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\begin{document}

\title{Determination of Solar Wind Angular Momentum and Alfv\textbackslash{}'en
Radius from Parker Solar Probe Observations}



\author[1]{Ying Liu}%
\author[2]{Chong Chen}%
\author[3]{Michael Stevens}%
\author[4]{Mingzhe Liu}%
\affil[1]{NSSC National Space Science Center}%
\affil[2]{NSSC National Space Science Center, CAS}%
\affil[3]{Smithsonian Astrophysical Observatory}%
\affil[4]{LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris}%


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  \date{May 21, 2024}


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\begin{abstract}
As fundamental parameters of the Sun, the Alfv\textbackslash{}'en radius
and angular momentum loss determine how the solar wind changes from
sub-Alfv\textbackslash{}'enic to super-Alfv\textbackslash{}'enic and how
the Sun spins down. We present an approach to determining the solar wind
angular momentum flux based on observations from Parker Solar Probe
(PSP). A flux of about \$0.15\textbackslash{}times10\^{}\{30\}\$ dyn cm
sr\$\^{}\{-1\}\$ near the ecliptic plane and 0.7:1 partition of that
flux between the particles and magnetic field are obtained by averaging
data from the first four encounters within 0.3 au from the Sun. The
angular momentum flux and its particle component decrease with the solar
wind speed, while the flux in the field is remarkably constant. A speed
dependence in the Alfv\textbackslash{}'en radius is also observed, which
suggests a ``rugged'' Alfv\textbackslash{}'en surface around the Sun.
Substantial diving below the Alfv\textbackslash{}'en surface seems
plausible only for relatively slow solar wind given the orbital design
of PSP. Uncertainties are evaluated based on the acceleration profiles
of the same solar wind streams observed at PSP and a radially aligned
spacecraft near 1 au. We illustrate that the ``angular momentum
paradox'' raised by R\textbackslash{}'eville et al. can be removed by
taking into account the contribution of the alpha particles. The large
proton transverse velocity observed by PSP is perhaps inherent in the
solar wind acceleration process, where an opposite transverse velocity
is produced for the alphas with the angular momentum conserved.
Preliminary analysis of some recovered alpha parameters tends to agree
with the results.%
\end{abstract}%



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