3E 2C6, Canada  Y. Yan  Bio-Inspired
Materials and Devices Laboratory (BMDL), Center for Energy Harvesting Material
and Systems (CEHMS), Virginia Tech, Blacksburg, Virginia 24061, USA  V. Zacek
Département de Physique, Université de Montréal, Montréal, H3C 3J7, Canada  J.
Zhang  [  Department of Physics and Astronomy, Northwestern University,
Evanston, Illinois 60208, USA

###### Abstract

Adopting the Standard Halo Model (SHM) of an isotropic Maxwellian velocity
distribution for dark matter (DM) particles in the Galaxy, the most stringent
current constraints on their spin-dependent scattering cross-section with
nucleons come from the IceCube neutrino observatory and the PICO-60 C3F8
superheated bubble chamber experiments. The former is sensitive to high energy
neutrinos from the self-annihilation of DM particles captured in the Sun,
while the latter looks for nuclear recoil events from DM scattering off
nucleons. Although slower DM particles are more likely to be captured by the
Sun, the faster ones are more likely to be detected by PICO. Recent N-body
simulations suggest significant deviations from the SHM for the smooth halo
component of the DM, while observations hint at a dominant fraction of the
local DM being in substructures. We use the method of Ferrer et al. (2015) to
exploit the complementarity between the two approaches and derive conservative
constraints on DM-nucleon scattering. Our results constrain
$\sigma_{\mathrm{SD}}\lesssim 3\times 10^{-39}\mathrm{cm}^{2}$ ($6\times
10^{-38}\mathrm{cm}^{2}$) at $\gtrsim 90\%$ C.L. for a DM particle of mass 1
TeV annihilating into $\tau^{+}\tau^{-}$ ($b\bar{b}$) with a local density of
$\rho_{\mathrm{DM}}=0.3~{}\mathrm{GeV/cm}^{3}$. The constraints scale
inversely with $\rho_{\mathrm{DM}}$ and are independent of the DM velocity
distribution.

††thanks: also at Università di Padova, I-35131 Padova, Italy††thanks: also at
National Research Nuclear University, Moscow
Engineering Physics Institute (MEPhI), Moscow 115409, Russia††thanks:
Earthquake Research Institute, University of Tokyo, Bunkyo, Tokyo 113-0032,
Japan

Email<EMAIL_ADDRESS>
now at ]Brookhaven National Laboratory

now at ]Canadian Nuclear Laboratories

now at ]Argonne National Laboratory

Email<EMAIL_ADDRESS>
##  1 Introduction

Based on inferences from observations of gravitational effects, it has long
been believed that a significant fraction of the Universe is made up of dark
matter (DM) (see van den Bergh et al. (1999)). However, very little is known
about its properties and interactions. A weakly interacting massive particle
(WIMP), whose relic abundance from a state of thermal equilibrium can make up
DM has been the subject of considerable theoretical attention and experimental
focus (see Bertone et al. (2004) for a comprehensive review).

Various complementary approaches have been pursued to detect the WIMPs that
may constitute the DM halo of our Galaxy. Terrestrial direct detection (DD)
experiments search for nuclear recoil events from the elastic scattering of
WIMPs with the target nuclei of their detectors. Neutrino and gamma ray
telescopes search for directional excesses over astrophysical backgrounds that
may indicate the pair-annihilation of WIMPs, while collider searches look for
the signatures of WIMPs being created in high-energy interactions of Standard
Model particles.

Although the different search strategies have attained the sensitivity to
probe the physically-motivated WIMP parameter space over the past few decades,
they have failed to detect any signal. In the absence of a convincing
detection, constraints have been derived on the interaction cross-sections of
these hypothetical particles with Standard Model particles. Such an inference
requires knowledge both of the density of DM $\rho_{\mathrm{DM}}$ and of its
velocity distribution function (VDF) $f(\vec{v})$.

In the Standard Halo Model (SHM) (Drukier et al., 1986), the DM of the halo is
a collisionless gas in hydrostatic equilibrium with the stars, retaining the
velocity distribution obtained during the formation of our Galaxy. An
isotropic Maxwell-Boltzman velocity distribution in the Galactic rest frame is
usually adopted.

Meanwhile, N-body simulations have hinted that a Maxwell-Boltzmann
distribution does not accurately represent even the smooth component of the
halo (Kuhlen et al., 2009; Lisanti et al., 2010; Mao et al., 2012). Recent
observations point to the possibility that a dominant fraction of the DM in
the Solar neighbourhood (Necib et al., 2018) may not yet have achieved
dynamical equilibrium, perhaps due to the infalling tidal debris of a
disrupted massive satellite galaxy of the Milky Way. New data also suggest
that a substantial fraction of our stellar halo may lie in a strongly radially
anisotropic population, the ‘Gaia sausage’ (Evans et al., 2019).

If so, constraints on WIMP-nucleon interactions derived assuming the SHM (from
both direct and indirect searches) may be weakened. Direct detection
experiments are preferentially sensitive to nuclear recoils from high velocity
DM particles, while capture in the Sun is more likely for the slower fraction
of the DM population. In this work we use the method of Ferrer et al. (2015),
which is independent of the velocity distribution of the halo model to exploit
this complementarity and derive _conservative_ , upper limits on the spin-
dependent DM-nucleon scattering cross-section by combining the results from
Aartsen et al. (2017) and Amole et al. (2017). Here the DM velocity
distribution is taken to be a completely general superposition of individual
’streams’ (delta functions in velocity), similarly to the halo-independent
analysis of direct detection experiments (Frandsen et al., 2012). Although
constraints from individual searches will now be dependent on the stream
velocity, by exploiting the complementarity of the IceCube and PICO searches,
constraints independent of the stream velocity can be obtained. This method
also improves on previous assessments of halo model uncertainties on indirect
DM detection (Choi et al., 2014), by allowing the velocity distribution to be
anisotropic. The resulting constraints are a factor of 2 to 4 worse than the
PICO SHM constraints at low DM masses and up to an order of magnitude worse at
high DM masses, depending upon the annihilation channel, but are independent
of the halo model.

##  2 Detectors and data samples

###  2.1 IceCube 3 year Solar WIMP search

IceCube is a cubic-kilometer neutrino detector installed in the ice at the
geographic South Pole between depths of 1450 and 2450 m. It relies on
photomultiplier tubes housed in pressure vessels known as digital optical
modules (DOM) for the optical detection of Cherenkov photons emitted by
charged particles traversing the ice. The principal IceCube array is sensitive
to neutrinos down to $\sim$100 GeV in energy (Achterberg et al.,, 2006; Abbasi
et al.,, 2009; Aartsen et al.,, 2017). The central region of the detector is
an infill array known as DeepCore optimized in geometry and DOM density for
the detection of neutrinos at lower energies, down to $\sim$10 GeV (Abbasi et
al.,, 2012).

Over a detector uptime of 532 days corresponding to the austral winters
between May 2011 and May 2014, two non-overlapping samples of upgoing track-
like events, dominated by muons from charged current interactions of
atmospheric $\nu_{\mu}$ and $\bar{\nu}_{\mu}$, were isolated (Aartsen et al.,
2017). During austral summers, the Sun being above the horizon, is a source of
downgoing neutrinos and the signal is overwhelmed by a background of muons
originating in cosmic ray interactions in the upper atmosphere.

The first sample, consisting of events that traverse the principal IceCube
array, is sensitive to neutrinos in the 100 GeV – 1 TeV range in energy, while
the second sample is dominated by events starting in and around the DeepCore
infill array, and is sensitive down to neutrinos of $\sim$10 GeV in energy.

An unbinned maximum likelihood ratio analysis of the directions and energies
of the events that make up the two samples was unable to identify a
statistically significant excess of neutrinos from the direction of the Sun.
This enabled 90% C.L. upper limits on the DM annihilation induced neutrino
flux to be computed according to the prescription of Feldman & Cousins (1998)
as presented in Aartsen et al. (2017).

This can be interpreted as both a constraint on the annihilation rate of DM
particles in the Sun, as well as on the scattering cross-section of DM with
nucleons, although this has been usually done under the SHM assumption. In
particle physics models where the DM couples to the spin of the nucleus and
annihilates preferentially into SM particles that decay to produce a large
number of high energy neutrinos (such as $\tau^{+}\tau^{-}$), the resultant
constraints are the most stringent for DM mass above $\sim 80$ GeV (Particle
Data Group, 2018).

###  2.2 PICO

The PICO collaboration searches for WIMPs using superheated bubble chambers
operated at temperature and pressure conditions which lead to being virtually
insensitive to gamma and beta radiation (Amole et al., 2019). Events in PICO
consist of the transition from liquid to gas phase, signalled by the
nucleation of a bubble in the target material. This phase change is imaged by
the cameras surrounding the active area, which trigger upon detecting the
formation of a pocket of gas. Additional background suppression is achieved
through the measurement of the acoustic signal generated by the event,
allowing alpha particles to be discriminated from nuclear recoils. Details of
the apparatus are available in Amole et al. (2015). The data used in this
study were obtained from the PICO-60 detector, consisting of a 52.2$\pm$0.5 kg
C3 F8 target, operated roughly two kilometres underground at SNOLAB in
Sudbury, Ontario, Canada. The results used here come from an efficiency-
corrected exposure of 1167 kg-days taken between November 2016 and January
2017 (Amole et al., 2017).

The response of the detector to WIMPs is dependent on the thermodynamic
conditions, and is calibrated using in situ nuclear and electronic recoil
sources. Additionally, the Tandem Van de Graaff facility at the University of
Montreal was used to determine the detector response, using well-defined
resonances of the 51V(p,n)51Cr reaction to produce mono energetic neutrons at
61 and 97 keV. The combination of these measurements is simulated using
differential cross-sections for elastic scattering on fluorine to produce the
detector response.

##  3 DM velocity distributions and impact on constraints: The method

Following the method of Ferrer et al. (2015), the velocity distribution of the
DM (WIMP) population in the Solar system, $f(\vec{v})$ can be expressed as the
superposition of streams with fixed velocity $\vec{v}_{0}$ with respect to the
Solar frame.

$f(\vec{v})=\int_{|\vec{v}_{0}|\leq
v_{\mathrm{max}}}d^{3}v_{0}\delta^{(3)}(\vec{v}-\vec{v}_{0})f(\vec{v}_{0})$
(1)

where $v_{\mathrm{max}}$ is the maximum velocity at which WIMPs can be found,
typically the escape velocity of the Galaxy. For every stream with velocity
$\vec{v}_{0}$ with respect to the Sun, upper limits can be derived from the
null results of IceCube by requiring that the capture rate for the stream
$C_{\vec{v}_{0}}$ be less than or equal to $C_{\mathrm{max}}$, the upper limit
on the capture rate from the results of the experiment. For a direct detection
experiment, which sees the same stream with velocity
$\vec{v}_{0}-\vec{v}_{\mathrm{E}}(t)$ with respect to the Earth, similar
constraints can be derived for each stream velocity by requiring that the
event rate for the stream $R_{\vec{v}_{0}}$ be less than or equal to
$R_{\mathrm{max}}$, the upper limit on the event rate from the results of the
experiment. $C_{\vec{v}_{0}}$ and $R_{\vec{v}_{0}}$ are computed by evaluating
the integrals of equations 2 and 3 of Ferrer et al. (2015). Since the PICO
exposure period was too short for the Earth’s velocity
$\vec{v}_{\mathrm{E}}(t)$ to average out to zero, velocities are
conservatively shifted by 30.29 km s-1 (the velocity of the Earth around the
Sun at perihelion (Tollerud  et al., 2017)) when computing $R_{\vec{v}_{0}}$.
For the capture rates in the Sun, the integrals were evaluated using the
density profile and nuclear abundances in the Sun for protons and nitrogen
nuclei (the second most abundant species with nuclear spin) in the standard
Solar model (Bahcall et al., 1988) as implemented in sunpy (SunPy Comm, 2015).
Nuclear form factors as implemented in dmdd (Gluscevic et al., 2015) for spin-
dependent scattering, corresponding to the $\Sigma^{\prime}_{1M}$ (Axial
transverse electric response) and $\Sigma^{\prime\prime}_{1M}$ (Axial
longitudinal response), table 1 of Fitzpatrick et al. (2013) were employed for
the event rate calculations in PICO.

Figure 1 demonstrates the evolution of the constraints on the spin-dependent
DM-proton scattering cross-section from both IceCube and PICO as $|v_{0}|$ is
varied. The individual constraints on the cross section are computed from the
constraints on the capture rate in the Sun already derived in Aartsen et al.
(2017) as well as the constraint on the event rate within PICO presented in
Amole et al. (2017). For a WIMP of mass $M$ scattering off a nucleus of mass
$m$, the maximum stream velocity at which capture is allowed is given by
(Ferrer et al., 2015):

$v_{\mathrm{max}}=2v_{\mathrm{esc}}\sqrt{\frac{Mm}{|M-m|}}$ (2)

where $v_{\mathrm{esc}}$ is the escape velocity. Consequently, above certain
threshold values of the stream velocity, capture by scattering off protons is
kinematically impossible and only nitrogen nuclei contribute to the capture
rate.

Figure 1: Constraints at $\gtrsim 90\%$ C.L. on the spin-dependent DM-proton
scattering cross-section from both IceCube and PICO for different values of
$|v_{0}|$, for 40 (700) GeV WIMPs annihilating to $b\bar{b}$ are shown on the
left (right). For 40 GeV WIMPs, as the efficiency of PICO falls off below
stream velocities of $c$ (the speed of light) $\times 10^{-3}$, Solar capture
by scattering off hydrogen nuclei provides a complementary bound, while for
700 GeV WIMPs, a bound is provided only by the much less abundant nitrogen
nuclei in the Sun.

Subsequently, the largest value of the scattering cross-section allowed by
both IceCube and PICO, $\sigma^{\mathrm{HI}}$, can be determined at the
velocity of least constraint, $v_{\mathrm{LC}}$, where
$\sigma^{\mathrm{PICO}}_{\mathrm{max}}(v_{\mathrm{LC}})=\sigma^{\mathrm{IceCube}}_{\mathrm{max}}(v_{\mathrm{LC}})$.
This procedure is illustrated in Figure 1 for two specific models, 40 GeV and
700 GeV WIMPs annihilating to $b\bar{b}$.

##  4 Results and Conclusions

The resultant DM velocity independent constraints are illustrated in Figure 2
and presented in Table 1. For the “hard” channels ( $W^{+}W^{-}$and
$\tau^{+}\tau^{-}$), which produce a relatively large number of neutrinos at
energies just below the DM mass, the DM-velocity-independent constraints are
in general worse only by a factor of 2 to 4 compared to the PICO SHM
constraints. However, at a DM Mass of $\sim$250 GeV ($\sim$700 GeV for
$b\bar{b}$), the constraints are significantly worse because the DM particle
velocities just below the PICO threshold are still too high to be captured by
scattering off protons in the Sun (see Figure 1). At immediately higher
masses, the constraints improve because the IceCube sensitivity improves with
the DM mass in this range. The constraints are in agreement with the findings
by Ibarra et al. (2017). The IceCube constraints were recomputed with Monte-
Carlo data sets under varying assumptions of all systematic uncertainties as
described in Aartsen et al. (2017). The dominant uncertainties were found to
originate in the photodetection efficiency of the photomultiplier tubes that
make up the DOMs, as well as the optical properties of the ice. Since these
constraints correspond to the same annihilation rates of DM particles in the
Sun reported in Aartsen et al. (2017), capture-annihilation equilibrium
continues to be a valid assumption. The dominant uncertainties in the detector
acceptance of PICO originate in the uncertainties of the neutron beam used in
the calibration process. These are propagated to the final level and shown as
shaded regions. Conservatively, the pessimistic efficiencies of PICO have been
used to derive the constraints. While these constraints are robust with
respect to any uncertainties in the velocity distribution of DM particles,
they are still susceptible to uncertainties and/or fluctuations in the local
density of DM, and are presented for the benchmark local density of
$\rho_{\mathrm{DM}}=0.3$ GeV cm-3, and scale inversely with this quantity.

Figure 2: DM velocity distribution independent constraints on the SD DM-nucleon interaction cross-section $\gtrsim 90\%$ C.L. Systematic uncertainties are presented as shaded regions. The traditional SHM upper limits at $90\%$ C.L. from IceCube and PICO are shown as dashed and dash dotted lines. The kinks in the constraints at $\sim 250$ GeV (for $W^{+}W^{-}$and $\tau^{+}\tau^{-}$) and $\sim 700$ GeV (for $b\bar{b}$) are explained in Section 4. Table 1: Constraints on the SD DM-nucleon cross-section. SHM constraints from PICO and IceCube, as well as the DM velocity distribution independent constraint are presented at $\gtrsim 90\%$ C.L. The velocity of DM particles at which the cross-section is least constrained ($V_{\mathrm{LC}}$) is also presented for each point. The constraints are conservative with respect to systematic uncertainties. $m_{\chi}$ | annih. | $v_{\mathrm{LC}}$ | PICO | IceCube | Combined | Syst unc.
---|---|---|---|---|---|---
(GeV) | channel | (km s${}^{-1})$ |  $\sigma_{\mathrm{SD}}^{\mathrm{SHM}}$ (pb) |  $\sigma_{\mathrm{SD}}^{\mathrm{SHM}}$ (pb) |  $\sigma_{\mathrm{SD}}^{\mathrm{HI}}$(pb) | (%)
20 | $\tau^{+}\tau^{-}$ | 229.7 | 3.78$\times$10-5 | 4.85$\times$10-4 | 2.29$\times$10-4 | 23.4
35 | $b\bar{b}$ | 131.5 | 3.43$\times$10-5 | 9.25$\times$10-4 | 1.26$\times$10-3 | 18.3
35 | $\tau^{+}\tau^{-}$ | 236.8 |  | 1.35$\times$10-4 | 9.74$\times$10-5 | 10.2
50 | $b\bar{b}$ | 137.3 | 3.72$\times$10-5 | 6.39$\times$10-3 | 8.24$\times$10-4 | 8.0
50 | $\tau^{+}\tau^{-}$ | 222.5 |  | 7.90$\times$10-5 | 1.08$\times$10-4 | 9.5
100 | $b\bar{b}$ | 141.5 |  | 3.29$\times$10-4 | 7.23$\times$10-4 | 9.7
100 | $W^{+}W^{-}$ | 167.8 | 5.36$\times$10-5 | 9.52$\times$10-5 | 3.56$\times$10-4 | 11.4
100 | $\tau^{+}\tau^{-}$ | 170.3 |  | 2.91$\times$10-5 | 3.34$\times$10-4 | 14.4
250 | $b\bar{b}$ | 106.2 |  | 2.80$\times$10-3 | 5.15$\times$10-3 | 26.7
250 | $W^{+}W^{-}$ | 108.3 | 1.09$\times$10-4 | 5.30$\times$10-5 | 4.85$\times$10-3 | 31.8
250 | $\tau^{+}\tau^{-}$ | 108.4 |  | 2.82$\times$10-5 | 3.12$\times$10-3 | 14.0
500 | $b\bar{b}$ | 76.4 |  | 3.06$\times$10-3 | 4.99$\times$10-2 | 54.1
500 | $W^{+}W^{-}$ | 122.7 | 2.06$\times$10-4 | 3.76$\times$10-5 | 3.04$\times$10-3 | 10.2
500 | $\tau^{+}\tau^{-}$ | 142.5 |  | 1.46$\times$10-5 | 1.58$\times$10-3 | 13.1
1000 | $b\bar{b}$ | 72.07 |  | 2.59$\times$10-3 | 5.72$\times$10-2 | 9.1
1000 | $W^{+}W^{-}$ | 126.0 | 3.90$\times$10-4 | 6.80$\times$10-5 | 4.81$\times$10-3 | 8.6
1000 | $\tau^{+}\tau^{-}$ | 145.3 |  | 2.07$\times$10-5 | 2.57$\times$10-3 | 10.8
3000 | $b\bar{b}$ | 100.3 |  | 6.76$\times$10-3 | 1.61$\times$10-1 | 19.8
3000 | $W^{+}W^{-}$ | 76.09 | 1.14$\times$10-3 | 5.42$\times$10-4 | 1.59$\times$10-1 | 21.4
3000 | $\tau^{+}\tau^{-}$ | 49.52 |  | 1.21$\times$10-4 | 1.48$\times$10-1 | 22.4
5000 | $b\bar{b}$ | 89.23 |  | 1.58$\times$10-2 | 3.11 | 25.4
5000 | $W^{+}W^{-}$ | 46.41 | 1.89$\times$10-3 | 1.37$\times$10-3 | 3.16 | 16.5
5000 | $\tau^{+}\tau^{-}$ | 46.41 |  | 3.28$\times$10-4 | 2.66 | 19.1

Acknowledgements: We would like to acknowledge valuable discussions with John
Ellis and Alejandro Ibarra about the analysis. IceCube Collaboration: USA –
U.S. National Science Foundation-Office of Polar Programs, U.S. National
Science Foundation-Physics Division, Wisconsin Alumni Research Foundation,
Center for High Throughput Computing (CHTC) at the University of Wisconsin-
Madison, Open Science Grid (OSG), Extreme Science and Engineering Discovery
Environment (XSEDE), U.S. Department of Energy-National Energy Research
Scientific Computing Center, Particle astrophysics research computing center
at the University of Maryland, Institute for Cyber-Enabled Research at
Michigan State University, and Astroparticle physics computational facility at
Marquette University; Belgium – Funds for Scientific Research (FRS-FNRS and
FWO), FWO Odysseus and Big Science programmes, and Belgian Federal Science
Policy Office (Belspo); Germany – Bundesministerium für Bildung und Forschung
(BMBF), Deutsche Forschungsgemeinschaft (DFG), Helmholtz Alliance for
Astroparticle Physics (HAP), Initiative and Networking Fund of the Helmholtz
Association, Deutsches Elektronen Synchrotron (DESY), and High Performance
Computing cluster of the RWTH Aachen; Sweden – Swedish Research Council,
Swedish Polar Research Secretariat, Swedish National Infrastructure for
Computing (SNIC), and Knut and Alice Wallenberg Foundation; Australia –
Australian Research Council; Canada – Natural Sciences and Engineering
Research Council of Canada, Calcul Québec, Compute Ontario, Canada Foundation
for Innovation, WestGrid, and Compute Canada; Denmark – Villum Fonden, Danish
National Research Foundation (DNRF), Carlsberg Foundation; New Zealand –
Marsden Fund; Japan – Japan Society for Promotion of Science (JSPS) and
Institute for Global Prominent Research (IGPR) of Chiba University; Korea –
National Research Foundation of Korea (NRF); Switzerland – Swiss National
Science Foundation (SNSF). United Kingdom – Department of Physics, University
of Oxford. PICO Collaboration: The PICO collaboration wishes to thank SNOLAB
and its staff for support through underground space, logistical and technical
services. SNOLAB operations are supported by the Canada Foundation for
Innovation and the Province of Ontario Ministry of Research and Innovation,
with underground access provided by Vale at the Creighton mine site. We wish
to acknowledge the support of the Natural Sciences and Engineering Research
Council of Canada (NSERC) and the Canada Foundation for Innovation (CFI) for
funding. We acknowledge the support from the National Science Foundation (NSF)
(Grant 0919526, 1506337, 1242637 and 1205987). We acknowledge that this work
is supported by the U.S. Department of Energy (DOE) Office of Science, Office
of High Energy Physics (under award DE-SC-0012161), by the DOE Office of
Science Graduate Student Research (SCGSR) award, by DGAPA-UNAM (PAPIIT No.
IA100118) and Consejo Nacional de Ciencia y Tecnoloǵıa (CONACyT, México,
Grant No. 252167 and A1-S-8960), by the Department of Atomic Energy (DAE),
Government of India, under the Centre for AstroParticle Physics II project
(CAPP-II) at the Saha Institute of Nuclear Physics (SINP), European Regional
Development Fund- Project “Engineering applications of microworld physics”
(No. CZ.02.1.01/0.0/0.0/16 019/0000766), and the Spanish Ministerio de
Ciencia, Innovación y Universidades (Red Consolider MultiDark,
FPA2017–90566–REDC). This work is partially supported by the Kavli Institute
for Cosmological Physics at the University of Chicago through NSF grant
1125897 and 1806722, and an endowment from the Kavli Foundation and its
founder Fred Kavli. We also wish to acknowledge the support from Fermi
National Accelerator Laboratory under Contract No.DE-AC02-07CH11359, and from
Pacific Northwest National Laboratory, which is operated by Battelle for the
U.S. Department of Energy under Contract No. DE- AC05-76RL01830. We also thank
Compute Canada (www.computecanada.ca) and the Centre for Advanced Computing,
ACENET, Calcul Quebeć, Compute Ontario and WestGrid for computational support.

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