text:
\section{Introduction}\label{sec:intro}

Accretion-powered pulsars are X-ray binaries consisting of a highly
magnetized neutron star ($\sim 10^{12}$ G) accreting from an ordinary donor star
\citep{Bildsten_1997}. The long-term evolution of these systems is
largely set by the mass of the donor \citep[see, e.g.,][]{Tauris_vdH_2006}.
Among high-mass X-ray binaries (HMXBs; donor mass $\gtrsim 8 M_\odot$),
we may identify two distinct types of systems: persistent or quasi-persistent X-ray sources accreting from
an OB-supergiant donor in a circular or low-eccentricity binary, and
episodic X-ray transients accreting from an Oe/Be-type main sequence
donor in an eccentric binary.  In the latter group are the so-called Be/X-ray
binaries. Two types of outbursts \citep{Stella+86} are generally
observed from these systems \citep[e.g.,][]{Paul2011, Laplace+17}. Type I or normal outbursts, which generally begin
around the time of the neutron star's periastron passage, and Type II
or giant outbursts, which are rarer, longer, reach higher luminosities
$L\geq 10^{37}$ erg s$^{-1}$, and can start at any orbital phase.
Until recently the giant outbursts were often considered to be the result
of an enlarged decretion disk around the Be star, but recent work \citep{Monageng+17}
shows no correlation between the Be disk radii and the occurrence of
giant outbursts. However, the normal outbursts were found to
occur generally when the Be disc truncation radius was close to or larger than the
Roche critical lobe radius at periastron passage.  In this paper, we describe observations of a new Be/X-ray
transient pulsar that is particularly luminous,
making it a superb target for detailed study.

The X-ray source Swift J0243.6+6124 was initially identified as a new
transient by \textit{Swift} BAT (15--50~keV) on 2017 October 3
\citep{Cenko_2017}, with 0.2--10~keV pulsations with a 9.86 s period also
detected with \textit{Swift} XRT \citep{Kennea_2017}. The onset of the
X-ray outburst was actually detected in the 2--10~keV band a few days
earlier by the \textit{Monitor of All-Sky X-ray Image (MAXI)} sky monitor on September 29, but was
initially misidentified as the nearby source LSI +61$^\circ$ 303
\citep{Sugita_2017a, Sugita_2017b} only 24$^{\prime}$ away. The X-ray pulsations were
confirmed in data from the \textit{Fermi}
(GBM, 12--25~keV) \citep{Jenke_2017}, \textit{Swift} XRT
\citep{Beardmore_2017} and \textit{NuSTAR}
\citep[3--79~keV;][]{Bahramian_2017,Jaisawal_2018}. \textit{NuSTAR}
observations also showed that the pulse shape is strongly
energy-dependent in the 3--79~keV band, but no cyclotron absorption
features have yet been detected in the hard X-ray spectrum \citep{Jaisawal_2018}.
Preliminary solutions for a 26--28~d eccentric ($e\approx 0.1$) pulsar
orbit were reported by \citet{Ge_2017} and \citet{Doroshenko_2017}, with an improved
solution given by \citet[][see also Section 4.1 below]{Jenke_2018}.

A variable 6~GHz radio counterpart was also detected,
with a flux of $<$27~$\mu$Jy on October 10 and 76$\pm$7~$\mu$Jy on
November 8 \citep{van_den_Eijnden_2017a, van_den_Eijnden_2017b}. An optical counterpart with magnitude $B=13$, USNO-B1.0 1514+0083050, was identified
by positional coincidence with the {\textit Swift} XRT source
\citep{Kennea_2017}. Optical spectroscopy corresponds to a late
Oe-type or early Be-type star \citep{Kouroubatzakis_2017, Bikmaev+17}. The optical counterpart shows evidence for long-term ($\sim$1000~d) $V$-band variability of order 0.15~mag \citep{Stanek_2017, Kochanek_2017, Nesci_2017}. The distance to the source was intially estimated to be 2.5$\pm$0.5~kpc, based on the estimated absolute magnitude of the stellar companion \citep{Bikmaev+17}.

However, on April 25, 2018, \textit{Gaia} Data Release 2 was made available, including an online catalog\footnote{\url{http://gaia.ari.uni-heidelberg.de/tap.html}} with derived distances for a large number of sources including USNO-B1.0 1514+0083050, with a measured parallax of $0.095 \pm 0.030$ milliarcsec. This catalog was based on \citet{Bailer-Jones2018}, where the \textit{Gaia} team applied best practices to derive distances for all of their stars. USNO-B1.0 1514+0083050 corresponds to source id 465628193526364416. The goal of the \citet{Bailer-Jones2018} study is to provide purely geometric distance estimates, independent of assumptions about the physical properties of or the interstellar extinction towards stars. The distance for Swift J0243.6+6124 from this catalog is 6.8 kpc, with a 1-$\sigma$ range of 5.7--8.4 kpc. A separate analysis, performed by a member of the \textit{Gaia} team, using different priors, resulted in a distance of 8 kpc, with a 5--95\% confidence range of (6.3--12.3 kpc) (M. Ramos, private communication). Since these distances are similar and the $\sim 7$ kpc distance is publicly available, for purposes of this paper, we adopt a distance of 7 kpc based on the \textit{Gaia} measurements.

Transient systems similar to Swift J0243.6+6124 are a particularly valuable laboratory for the study of
magnetically-channeled accretion as they trace through a large dynamic
range of luminosity and mass accretion rate over the course of an
outburst on timescales of days to weeks, before subsiding into X-ray
quiescence. The goal of this paper is to use detailed analyses of the pulse profiles, pulsed fraction, power spectra, and hardness ratios over a broad energy range to understand the changes in accretion column geometry and characteristics as the mass accretion rate evolves in the Swift J0243.6+6124 system.  In this paper, we describe 0.2--12~keV \textit{NICER} and 8-100 keV GBM observations of
Swift J0243.6+6124 obtained throughout the full outburst. Swift J0243.6+6124 evolved over nearly three orders of magnitude in luminosity during this outburst, reaching a peak count rate in the \textit{NICER} energy band of 63,000 cts s$^{-1}$ (see Figure~\ref{fig:lcandprofiles}), nearly 6 times the nominal flux from the Crab nebula and pulsar (11,000 cts s$^{-1}$). As the intensity increased, the pulsar underwent dramatic spin-up, as measured with \textit{Fermi} GBM (see Figure~\ref{gbm:spin_flux}).  We describe the extremely detailed 0.2--12 keV (Section~\ref{subsec:nicerpulse}) and 8--100 keV pulse profile datasets obtained by \textit{NICER} and GBM, respectively, which show considerable evolution with luminosity and energy. Detailed plots of pulse profiles vs. energy as a function of time are shown in the Appendix. Like the pulse profiles, the pulsed fraction (Section~\ref{subsec:nicerpulse}) and power spectra (Section~\ref{subsec:powspec}) measured with \textit{NICER} also evolve with luminosity. Hardness ratio histories measured with \textit{NICER} and GBM (Section~\ref{subsec:hardness}) show a turnover, above which hardness is anti-correlated with luminosity.  Luminosities in the 0.1--10 keV band were estimated from preliminary spectral fits to the \textit{NICER} data (Section~\ref{subsec:spectral}). Implications of these results, which suggest a transition in accretion regimes, are discussed in Section~\ref{sec:discuss}.

\begin{figure}
\begin{center}
\includegraphics[width=1.1\textwidth]{long_term_lc_and_profiles4.pdf}
\end{center}
\caption{Outburst light curve and pulse profile evolution for Swift~J0243.6+6124. The large plot shows the evolution of the average count rate for each \textit{NICER} observation in the 0.2--12 keV range.  The insets to the left and right show the dramatic 0.2--12 keV pulse shape variations as the outburst progresses. For the inset plots, time goes from bottom to top of the page for the rising portion of the outburst (left) and down from top to bottom of the page for the declining part of the outburst (right). }\label{fig:lcandprofiles}
\end{figure}

\begin{figure}
\includegraphics[width=\textwidth]{swiftj0243_energy_res_amp.pdf}
\caption{Top: Barycentered and orbit-corrected spin-frequency history measured with GBM. Bottom: Pulsed flux measured with GBM \label{gbm:spin_flux} in nine energy bands. Swift J0243.6+6124 was detected from 2017 October 1 through 2018 February 25 (MJD 58027--58174) in single day integrations and through 2018 March 3 (MJD 58180) in 3-day integrations.}
\end{figure}

\section{Observations of Swift J0243.6+6124}\label{sec:generalobs}

\subsection{\textit{NICER} Instrument and Data}\label{subsec:nicerxti}

The Neutron star Interior Composition Explorer (\textit{NICER}) was launched and installed as an external payload on the International Space Station in 2017 June. \textit{NICER}  contains one instrument, the X-ray Timing Instrument (XTI), sensitive in the 0.2--12 keV range, described in detail in \citet{2016SPIEGendreau} and briefly summarized here. The XTI is composed of an array of 56 X-ray ``concentrator" optics each with an associated focal plane module (FPM) containing a single-pixel detector. Each of the 56 X-ray-concentrator modules consists of 24 nested grazing-incidence gold-coated aluminum foil mirrors, parabolically shaped with a common focal length. Details of the XTI detector subsystem are described in detail in \citet{2016SPIEPrigozhin} and summarized here. The FPMs each consist of a silicon drift detector integrated with a custom pre-amplifier. The FPMs, 52 of which are operating on-orbit, are arranged into 7 groups of 8. Each group of FPMs is controlled by a set of electronics called a Measurement/Power Unit (MPU) slice. Each MPU slice provides the readout and supporting circuitry for its group of 8 FPMs and is completely independent of the other six slices.

\subsection{\textit{Fermi} GBM Instrument and Data}\label{subsec:GBM_instrument}

The GBM instrument comprises 14 detectors, 12 Sodium Iodide (NaI) detectors sensitive from 8 keV to 1 MeV pointed at various directions in order to cover the whole unocculted sky and two Bismuth germanate (BGO) detectors sensitive from 200 keV to 40 MeV on either side of the  \textit{Fermi} spacecraft \citep{Meegan2009}. Only the NaI detectors are used for this analysis. GBM data are available continuously, when the spacecraft is outside of the South Atlantic Anomaly. There are three continuous data types: CTIME (0.256 s, 8 energy channels) used for the public pulse frequency and pulsed flux measurements (shown in Figure~\ref{gbm:spin_flux} with updates found at \url{https://gammaray.nsstc.nasa.gov/gbm/science/pulsars.html}) and total flux measurements (\url{https://gammaray.nsstc.nasa.gov/gbm/science/earth_occ.html}), CSPEC (4.096 s, 128 energy channels), and CTTE (10 $\mu$s, 128 channels) event by event data, used for this analysis.

\subsection{\textit{Swift} BAT Instrument and Data}\label{subsec:BAT_instrument}

The \textit{Swift} Burst Alert Telescope (BAT) is a hard X-ray monitor \citep{H_Krimm_2013} composed of an array of CdZnTe detectors that are sensitive in the 15--150 keV range with a total detecting area of 5200 cm$^{2}$. It is a coded mask instrument with a 1.4 steradian field-of-view. We use the BAT transient monitor results\footnote{\url{http://heasarc.gsfc.nasa.gov/docs/swift/results/transients/}}  (15--50 keV), provided by the BAT team, to model the accretion torques applied to the neutron star.

\section{\textit{NICER} Observation Analysis}\label{sec:nicerobs}

\subsection{\textit{NICER} Event Deadtime Analysis}\label{subsec:nicerdeadtime}
\begin{deluxetable}{ccccccc}
\tabletypesize{\tiny}
\tablecolumns{8}
\tablewidth{0pt}
\tablecaption{\textit{NICER} Observations of Swift~J0243.6+6124 \label{table:nicerobs}}
\tablehead{
\colhead{NICER ObsID} & \colhead{Date} & \colhead{MJD epoch} & \colhead{On-source} & \colhead{Deadtime corrected} & \colhead{Average rate} & \colhead{Luminosity\tablenotemark{a}} \\
      &  & & time (s)& average exposure &0.2--12 keV & 0.1--10 keV  \\
      &  & &         & per MPU slice (s)& (counts s$^{-1}$) & (erg s$^{-1}$) }
\startdata
1050390101 & 2017-10-03 & 58029.805 & 3099 & 2643.4 & 164.8 &  1.19E+37\\
1050390102 & 2017-10-04 & 58030.922 & 4171 & 2782.6 & 239.9 & 1.75E+37 \\
1050390103 & 2017-10-04 & 58031.434 & 21590 & 16645.4 & 281.9 & 2.05E+37\\
1050390104 & 2017-10-06 & 58032.456 & 24029 & 19320.5 & 423.7 & 2.99E+37\\
1050390105 & 2017-10-11 & 58037.128 &2497 & 2198.3 & 1782.9 &  1.08E+38 \\
1050390106 & 2017-10-12 & \nodata & 41 & 0 & \nodata & \nodata \\
1050390107 & 2017-10-16 & 58042.455 & 1495 & 420.9 & 3686.8 & 2.01E+38 \\
1050390108 & 2017-10-21 & 58047.663 & 1394 & 615.7 & 4979.0 & 2.86E+38 \\
1050390109 & 2017-10-22 & \nodata & 2334 & 0 & \nodata & \nodata \\
1050390110 & 2017-10-23 & 58049.271 & 900 & 735.4  & 6312.7 &  3.31E+38\\
1050390111 & 2017-10-24 & \nodata & 689 & 0 & \nodata & \nodata \\
1050390112 & 2017-10-25 & 58051.364 & 1003 & 495.8 & 7484.5 &  4.01E+38 \\
1050390113 & 2017-11-02 & 58058.386 & 4566 & 3126.0 & 26583.5 &  1.31E+39\\
1050390114 & 2017-11-06 & 58063.989  & 311 & 257.4 & 36333.8 &  1.77E+39\\
1050390115 & 2017-11-07 & 58064.414 & 1495 & 1276.5 & 33175.4 &  1.66E+39 \\
1050390116 & 2017-11-08 & 58065.381 &3816 & 1915.8 & 31833.4 &  1.58E+39\\
1050390117 & 2017-11-14 &  \nodata & 18 & 0 & \nodata & \nodata \\
1050390118 & 2017-11-15 & 58072.846 & 405 & 374.9 & 20774.0 &  1.32E+39 \\
1050390119 & 2017-11-16 & 58073.460 & 3917 & 2171.9 & 18636.9 &  9.98E+38 \\
1050390120 & 2017-11-17 & 58074.263 & 3916 & 2240.9 & 17297.2 &  1.03E+39 \\
1050390121 & 2017-11-17 & 58074.737 & 1610 & 1517.3 & 16359.3 &  9.40E+38\\
1050390122 & 2017-12-02 & 58089.626 & 3756 & 3676.9 & 5864.4 & 3.25E+38\\
1050390123 & 2017-12-04 & 58091.203 & 1291 & 1016.0 & 5341.7 & 2.70E+38\\
1050390124 & 2017-12-05 & 58092.558 & 1704 & 1590.0 & 4943.2 & 2.71E+38\\
1050390125 & 2017-12-06 & 58093.528 & 1887 & 1854.5 & 4721.4 &  2.65E+38\\
1050390126 & 2017-12-11 & 58098.909 & 210 & 109.0 & 4187.3 &  2.22E+38 \\
1050390127 & 2017-12-12 & 58099.463 & 733 & 640.9 & 4116.8 &  2.23E+38\\
1050390128 & 2017-12-13 & 58100.646 & 482 & 263.5 & 3853.4 &  2.21E+38\\
1050390129 & 2017-12-19 & 58106.402 & 1034 & 594.0 & 3209.5 &  1.84E+38\\
1050390130 & 2017-12-20 & 58107.913 & 528 & 279.7 & 3000.0 & 1.61E+38\\
1050390131 & 2017-12-21 & 58108.237 & 718 & 618.5 & 3110.9 & 1.77E+38\\
1050390132 & 2018-01-07 & 58125.646 & 210 & 208.1 & 2120.3 & 1.29E+38\\
1050390133 & 2018-01-08 & 58126.691 & 990 & 645.3 & 2020.6 &  1.30E+38\\
1050390134 & 2018-01-09 & 58127.622 & 5319 & 3193.7 & 1823.4 &  1.09E+38\\
1050390135 & 2018-01-10 & 58128.492 & 3133 & 2029.3 & 1844.4 &  1.11E+38 \\
1050390136 & 2018-01-10 & 58129.326 & 3288 & 2686.1 & 1775.0 &  1.00E+38\\
1050390137 & 2018-01-12 & 58130.323 & 4541 & 3368.9 & 1755.2 &  1.04E+38\\
1050390138 & 2018-01-17 & 58135.850 & 3230 & 3207.7 & 1399.6 & 8.76E+37\\
1050390139 & 2018-01-27 & 58145.715 & 2266 & 2127.0 & 941.5 &  5.89E+37\\
1050390140 & 2018-02-02 & 58151.352 & 2114 & 2104.8 & 581.6 & 3.83E+37\\
1050390141 & 2018-02-13 & 58162.251  & 3636 & 3492.7 & 236.6 &  1.66E+37\\
1050390142 & 2018-02-17	& 58166.141 & 2768 & 2755.4 & 190.8 &  1.30E+37\\
1050390143 & 2018-02-20 & 58169.900 & 2326 & 1564.1 &  131.5 &  8.57E+36 \\
1050390144 & 2018-02-26 & 58175.852 & 2175 & 1805.5 &  49.8 & 3.00E+36\\
1050390145 & 2018-02-27 & 58176.206 & 7058 & 6964.3 &   45.2 &  2.81E+36\\
1050390146 &  2018-03-04 &  58181.9 &  1535 & 1442.7 &  45.7 &  2.49E+36\\
 1050390147 &  2018-03-25 &  58202.4 &  1251 &  1077.7 &  22.0 &   1.20E+36 \\
 1050390148 &  2018-03-27 &  58204.7 &  1705 &  1649.0 &  14.8 &  6.85E+35 \\
 1050390149 & 2018-04-09 &  58217.8 &  5003 & 3966.1 &  104.3 &  6.16E+36 \\
 1050390150 &  2018-04-10 &  58218.1 &   2025 &  1917.4 & 108.7 &  6.22E+36 \\
 1050390151 &  2018-04-11 &  58219.7 &  2278 &  1699.0 &  122.5 &  7.03E+36 \\
 1050390152 &  2018-04-12 &  58220.1 &   1606 &   1111.4 & 120.2 &  6.76E+36 \\
 1050390153 &  2018-04-13 &  58222.0 &  500 & 370.4 &  98.0 &  5.06E+36 \\
 1050390154 &  2018-04-14 &  58222.5 &   19208 &  16463.2 &  102.4 &  5.58E+36 \\
1050390155 &  2018-04-15 &  58223.5 &  14521 &   12004.6 &  90.7 &  4.81E+36 \\
 1050390156 &  2018-04-16 &  58224.5&   7735 &  6281.5 &  78.6 & 4.10E+36 \\
 1050390157 &  2018-04-17 &  58225.3 &  5955 &  5513.6 &  69.8 & 3.57E+36 \\
 1050390158 &  2018-04-20 & 58228.2 &  2785 &   2621.7 &  47.5 &  2.47E+36 \\
1050390159 &  2018-04-23 &  58232.0  &  492 &  459.3 &  24.4 &  9.17E+35 \\
 1050390160 &  2018-04-24 &  58343.4 &   643 &  149.1 & 18.6 & 6.28E+35 \\
\enddata
\tablenotetext{a}{Luminosity calculation assumes isotropic emission and distance = 7 kpc}
\end{deluxetable}

The data analysis procedure for this bright source differs from that used for fainter sources in order to correctly account for detector deadtime. Analysis was done beginning with the unfiltered event files for each MPU slice and the individual slice datasets were kept separate. HEASOFT version 6.22.1 and NICERDAS version 2018-02-22\_V002d were used for this analysis. Good time intervals (GTI) were selected using the {\tt FTOOL} {\tt nimaketime} with the following screening criteria: ISS outside the \textit{NICER}-specific South Atlantic Anomaly (SAA) boundary, \textit{NICER} in tracking mode with pointing direction $<0.015$\degr\ from the source direction with at least 38 detectors enabled, source elevation $>30$\degr\ above the Earth limb, and source direction at least 40\degr\ from the bright Earth. These GTIs were applied to the unfiltered and uncalibrated events for each MPU slice separately using \texttt{niextract-events}.

Two types of deadtime must be separately accounted for in our analysis. First, event-by-event deadtime occurs because processing each event in each detector takes a certain amount of time and that detector is inactive, hence ``dead" while processing an individual event. Second, deadtime can occur because the buffer in each MPU slice reaches its maximum and events are dropped because there is no further room to record them. The first type of deadtime is tracked as a {\tt DEADTIME} column in the \textit{NICER} event files and the second (called GTI exposure in this paper) is tracked in the GTI extensions of the \textit{NICER} event files. Below we account for both types of deadtime in the generation of our \textit{NICER} pulse profiles and light curves.

The standard \textit{NICER} calibration was applied to the events from each MPU slice separately, using {\tt nimpucal}. This tool produces a Pulse Invariant (PI) column by applying the gain correction specified in the calibration database, \texttt{nixtiflightpi20170601v001.fits}, to the raw pulse height measurements. The gain scale is set so that PI$ = E/10$ eV, where $E$ is the nominal photon energy. Both the calibrated and uncalibrated files are barycentered using {\tt barycorr} with the DE430 JPL ephemeris. The {\tt nimpucal} tool automatically removes events that cannot be calibrated. Because deadtime arises from all events, processing from this point proceeds in parallel for each MPU slice, with the calibrated files for each MPU slice being used to accumulate X-ray events and GTI exposure in the pulse profiles while the uncalibrated files are used to accumulate deadtime.

Pulse profiles were generated for each observation using the \textit{Fermi} GBM orbital ephemeris described in Section~\ref{subsec:gbmorbit} along with the spin frequency and frequency derivative measured with GBM on the same day as the \textit{NICER} observation, and corrected to the mid-point time of the \textit{NICER} observation. This process was done in a series of steps described in the following paragraphs.

First, source events were selected to form the pulse profiles. Starting with the barycentered, calibrated, but unfiltered event files for each MPU slice, events were selected that were in the chosen energy range (e.g., PI=20--1200 for 0.2--12 keV for the full profiles, PI corresponding to 0.2--1, 1--2, 2--3, 3--5, 5--8, and 8--12 keV for the individual energy bands, and PI corresponding to 4--7 and 7--10 keV for the hardness ratio comparisons with \citealt{Reig+13}). Forced triggers, overshoot, and undershoot events (those events with bits 5, 6, or 7, respectively, set in the {\tt EVENT\_FLAGS} column) were excluded. After correcting the event times for the pulsar's orbit, the pulse phase was computed and events were accumulated in each of 100 phase bins across the pulse period. These folded event profiles were accumulated separately for each MPU slice.

Second, the GTI exposure for each individual phase bin was then computed, again separately for each MPU slice. These good time intervals were taken from the GTI extension of the calibrated event files. In the brightest observations, shown in Figure~\ref{fig:gtiexposure}, the exposure time per phase bin varies dramatically from bin-to-bin. This is caused primarily by buffers filling up at each MPU slice, which results in very short GTIs. To account for these bin-to-bin exposure time variations, the GTIs longer than a phase bin were divided into pieces 1/10 of a phase bin long. Their start times were corrected for the pulsar's orbit, a pulse phase was computed for each time, and the total exposure was accumulated for each phase bin. GTIs shorter than a phase bin were corrected and accumulated without slicing.

Third, deadtimes were obtained from the unfiltered event files in order to include all events that could contribute to deadtime, both the good events included in the pulse profile, and the non-source events filtered out of the profile. Deadtime for each event is stored in the \textit{NICER} fits files as a value from 0--127. Each of these values $V_{\rm{dead}}$ corresponds to a range of 16 clock ticks, i.e., 0 is 0--15 ticks, 1 is 16--31, and so on, with a maximum recorded dead time of 127 or 2032 ticks. The dead time is computed in seconds as $t_{\rm{dead}} = (V_{\rm{dead}}+0.5) \times 16/(25.8 \times 10^6$ Hz), where the factor of 0.5 shifts to the center of the recorded interval, 16 is the number of ticks per interval, and 25.8 MHz is the clock frequency. For each event, the event times were corrected for the pulsar's orbit, phases were calculated, and the dead time was accumulated in each phase bin. Like the folded events and folded GTI intervals, the deadtimes were accumulated for each MPU slice separately.

Fourth, to obtain the deadtime corrected exposure time for each phase bin, $\epsilon$, the total deadtime for each phase bin was subtracted from the GTI exposure for each bin. This resulted in an exposure time for each of 100 phase bins for each MPU slice. Table~\ref{table:nicerobs} lists the total deadtime corrected exposure averaged over the seven MPU slices for each observation. The exposure is typically the same for all MPU slices to within 1\% for average count rates $< 1000$ counts/s. For the highest count rates, the exposure can vary by as much as 10\% from MPU slice to MPU slice.

Finally, the count rate in each phase bin was obtained by simply dividing the total number of filtered events in each phase bin by the deadtime corrected exposure in each phase bin. Poisson-distributed uncertainties were assumed, and were calculated as the square root of the counts divided by the deadtime corrected exposure in each bin. The last step was to combine the count rate pulse profiles for each MPU slice into a single \textit{NICER} pulse profile for each observation. Because 52 of 56 \textit{NICER} detectors are operating on orbit, the MPU slices have differing numbers of inputs. The count rate profiles were corrected by a simple factor so that all would have the expected rate for eight detectors. The profiles from MPU slices 1 and 6 were multiplied by $8/7$, and the profile from MPU slice 2 was multiplied by $8/6$, then the profiles from all seven MPU slices were added together and their errors were combined in quadrature.

\begin{figure}
	\begin{center}
     \includegraphics[width=4in]{1050390115_corrected_profile_and_exposure_plot3.pdf}
	\end{center}
\caption{Swift~J0243.6+6124 folded pulse profile (two cycles plotted) of one of the brightest \textit{NICER} observations, ObsID \# 1050390115, on 2017 November 7. The black histogram and left-hand y-axis denote the folded pulse profile in the 0.2--12 keV band, averaged over the 7 MPU slices, after corrections for GTI exposure and deadtime have been applied. The green curve and right-hand y-axis denote the deadtime corrected exposure per phase bin, averaged over the 7 MPU slices for this observation. The total deadtime corrected exposure, averaged over MPU slices, for this observation is 1276.5 s. If the bin-to-bin variations were not present, each bin would have an exposure of 12.765 s. The exposure per bin differs for each observation and shows bin-to-bin variations $>$1\% compared to uniform exposure for total count rates $> 2000$ counts s$^{-1}$.  \label{fig:gtiexposure}}
\end{figure}

\subsection{\textit{NICER} Pulse Profile Analysis}\label{subsec:nicerpulse}

\textit{NICER} observations of Swift J0243.6+6124 began early in the outburst on 2017 Oct 2, triggered by an alert from \textit{MAXI} \citep{Sugita_2017} on 2017 September 29.
The outburst profile is asymmetric, with a faster rise than fall as shown in Figure~\ref{fig:lcandprofiles}, as is common for giant outbursts in Be/X-ray binaries \citep{Reig+13}. Inset plots in Figure~\ref{fig:lcandprofiles} show pulse profile evolution  in the full 0.2--12 keV band throughout the outburst. The pulse shapes are similar at similar count rates both in the rise and fall of the outburst, evolving from highly complex  (Fig.~\ref{fig:lcandprofiles} insets a \& h) at lower count rates, to single peaked  (inset b \& g), to double peaked and nearly symmetric  (inset c \& f), and to double peaked but asymmetric at the outburst peak  (inset d \& e). Detailed energy dependent pulse profiles for each \textit{NICER} observation are shown in the Appendix.

 \textit{NICER} observations continued as the outburst faded. The flux reached a minimum in the \textit{NICER} band on MJD 58204 (See Table 1). Pulsations were still detected and the 0.2--12 keV profile was a simple symmetric single peak, similar to MJD 58176, the last profile shown in Figure~\ref{fig:A1} in the Appendix. Then the flux again began to increase and a normal (type I) outburst was detected with \textit{NICER}, GBM, and \textit{Swift} BAT peaking on MJD 58220. A second normal outburst peaking near MJD 58247 was detected with GBM and \textit{Swift} BAT, but was not observed with \textit{NICER}.

The root-mean-squared pulsed fraction $f_{\rm rms}$ was computed for the full 0.2--12 keV band and for each of six energy bands: 0.2--1, 1--2, 2--3, 3--5, 5--8, and 8--12 keV. The pulsed fraction is given by
\begin{equation}
\label{eq:rms}
f_{\rm rms} = \frac{(\Sigma^{N}_{j=1} (r_j - \bar{r})^2/N)^{1/2}}{\bar{r}}
\end{equation}
where $r_j$ is the count rate in phase bin $j$ and $\bar{r}$ is the phase-averaged count rate. The time history of the pulsed fraction for the six energy bands is shown in Figure~\ref{fig:nicer_fraction} (left panel).
The time evolution of $f_{\rm rms}$ in the individual energy bands is similar to the full-band $f_{\rm rms}$. However, the peak pulsed fraction increases substantially with energy.  The relationship between the full 0.2--12 keV band $f_{\rm rms}$ and the 0.1--10 keV luminosity (see Table 1) is shown in Figure~\ref{fig:nicer_fraction} (right panel). A clear turn-around is present in both the rising and fading portions of the outburst.

\begin{figure}\label{fig:pulse_fraction}
\begin{center}
\includegraphics[width=0.475\textwidth]{pulse_fraction_vs_time_and_energy2.pdf}
\includegraphics[width=0.475\textwidth]
{nicer_pulse_fraction_vs_lum_linlog.pdf}
\end{center}
\caption{(Left):Swift J0243.6+6124 root-mean-squared pulsed fraction in several energy bands versus time from \textit{NICER} observations.  (Right): Swift J0243.6+6124 0.1--10 keV luminosity (d=7 kpc) vs. root-mean-squared pulsed fraction (0.2--12 keV). The rising portion of the outburst and the fading portion are denoted by blue squares and red diamonds, respectively.  During the main peak of the outburst, the pulsed fraction generally increases with increasing count rate and increasing energy, especially after a striking turn-around near $L > 10^{38} (d/7\,{\rm kpc})^2$. Error bars are smaller than the plotted symbols in both panels.}
\label{fig:nicer_fraction}
\end{figure}

\subsection{\textit{NICER} Power Spectra}\label{subsec:powspec}
We analyzed variability on time-scales other than the neutron star
spin period by estimating the power spectral density (PSD; $P(f)$) for
each epoch.  First, we binned the data in 100\,ms bins using photon
times that had been corrected to the solar system barycenter.  We computed deadtime and exposure, $\epsilon_i$, as above, allowing an estimate
of the true count rate, $r_i=c_i/\epsilon_i$.

Because \textit{NICER} only views the source for a fraction of each
ISS orbit, the window function for a given epoch is typically complicated, leading to a convolution of the true power spectrum with a series
of $\mathrm{sinc}$ functions.  In the PSD, this is squared, so a pure tone
will be spread into side lobes whose magnitude decreases as $1/f^2$, a phenomenon known as spectral leakage.  It is
therefore critical both to eliminate as much pulsed power from the
signal as possible and to pay careful attention to the resulting
spectra for evidence of such leakage.

To reduce the pulsed signal, we first estimate the spin period and
period derivative for each epoch, taking into account binary motion,
and use this to assign a pulse phase to each time bin, $\phi(t_i)$.
We then approximate the power at the spin frequency with a truncated
Fourier series whose coefficients we estimate as, e.g., $\sum_i r_i
\cos(2\pi k\phi_i) / \sum_i r_i$, with $k$ between 1 and 10.  We
evaluate the Fourier series at each time bin using $\phi(t_i)$ and $\epsilon_i$ and
subtract this from the observed rate.

To compute a PSD for visualization for each epoch, we selected contiguous segments of data with at least 2048 samples, then zero-padded the (mean subtracted) data to $2^{14}$ samples.  Most segments were shorter than this.  We computed the discrete Fourier transform using the FFT algorithm and co-added the resulting spectra using the interval lengths as weights. We normalized the spectra according to the convention common
in the literature \citep[e.g.,][]{Nowak99}, in which the PSD integrated
over frequency yields the rate-normalized variance, $f_{\rm rms}^2$ (see
Equation \ref{eq:rms}).  Using shorter, contiguous segments degrades spectral resolution and precludes examination of frequencies $<$1\,mHz, but it provides superior window functions and is more robust against any uncorrected deadtime effects that evolve over an epoch.

The resulting PSDs for 16 epochs appear in Figure \ref{fig:powspec}, which we
explain in detail here.  For display purposes, all spectra have been logarithmically smoothed with a resolution of about 0.05 dB.  The tan trace in each panel of Figure \ref{fig:powspec}, with an obvious harmonic
series, is the PSD of the mean pulsed signal, computed as described above,
multiplied by the exposure for the particular observation.  The fundamental appears at the spin frequency 0.1014\,Hz.  It is
typically quite strong compared to the broadband variations.  Because
the exposure (window function) is the same as for the real data, this
PSD is useful for assessing the effect of the window function on pure
tones.   We also include a dashed gray line whose slope is fixed to $1/f^2$ to aid in assessing spectral indices and leakage.  The blue trace shows the PSD of the observed count rate after
subtracting the mean pulsed component.  Some remaining pulsed power is
evident, e.g., in the observation on MJD 58031.0, but such power is small compared to the broadband
features.  The dark horizontal line shows the white noise level, which for Poisson statistics is given by $<$$r/\epsilon$$>$.  We find this to be in good agreement with the observed spectra.   Finally, the black trace shows the power spectrum with white noise subtracted.  This is the best empirical estimate of the aperiodic PSD and can be used for visual characterization.  We note here that we also computed PSDs by omitting each MPU slice in turn, and found no substantial difference.  Finally, we note that the relative power levels are high, such that any contributions from, e.g., pointing jitter, are negligible by comparison.

We have also fit functional forms to the power spectra using a maximum
likelihood approach.  For this purpose, we did not co-add the segments within an epoch, but rather computed FFTs with lengths exactly equal to the segments, such that the resulting FFT bins are statistically independent.  The elements of the PSD then follow a $\chi^2_2$ distribution when scaled
appropriately, so the log likelihood becomes $\log\mathcal{L}=-\sum_i
\log P_m(f_i,\lambda) + P(f_i)/P_m(f_i,\lambda)$, where $P_m(f)$ is
the model PSD for parameters $\lambda$, and we maximize this
likelihood evaluated over the unsmoothed power
spectra.  We exclude spectral bins with $f>2$\,Hz to minimize the effects of aliased power from $f>5$\,Hz (the Nyquist frequency).  In the literature, lorentzians of various widths are widely
used to model PSDs \citep[e.g.,][]{Reig+13}, but they asymptotically follow
$1/f^2$.  The observed PSDs are typically shallower than this, so we
have instead fit the broadband power with a power law with a low
frequency cutoff, $P(f)\propto[1+(f/f_c)^2]^{\alpha/2}$.  We model
narrower features with a lognormal function, and we include the white noise contribution given above.  The resulting power
law fits are shown with red traces, individual components appearing as dashed lines and the total model solid.

There is clear evolution in the power spectra.  The earliest observation is essentially white at low frequencies with a low quality QPO-like feature at 50\,mHz.
QPOs have been observed already in a number of accreting pulsars ranging from $\sim1\,$mHz to $\sim40\,$Hz (see, e.g., \citealt{Paul2011,Reig+13}), and are generally associated with inhomogeneities in the inner accretion disk.
The spectral break is almost exactly at the neutron star spin frequency ($0.1014\,$Hz), and the high-frequency behavior is slightly shallower than $1/f^2$.  Inspection of the window function shows this steeper tail cannot simply be spectral leakage from the QPO, so it reflects a distinct physical process.  On MJD 58030.9, the QPO is stronger, narrower, and at higher frequency, about 70\,mHz.  However, because of the low spectral resolution at these frequencies, we are unable to quantitatively characterize any evolution of the QPO frequency and shape with luminosity.

As the luminosity increases, the power law cutoff disappears and the power law becomes harder with typical indices of $-1.1$ to $-1.3$.  At higher frequencies, a broad peak of power, about a decade wide and largely overlapping the band including the spin frequency and its harmonics, appears (MJD 58031.0--58049.0).  At these epochs, this broad peak can be identified with the lognormal component (dashed red lines) of the model fit.  Interestingly, this component is not necessarily new, as the normalized power at $\sim$0.5\,Hz is almost constant at all epochs; thus, this component may instead model a deficit in power around 0.1\,Hz.  In the brightest part of the outburst (MJD 58049.0--58073.1, the spectra are consistent with a single power law.  As the luminosity decays, the broad high frequency peak re-appears (MJD 58089.4--58151.3).  Finally, the spectrum returns to a flat low frequency pedestal terminated by a cutoff/QPO near the spin frequency and a steep ($\sim$$-1.7$ to $-2.0$) high-frequency tail.

\begin{figure}
\begin{center}
\includegraphics[width=\textwidth]{power_spectra_v2.pdf}
\end{center}
\caption{The power spectral densities for 16 epochs with \textit{NICER}.  The MJD and count rate (from Table \ref{table:nicerobs}) are given for each observation.  The main features are described in the text, and are briefly: light tan, estimated pulsed PSD; blue, smoothed PSD; dark horizontal line, white noise level; black, smoothed and noise-subtracted PSD; red, total (solid) and component (dashed) fits; dashed gray line, a $1/f^2$ line for visual comparison. }
\label{fig:powspec}
\end{figure}

\subsection{\textit{NICER} hardness ratios}\label{subsec:hardness}

In many accreting X-ray pulsars the source spectrum is found to be flux-dependent.
When the observed spectrum is fit using a power-law component, the spectral photon index $\Gamma$ proportionally or inversely correlates with the source luminosity, according to the accretion regime.
A critical luminosity $L_c$ distinguishes between two accretion regimes \citep{Basko+Sunyaev76}: at relatively low luminosities $L<L_c$, the height of the accretion structure is governed by the ram pressure of the infalling material, called ``sub-critical'', while at higher luminosities $L>L_c$ a radiation-dominated shock rises in the magnetic column, governed by radiation pressure in the accreting material, called ``super-critical''.
For sub-critical sources the spectrum of many accreting X-ray pulsars has been found to harden as the observed X-ray flux increases
\citep{Klochkov+11, Fuerst+14, Malacaria+15, Postnov+15, Epili+17}.
On the other hand, super-critical sources show the opposite behavior, that is a spectral softening as the flux increases (\citealt{Reig+13,Postnov+15,Epili+17}).
Therefore, thanks to the opposite observed behaviors, the flux dependence of the spectral photon index can be used to identify the accretion regime.

A model-independent way to probe whether a source is accreting at sub- or super-critical regime is through the analysis of the hardness ratio.
\citet{Reig+13} studied the patterns of variability of the hardness ratio during outbursts in a number of Be/X-ray pulsars.
Those authors identified two branches, the horizontal branch (HB) and the diagonal branch (DB), in the hardness-intensity diagrams for these sources. The spectral hardness follows a certain path in the hardness-intensity diagram and undergoes state transitions from one branch to another, that is, it ``turns over" if the source luminosity passes through a certain critical value.
These diagrams used a intensity in the $4-30\,$keV band, using data from the \textit{RXTE} Proportional Counter Array (PCA, \citealt{Jahoda_1996}) and a soft color defined as the ratio between the count rates in two energy bands, namely $7-10\,$keV and $4-7\,$keV.

We investigated the spectral behavior of Swift~J0243.6+6124 by examining the hardness ratio evolution throughout the entire outburst, with both \textit{NICER} and \textit{Fermi} GBM data.
\textit{NICER} data are useful for reproducing the original \citet{Reig+13}'s soft color (SC, $7-10\,$keV/$4-7\,$keV), while GBM enables one to explore the hardness ratio behavior at higher energy and offers uniformly sampled coverage of the entire outburst.
The $4-10\,$keV \textit{NICER} count rate has been used as a proxy for the $4-30\,$keV total intensity originally employed by \citet{Reig+13}.
For GBM, the hardness ratio has been chosen as the ratio between the pulsed flux levels in the $12-16$ and $8-12\,$keV energy ranges, whose edges are defined by the channel edges of CSPEC data (See Section~\ref{subsec:GBM_instrument}), while the chosen bands are such that the intervals are insensitive to interstellar absorption while guaranteeing sufficient statistics.
Likewise, the $8-16\,$keV pulsed flux has been used to represent the GBM outburst intensity.
Fig.~\ref{fig:soft_color} shows the evolution of the hardness ratios with intensity for both the \textit{NICER} and the GBM energy bands.
GBM data clearly show both the HB at lower intensity and the DB at higher intensity, with a turn-over taking place in between.
However, \textit{NICER} seems to trace the DB more clearly, while only a hint of the HB appears as the luminosity decreases along the decay stage of the outburst.
Moreover, the turn-over traced in the hardness-intensity diagram by \textit{NICER} data seems to happen at a lower luminosity than GBM's.
We will discuss possible implications of these results in Sect.~\ref{subsec:hardness_discussion}.

\begin{figure}[ht!]
\plotone{nicer+gbm_ratios.png}
\caption{Hardness ratio evolution with flux for Swift~J0243.6+6124. Squares show the rise stage of the outburst, and diamonds the decay. Both \textit{NICER} (blue squares and red diamonds connected by a solid line) and \textit{Fermi} GBM (green squares and cyan diamonds connected by dashed line segments) hardness ratios are shown.
Error bars are smaller than the plotted symbols.
Note the different scales on the y-axis: logarithmic for \textit{NICER} counts, linear for GBM pulsed fluxes.
Spectral evolution and hysteresis at high luminosity are evident.}\label{fig:soft_color}
\end{figure}

\subsection{\textit{NICER} spectral analysis}\label{subsec:spectral}

The energy spectra of accretion powered X-ray pulsars can be described by simple phenomenological models despite the complex emission processes acting close to the neutron star. In support of our timing studies and to explore the nature of X-ray emission, we attempted to understand the spectral behavior of Swift~J0243.6+6124 during the outburst. Photon energy spectra were extracted from all available  data (see Table~\ref{table:nicerobs}). We followed the standard analysis method as described in Sections~\ref{subsec:nicerxti} and \ref{subsec:nicerdeadtime}. In addition to conventional filtering criteria, a {\tt SUNSHINE} flag was also added to GTI that can separate the data
at times when \textit{NICER} was exposed to direct sunlight (``day'' orbits), and times when \textit{NICER} was shadowed by the Earth (``night'' orbits). This was done as a first step to address the known instrument artifacts from O, Si and Au in the \textit{NICER} spectra at energies close to 0.5, 1.8 and 2.2~keV, respectively (see also \citet{Ludlam2018}). These residuals were  more prominent in high count rate observations, complicating spectral analysis at present for brighter sources.

We adopted a normalization technique that uses the Crab Nebula's observed spectrum to mitigate these instrument features. For this, we extracted Crab spectra from (ObsIDs 1011010101, 1011010201, and  1013010101-1013010122), in a manner similar to Swift J0243.6+6124. The products from day and night orbits were combined into respective groups using the FTOOL {\tt addspec}. We accumulated time-averaged spectra of the Crab with an effective exposure of $\sim$26 ks for day and $\sim$14~ks for night orbits. Together with a background dataset (\textit{RXTE} blank sky field 6; \citealt{Jahoda2006}), and the instrument response (energy redistribution matrix and effective area files, version 0.06), the Crab spectrum was described in the 0.25--10~keV range by an absorbed power-law. A poor fit was obtained at this point due to residuals in the soft X-rays arising from the preliminary instrument calibration at this stage. We froze the absorption column density from the above fit and refitted the continuum in a flat, feature-less (4--10 keV) range. At these energies the model yielded a better fit with a photon index close to 2. We next extrapolated the energy spectrum back down to 0.25~keV and created a fake spectrum using the {\tt fakeit} command in {\tt XSPEC} for  the Crab exposure. By construction, simulated data was free of significant instrumental bias below 4~keV, and taking its ratio with the Crab spectrum, therefore, generated a  ``template'' that carried the artifacts. Finally we divided the Swift~J0243.6+6124 spectrum by the template, using the FTOOL {\tt MATHPHA}.

The 3--79 keV energy spectrum of the pulsar with {\it NuSTAR} can be expressed by a cutoff power-law, high energy cutoff power-law, and/or negative and positive exponential cutoff power-law models modified with a blackbody component \citep{Jaisawal_2018}. For the purpose of estimating the pulsar's unabsorbed flux from \textit{NICER} spectral analysis, we instead considered a simple cutoff power-law  to fit the  0.3--10 keV continuum. We noted that spectra at brighter phases of the outburst ($>$3 Crab intensity) suffered from instrument features, despite the Crab-renormalization technique, limiting the present study. Nevertheless, our results show a remarkable intensity variation and gradual spectral evolution across the outburst consistent with the
accretion-regime transition scenario outlined in Sect.~\ref{subsec:hardness} and discussed in greater detail in Sect.~\ref{sec:discuss}. The unabsorbed flux has been approximately corrected for deadtime as derived in Section~\ref{subsec:nicerdeadtime} for each observation.  The 0.1--10 keV luminosity was calculated by assuming isotropic emission and  a source distance of 7~kpc \citep{Bailer-Jones2018} and is presented in Table~\ref{table:nicerobs}. A detailed spectral analysis of the pulsar will be presented in a future paper using refined calibration, response, and effective area files.

\section{GBM Observations of Swift J0243.6+6124}\label{sec:gbm_analysis}

\subsection{GBM Orbital analysis}\label{subsec:gbmorbit}

We have determined an orbital ephemeris for Swift J0243.6+6124 using pulse frequencies from GBM and the 15--50 keV count rates from \textit{Swift} BAT. We binned the GBM Channel 1 (12--25 keV) CTIME data from MJD 58027--58150 to 250 ms and then fitted it to a semi-empirical background model.  Next we subtracted the background model and extracted pulsed flux and frequencies for Swift J0243.6+6124 in the manner described in \citet{Finger_1999, Jenke_2012}.  We performed a search for frequency and frequency derivative using pulse profiles folded over one day intervals.
The intrinsic spin--up of an accreting HMXB pulsar, $\dot{\nu}$, is proportional to $L^{6/7}$ when accretion is mediated through a disk \citep{Lamb1973}.  We applied the techniques described in \citep{Tsygankov2016} to model this intrinsic spin--up using the \textit{Swift} BAT rates as a proxy for the X-ray luminosity, because simple polynomial models failed to fully model the observed spin-up.

The BAT had considerable issues with measuring the rates for this source between MJD 58060 and 58075. This was caused by a known data overflow problem at very high count rates. When the counts exceeded the maximum value that could be stored, they wrapped and were instead stored as extremely low values\footnote{\url{https://swift.gsfc.nasa.gov/results/transients/weak/SwiftJ0243.6p6124/}}.  In order to correct the rates, only the peak rates during this period were used and the rates and errors corresponding to the times of measured frequencies were interpolated.  The model emission frequencies were determined by integrating the modeled spin-up determened from the \textit{Swift} BAT rates.  The model frequencies were corrected for the current orbital parameters as described in \citep{Deeter1981}.  The model frequencies were then compared to the measured frequencies.  Using the Metropolis-Hastings Algorithm \citep{Hastings70}, a search was performed to find the best-fit orbital parameters.  The torque model based on the \textit{Swift} BAT rates failed to produce a reasonable fit to the data due to the high spin-up during the peak of the outburst.  Parameters that increased the index on the BAT rates at peak flux were added to the torque model: one parameter that increased the power index on the BAT rates above a threshold and, $\beta$, the threshold on the BAT rates in which the addition to the index would be applied.  The new model for the spin-up rate was:
\begin{eqnarray}
\dot{\nu} \propto R^{i_1 + i_2}
\end{eqnarray}
where $R$ are the interpolated BAT rates, $i_{1}$ is the index when the BAT rates are below $\beta$ and $i_{1} + i_{2}$ is the index when the BAT rates are above $\beta$.

The new model produced a better fit to the data but there were still significant residuals remaining.  Using the best-fit parameters to the orbit, the measured frequencies where corrected for the best-fit orbit and a detailed phase model was determined.  Using the new phase model, a new search for pulsations was performed.  A phase offset $\delta \phi$ from the phase model was estimated for each 1 day mean pulse profile by fitting the Fourier amplitudes of the profile to a scaled and shifted template profile.  The new pulsar orbital phase offsets were fit to the orbital model given by \cite{Deeter_1981} using circular orbital elements an a polynomial background model to remove the remaining residuals.  Only the tail of the outburst (between MJD 58098 and 58154) was used to avoid the large torque noise during the peak of the outburst.   The refined orbital elements were used to further refine the phase model and again a new search for pulsations was performed.  This was repeated until there was no significant change in the best fit orbital elements.  To quote orbital element uncertainties representative of systematic effects, statistical errors in the frequency measurements were inflated to obtain a reduced chi-squared near 1.0 (46.6/43 dof). Sources of systematic error may include changes in the emission beam within the integration interval or throughout the outburst.

\begin{table*}[h!]
\begin{center}
\caption{Orbital Ephemeris for Swift J0243.6+6124.}
\begin{tabular}{lcc}
\tableline\tableline

$P_{\rm orb}$        &   27.587 $\pm$ 0.016  & days   \\
$T_{\pi/2}$                     &   58115.6640  $\pm$  0.0049 & MJD   \\
$a_{\rm x}\sin i$                   &   115.84  $\pm$ 0.32 & lt-sec     \\
$e$             &    0.09848  $\pm$  0.00042 &     \\
$\omega$  &   286.44  $\pm$  0.16 & degrees      \\
$f(M)$             &   2.138 $\pm$  0.015 & M$_\odot$    \\
$\chi^{2}$                      &    46.6 / 43 dof &              \\

\tableline
\end{tabular}
\end{center}
\end{table*}

The frequency history, pulsed flux and ephemeris for this source and all other sources monitored by the GBM Pulsar Monitoring team may be found at the GBM pulsar website\footnote{\url{http://gammaray.msfc.nasa.gov/gbm/science/pulsars.html}}.  See Appendix A for a detailed analysis of GBM energy dependent pulse profiles and their comparison with \textit{NICER}.

\section{Discussion}\label{sec:discuss}

\subsection{Pulse profile evolution at different accretion regimes}\label{subsec:regimes}

The amount of data that \textit{NICER}, \textit{Fermi} GBM and \textit{Swift} have accumulated on the outburst of Swift J0243.6+6124 is very large and it is not easy to understand every detail in light of our current understanding of the accretion flows onto magnetic neutron stars. That the neutron star is magnetic is clear from the fact that we see distinct pulses at a discrete frequency with clear indications of spin period changes over the course of the outburst. And further, those spin period changes appear to be correlated with the luminosity (thus the accretion rate onto the neutron star) lending confirmation to the idea that we are seeing rapid spin-up of a neutron star in a close orbit around a Be early-type star.
The observation of a spin-up torque that is correlated with the luminosity is a clear indication that the accretion is mediated through an accretion disk. More quantitatively, an accretion disk will form around the pulsar if the matter in the Be-star's circumstellar disk has a net angular momentum greater than the angular momentum of matter being spun around by the rotating magnetosphere. We can calculate the radius of the Be star's circumstellar disk  $R_{\rm disk}$ using the relation from \citet{Hanuschik1989} that relates it to the measured  H$\alpha$ equivalent width, $EW=-10.3\mbox{\AA}$ from \citet{Kouroubatzakis_2017}, to obtain $R_{\rm disk}\approx 11 R_{\rm c}$.  Then using this value in the criterion from \citet{Klus2014} (see also \citealt{Shapiro1976,Wang1981}) along with parameters of the system (i.e., companion mass and radius of $\sim 16M_\odot$ and $\sim 7R_\odot$, respectively, from \citet{Bikmaev+17}), a range of mass accretion rates $\dot{M}\sim 10^{-11}-10^{-8}M_\odot$~yr$^{-1}$, and an assumed magnetic field for the neutron star in the range $B\sim 10^{12}-10^{14}$~G, we find that matter accreted onto the pulsar from the circumstellar disk of the Be star first forms an accretion disk around the pulsar.

Early in the outburst, before approximately MJD~58033, the pulse profile is complex, but dominated by a single asymmetric peak (see Fig.~\ref{fig:lcandprofiles} inset a).
A remarkable change occurs near MJD~58037, in that the pulse shape transitions to a single simpler peak, both in the \textit{NICER}  (Fig.~\ref{fig:lcandprofiles} inset b) and GBM energy bands (See Appendix, Fig.~\ref{fig:A1}).
Then, as the accretion luminosity takes off, a clear two-peak structure emerges (Fig.~\ref{fig:lcandprofiles} inset c) and dominates the emission pattern at all energy ranges (See also Fig.~\ref{fig:A3}).
This two-peak flow arrangement lasts through the peak luminosity of $ \sim1.8\times 10^{39}$ erg s$^{-1}$ at MJD~58064  (Fig.~\ref{fig:lcandprofiles} insets d, e, \& f) and as the luminosity goes down below $ \sim 2 \times 10^{38}$ erg s$^{-1}$. Once MJD~58100 is past, both the \textit{NICER}  (Fig.~\ref{fig:lcandprofiles} inset g) and GBM (Fig.~\ref{fig:A4}) pulse profiles appear to go back to a single-peak configuration.
The pulses are very broad at this point and it is not clear if the emission is from one pole or two poles that are essentially blended together in the light curve.
Later on, past MJD~58135 the accretion configuration changes again in that now the soft \textit{NICER} band stays single-peaked  (Fig.~\ref{fig:lcandprofiles} inset h) while the higher energy bands  return to a complex structure dominated by a single asymmetric peak. At the same time, past MJD~58135 GBM gets the double-peaked pulse profile structure back (Fig.~\ref{fig:A5}).

Such extreme luminosity-dependent character of the pulse profiles is usually interpreted in terms of a change in the accretion regime.
At lower luminosity the flow may be stopped primarily by coulomb collisions between particles as suggested by \cite{Basko+Sunyaev76} \citep[see also][]{Becker+12}.
In this regime, the flow stopping region is located near the neutron star surface where the plasma density is very high while the emission from the stopping region may be dominated by a pencil beam component.
However, once the accretion rate goes above a certain critical value, radiation pressure becomes the dominant stopping mechanism via photon scattering off of the electrons in the accretion flow.
This is when the radiation-dominated shock transition begins to work its way up the magnetic column, and an accretion column emerges, while a fan-beam emission pattern escaping the accretion column walls dominates the emission.

The critical luminosity $L_c$ that marks the transition between the coulomb dominated and radiation-pressure dominated accretion flow, that is the transition from the sub-critical to super-critical accretion regime, has been calculated by \citet{Becker+12} and \citet{Mushtukov+15}.
The computation of the exact value of critical luminosity strongly depends on a number of parameters that reflect the accretion physics and are currently not fully understood or constrained, such as the geometrical parameter $\Lambda$ characterizing whether the NS accretes from a wind
or from a disk, the shape of the photon spectrum inside the column, and the magnetic field strength $B$.
However, assuming canonical neutron star parameters, the standard critical luminosity is of the order of $L_c\sim10^{37}\,$erg\,s$^{-1}$.
This luminosity level is reached around MJD~58029 and 58166, very early and very late in the outburst, respectively (see Table~\ref{table:nicerobs}). In fact, the above described pulse profile changes show clear transitions around a much higher luminosity, $\sim 10^{38}\, $erg\, s$^{-1}$, around MJD~58037 and 58135, suggesting a much higher than typical value for the critical luminosity.
This finding is further corroborated by the spectral analysis and the study of the pulsed fraction discussed in the next sections, where additional observational evidence is gathered in support of the accretion regime transition scenario, and to further constrain the value $L_c$ of the critical luminosity.

\subsection{Hardness ratio evolution}\label{subsec:hardness_discussion}

Fig.~\ref{fig:soft_color} shows the hardness-intensity diagram for both the \textit{NICER} and GBM energy bands throughout the entire outburst of Swift~J0243.6+6124.
This diagram represents a model-independent way to probe the correlation between the spectral hardness and the observed source intensity, which has already been demonstrated for a number of accreting pulsars (e.g., \citealt{Reig+13}).
However, the exact mechanism that leads to the spectral hardness dependence on flux is not yet clear.
It is generally accepted that at the sub-critical regime ($L<L_c$), when the accretion rate grows the Coulomb layer that halts the accreting matter is pushed down into the accretion structure, where the electron gas becomes denser and hotter.
Within this scenario, radiation is scattered up to higher energies via the inverse Compton effect, and a harder spectrum emerges. Super-critical sources ($L>L_c$) show the opposite behavior, that is a spectral softening at higher flux levels.
This can be understood in the framework of two different scenarios, both of them involving the rise of an accretion column.
On the one hand, the turn-over to softer spectra at higher luminosity is due to the plasma temperature decrease upwards in the column \citep{Basko+Sunyaev76,Becker+12} which leads to the emission of softer photons.
On the other hand, the taller column leads to a lesser fraction of radiation reflected by the neutron star atmosphere (a process that induces spectral hardening), and therefore to a softer spectrum \citep{Postnov+15}.

Even if the exact mechanisms responsible for the spectral dependence on flux are not yet fully understood, \citet{Reig+13} showed that the turn-over present between the HB and the DB is happening at a luminosity level comparable to the critical luminosity.
Therefore, deriving the source luminosity at the turn-over level is of key importance.

In the \textit{NICER} energy bands, the hardness ratio shows a hint of a turn-over near the beginning of the outburst, where a transition occurs from the HB to the DB (see Fig.~\ref{fig:soft_color}).
The farthest-right SC (soft color; Section~\ref{subsec:hardness} for \textit{NICER} occurred on MJD 58031.4.
Recognizing that \textit{NICER} observations are sparse and there is possible jitter in the SC value based on other sources in \citet{Reig+13}, we conservatively estimate that this turn-over occurred sometime between MJD 58031 and MJD 58037.
On the other hand, the red diamonds denoting the outburst decay in Fig.~\ref{fig:soft_color} show that if indeed we saw the turn-over during the outburst rise, we missed it on the decay.
The more frequent observations obtained during the rise help to constrain the decay turn-over between MJD 58145 and MJD 58162.
Comparing those events with our spectral results (see Sect.~\ref{subsec:spectral} and Table~\ref{table:nicerobs}), we derive a luminosity for the turn-over in the range  $ L_{0.1-10\,{\rm keV}}\sim (0.2-1.1) \times 10^{38}$ ergs s$^{-1}$.
We note that \citet{Jaisawal_2018} measured $ L_{3-70\,{\rm keV}}\sim 5.1\times 10^{37}$ erg s$^{-1}$ (corrected to d=7 kpc) with \textit{NuSTAR} on MJD 58031, thus \textit{NICER} and \textit{NuSTAR} derived luminosities are consistent within a factor of $\sim 2$.
As a comparison, for typical values of the neutron star parameters, \citet{Becker+12} calculate the critical luminosity as
\begin{equation}
L_{\rm c}\sim1.5\times10^{37}\,B_{12}^{16/15}\, {\rm erg}\,{\rm s}^{-1}
\label{eqn:lcrit}
\end{equation}
where $B_{12}$ is the magnetic field strength in units of $10^{12}\,$G, which is consistent with the value obtained in this work with \textit{NICER}, if the magnetic field is higher than the typical $\sim 10^{12}$G.

On the other hand, Fig.~\ref{fig:soft_color} shows that in the \textit{Fermi} GBM energy bands, the turn-over takes place at $\sim2\,$photons cm$^{-2}$ s$^{-1}$ keV$^{-1}$, corresponding to MJD $58040-58043$ and $58098-58105$, for the rising and the decay stages of the outburst, respectively.
GBM pulsed fluxes at the turn-over can be converted into a critical luminosity value by a simple scaling of the \textit{NuSTAR} observed luminosity.
In addition, as a consistency check, we also converted GBM pulsed fluxes into luminosity by comparing them with the \textit{Swift} BAT count rates in the same time windows, and using a conversion factor of $1.54\times10^{-7}\,$erg cm$^{-2}$\,cnt$^{-1}$ \citep{Doroshenko_2017}.
In the former case, the critical luminosity that results is  $ L_{3-70\, {\rm keV}} \sim (2.6-3.4)\times10^{38}\,$erg s$^{-1}$ for the rising stage of the outburst, and  $ L_{3-70\, \rm{keV}} \sim (2.2-3.4)\times10^{38}\,$erg s$^{-1}$ for the decay.
In the latter case, the resulting critical luminosity is $ L_{15-50\,{\rm keV}} \sim (3.2-4.3)\times10^{38}\,$erg s$^{-1}$ for the rising stage of the outburst, and  $ L_{15-50\, \rm{keV}} \sim (3.8-4.8)\times10^{38}\,$erg s$^{-1}$ for the decay.
In any case, the turn-over in the GBM energy bands happens at significantly higher luminosities than \textit{NICER}'s.
To the best of our knowledge, we excluded any instrumental origin for such an effect, thus concluding that the dependence of the turn-over luminosity on the energy band represents a physical effect.
An energy- and luminosity-dependent hardness ratio could, in fact, reflect a dependence of the spectral cutoff energy on the luminosity.
Previous works showed that, when the spectra of accreting pulsars are fit with a cutoff power-law model, the cutoff energy is directly correlated with the power-law photon index and, at the same time, inversely/directly correlated with the luminosity for the sub-/super-critical accretion regimes, respectively \citep{Ferrigno+13,Mueller+13,Reig+13,Malacaria+15}.
Since the cutoff energy is indicative of the electron temperature, its variability can be interpreted as the result of a Compton cooling efficiency dependence on the luminosity and the accretion regime.
Furthermore, we note that the typical cutoff energy in accreting X-ray pulsars is $E_{cut}\sim15-20\,$keV, that is around the GBM bands used to constrain the turn-over.
Following this qualitative scenario, the combination of luminosity-dependent cutoff energy and photon index can lead to a difference in the turn-over luminosity measured in different energy-bands.
However, we note that the energy bands used here to measure the turn-over can be affected by other factors, such as the Fe K line complex around $6-7\,$keV and the so-called ``10 keV feature'' \citep{Coburn+02}, commonly observed among accreting X-ray pulsars.

Considering these findings, we estimate a conservative value for the critical luminosity bracketed by the values separately derived with \textit{NICER} and GBM data, that is $(0.2-4.8)\times10^{38}\,$erg s$^{-1}$.
Given these bounds, the turn-over luminosity can be used to constrain the surface magnetic field value.
Following the approximate equation for critical luminosity provided by \citet{Becker+12} and cited above,
we constrain the magnetic field to lie within the range $ (0.2-2.6)\times10^{13}\,$G.

\subsection{Constraints on the magnetic field from the QPO-like feature}

In the power spectra, a QPO-like feature at 50--70 mHz is found in the 0.2--12 keV band with \textit{NICER} early (MJD 58029--58031) and late (MJD 58166--58176) in the outburst. This feature can be used to estimate the magnetic field if we assume that the QPO frequency $\nu_{\rm QPO}$ is equal to the Keplerian orbital frequency $\nu_{\rm K}$ at distance $r_{\rm K}$, where
\begin{equation}
r_{\rm K} = \left[ \frac{GM}{(2 \pi \nu_{\rm K})^2}\right]^{1/3}.
\end{equation}
Next we assume that the magnetospheric radius is equal to the Alfven radius $r_{\rm A}$, where
\begin{equation}
r_{\rm A} = \left(\frac{\mu^4}{8G M \dot{M}^2}\right)^{1/7}
\end{equation}
and $\mu \approx BR^3$ is the magnetic dipole moment (see, e.g., \citealt{2002apa..book.....F}).
Setting $r_{\rm A} = r_{\rm K}$ yields
\begin{equation}
\mu = 4 \times 10^{31} {\rm G\ cm}^3 M_{1.4}^{5/6}\dot{M}_{-8}^{1/2} \left(\frac{\nu_{\rm K}}{50\,{\rm mHz}}\right)^{-7/6},
\end{equation}
where $M_{1.4} = 1.4\,M_{\odot}$ and $\dot{M}_{-8} = 10^{-8}\,M_{\odot}$ yr$^{-1}$. Finally we take $R = 10$~km to obtain
\begin{equation}
B = 4\times 10^{13}\,{\rm G}\ M_{1.4}^{-5/6} R_6^{-3} \dot{M}_{-8}^{1/2} \left(\frac{\nu_{\rm K}}{50\,\rm{mHz}}\right)^{-7/6}.
\label{eqn:bfield}
\end{equation}
When the QPO was detected, the 0.1--10 keV luminosity was $(1.2-2.0) \times 10^{37} (d/7 \rm{kpc})^2$ for MJD 58029-58031. This corresponds to a mass accretion rate of $\dot{M} = (0.9-1.7) \times 10^{-9} M_{\odot}$ yr$^{-1}$. Substituting this rate and the QPO frequencies of 50 and 70 mHz respectively into Equation~\ref{eqn:bfield} yields $B\sim 1\times 10^{13} (d/7\,{\rm kpc})$ G. Substituting this value back into Equation~\ref{eqn:lcrit}, we obtain a critical luminosity of $L_{\rm c} \sim 1.7 \times 10^{38}$ erg s$^{-1}$ $(d/7\,{\rm kpc})^{16/15}$, consistent with and better constrained than that from the hardness ratio calculations.

\subsection{Pulsed fraction evolution}\label{subsec:pulse_fraction}

Another indication of changes happening at the times corresponding to the turn-over or, equivalently, to the critical luminosity, is found in the analysis of the pulsed fraction evolution (Fig.~\ref{fig:nicer_fraction}).
At the earliest, rising stage of the outburst, the pulsed fraction decreases with increasing flux, down to a local minimum around MJD $58037-58042$.
The pulsed fraction then rises up to a maximum around the outburst peak, then decreasing again during the decay stage, down to a second local minimum at MJD $58099-58106$, after which a new increase takes place, somehow symmetrically to the first half of the outburst. Above the critical luminosity, the pulse fraction clearly increases with increasing luminosity (See Figure~\ref{fig:nicer_fraction}, right panel), below the critical luminosity, especially as the outburst declines, the relationship is less clear.
Once again, the local minimum occurrence times coincide with the turn-over times, and therefore with the critical luminosity, with the pulsed fraction changes closely tracking the pulse profile changes.

The exact mechanism of the pulsed fraction dependence on the luminosity is not yet clear.
To complicate the matter further, the dependence is not unique: some sources exhibit pulsed fraction decreases with increasing luminosity (e.g., 4U~0115+63, \citealt{Tsygankov+07}; EXO~2030+375, \citealt{Epili+17}), while others show the opposite trend along with a non-monotonic evolution of the pulsed fraction with luminosity (see, e.g. V~0332+53, \citealt{Tsygankov+10}; SMC~X-2, \citealt{Jaisawal2016}).
Our observations suggest that the two opposing behaviors, that is the negative and positive dependence of the pulsed fraction on luminosity, are distinctive of sub- and super-critical accretion regimes, respectively.
However, we note that this is a simplistic scenario, and that more-detailed models need to be considered to take into account the diverse behavior of the pulsed fraction dependence on luminosity observed in different sources and at different accretion regimes.

\subsection{Swift J0243.6+6124 as the first known Galactic ULX Pulsar}

Ultraluminous X-ray sources (ULX) have been identified in a number of galaxies. A common definition is a luminosity $> 10^{39}$ erg s$^{-1}$ \cite{Kaaret2017}. At first, some of these systems were thought to contain intermediate mass black holes, $\sim 100-10000 M_{\odot}$ \citep{Sutton2012}. In 2014, the first ULX pulsar, M82 X--2, was discovered with \textit{NuSTAR} \citep{Bachetti2014}, with $L_{\rm 0.3-10 keV} = 1.8 \times 10^{40}$ erg s$^{-1}$ and a pulse period of 1.37 s. Since then, several other ULX pulsars have been discovered, including NGC 7793 P13, with a 0.42 s period and an observed peak luminosity of $\sim 10^{40}$ erg $s^{-1}$ \citep{Furst2016, Israel2017b}, and NGC 5907 ULX \citep{Israel2017a}, with a period of 1.13 s and a peak luminosity of $\sim 10^{41}$ erg s$^{-1}$. All three of these systems show rapid spin-up, have sinusoidal pulse profiles, and relatively low pulsed fractions that increase with increasing energy. They exhibit both bright and faint phases with luminosities of $\sim 10^{40-41}$ erg s$^{-1}$ and $\sim 10^{38}$ erg s$^{-1}$, respectively \citep{Kaaret2017}. All three systems were known as ULX sources before their identification as pulsars. Recently, a fourth ULX pulsar, NGC 300 ULX1, with an initial period of 32 s, rapidly spinning up, and a peak luminosity of $4.7 \times 10^{39}$ erg s$^{-1}$, was discovered \citep{Carpano2018}. This pulsar has a potential cyclotron feature at $\sim 13$ keV, suggesting a magnetic field of $B \sim 10^{12}$ G. \textit{Chandra} observations show a potential proton resonance scattering feature at 4.5 keV in M51 ULX8 that implies a neutron star surface magnetic field of $B \sim 10^{15}$ G \citep{Brightman2018}, although no periodicity has been reported in this case.

With a peak 0.1--10 keV luminosity of $2 \times 10^{39}$ erg s$^{-1}$, Swift J0243.6+6124 crosses the threshold for a ULX pulsar. Incorporating the \textit{Gaia} distance ranges, the dominant error on the luminosity, results in a peak luminosity of $(1.2-2.6) \times 10^{39}$ erg s$^{-1}$ for the \citet{Bailer-Jones2018} $\pm 1\sigma$ range of 5.7-8.4 kpc, and $(1.5-5.6) \times 10^{39}$ erg s$^{-1}$ for the 5-95\% confidence range of 6.3-12.3 kpc (M. Ramos, private communication), all above the $10^{39}$ erg s$^{-1}$ threshold for ULXs.  Swift J0243.6+6124 also shows rapid spin-up, exhibits an increasing pulsed fraction with energy, and has a relatively short spin period of $\sim 9.8$ s. \citet{Mushtukov2017} describe an optically thick envelope around accreting ULX pulsars that  produces a smooth pulse profile for $L>10^{39}$ erg s$^{-1}$ with a pulsed fraction that increases with energy. This optically thick envelope masks the observer's view of the neutron star surface. The profiles from Swift J0243.6+6124 are quite smooth at high luminosities but are more complex than the simple single peaked profiles observed from the other ULX pulsars, suggesting a different viewing geometry or that Swift J0243.6+6124 may be close to the threshold for this effect, similar to SMC X-3 \citep{Koliopanos+18}. \citet{Mushtukov2015} proposed that ULX sources and accreting pulsars are connected, with the brightest ULX pulsars having magnetar-like fields of $\sim 10^{14}$ G. They define an admissible luminosity range for accreting pulsars and ULX pulsars alike, where the maximum accretion luminosity can be approximated by $L_{\rm acc} \approx 0.35 B_{12}^{3/4} \times 10^{39}$ erg s$^{-1}$, for $10^{13}$ G $< B < 10^{15}$ G, shown in Figure~\ref{fig:ulx} as the solid dark line. They also define a minimum luminosity (denoted by a dashed line), based on the propeller effect which depends on the spin period of the pulsar. We demonstrate that Swift J0243.6+6124 is consistent with this picture, based on the luminosities measured with \textit{NICER} (keeping in mind that the total accretion luminosity is likely at least a factor of 2 higher to incorporate flux $>10$ keV) and  our estimate of Swift J0243.6+6124's magnetic field based on our critical luminosity estimate from the hardness ratios, pulse fraction, and pulse profiles, and  the magnetic field estimate from the QPO measured in with \textit{NICER}.

\begin{figure}
\plotone{J0243_08.pdf}
\caption{Adapted from \citet{Mushtukov2015}. The solid black line represents the maximum luminosity for magnetized NSs as a function of magnetic field strength. The dotted line and shaded region above it indicates the upper limit where the spherization radius is smaller than the magnetospheric radius.  Dashed lines represent the lower limit on the X-ray luminosity due to the propeller effect. The dash-dotted line represents the critical luminosity function. The range of observed luminosity for Swift J0243 (for a distance of 7 kpc) is indicated by an orange vertical dashed-line at the magnetic field value derived from the QPO, and the blue-grey shaded box indicates the estimated range of magnetic field values derived from the critical luminosity (see text Sect. 5.2 and 5.3). For comparison, Eddington luminosity (for a 1.4 $M_{\odot}$ NS) is also indicated (long dash-double dotted horizontal turquoise line). \label{fig:ulx}}
\end{figure}

\section{Summary}\label{sec:summary}

Swift J0243.6+6124 underwent a giant outburst lasting about 150 days from October 2017 to February 2018, peaking well above Eddington luminosity at $ 1.8 \times 10^{39}$ erg s$^{-1}$ (0.1--10 keV).  This luminosity places it in the ULX category, making it the first known galactic ULX pulsar. Strong spin-up torques, high luminosities, and inferred mass accretion rates indicate that the pulsar was accreting from a disk, not a wind.

Near a luminosity of $10^{38}$ ergs s$^{-1}$ we identify a transition indicated by the following observations:
\begin{itemize}
\item{The pulse profiles (0.2--100 keV) evolve from single peaked to two distinct peaks in both \textit{NICER} and GBM data.}
\item{The pulsed fraction reaches a minimum and then increases with increasing intensity. Increases in pulsed fraction with energy are also seen, with the fraction approaching 100\% in the 8--12 keV band at the outburst peak.}
\item{The power spectra evolve with increasing intensity, with a QPO-like feature and a broad high frequency peak below $L \sim 10^{38}$ erg s$^{-1}$, becoming consistent with a single power-law in the brightest part of the outburst.}
\item{The hardness ratios become anticorrelated with intensity above $L \sim 10^{38}$ erg s$^{-1}$ in both \textit{NICER} and GBM data.}
\end{itemize}
All of these behaviors repeat as the source passes through the same luminosity ranges during the outburst decay. We interpret this as evidence for two accretion regimes that depend on
the accretion luminosity. The first regime shows a somewhat harder spectrum in the \textit{NICER} energy range and gives way to a somewhat softer spectrum as the source luminosity goes above $ \sim 10^{38}$ erg s$^{-1}$. We have identified the transition between these two regimes as the
accretion structure on the neutron star surface transitioning from a Coulomb collisional stopping mechanism to a radiation-dominated stopping mechanism and have estimated that this occurs at a critical luminosity of $L_c = (0.2-4.8) \times 10^{38}$ erg s$^{-1}$, based on hardness ratios, and $L_c \sim 1.7 \times 10^{38}$ erg s$^{-1}$,  using the QPO features to estimate the magnetic field.
This lends support to models for the accretion flows put forward by \citet{Becker+12} and \citet{Mushtukov+15}. A critical luminosity of $~\sim 10^{38}$ erg s$^{-1}$ is the highest measured to date, suggesting a higher than average magnetic field of $\sim 10^{13}$ G for Swift J0243.6+6124.

\acknowledgements
This work was supported by NASA through the \textit{NICER} mission and the Astrophysics Explorers Program. This work was also supported by NASA through the Fermi Guest Investigator Program. GKJ acknowledges support from the Marie Sk{\l}odowska-Curie Actions grant no. 713683 (H2020; COFUNDPostdocDTU).
This research has made use of data and software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory.
Work at the Naval Research Laboratory by MTW, PSR, and MK was supported by NASA.
CM's research was supported by the NASA Postdoctoral Program at the MSFC, administered by USRA.

\bibliographystyle{aasjournal}


text:
Home Special News Corruption Scandal Hits Macron's Chief of Staff
Corruption Scandal Hits Macron's Chief of Staff
By Sam J. KohnJun 04, 2018, 16:55 pm0
The French Prosecutor's Office for Financial Infringements launched an investigation against the chief of staff of the Elysée Palace. The prebe was opened after the public organization Anticor accused Alexis Kohler, 44, of corruption, as reported by AFP.
Anticor condemned Kohler's family ties with the Italian-Swiss maritime transport company Mediterranean Shipping Company (MSC), a major customer of the French shipyard STX France. The complaint stated that Kohler, from 2010, is on the board of directors of STX France and "could not help knowing" that the MSC was founded and managed by his mother's cousins.
The anti-graft organization described Kohler's actions as "passive corruption" and "abuse of power." As the RTL radio station notes, MSC received a lot of government contracts from the French authorities and participates in the work of the largest shipyards in Saint-Nazaire.
The Elysee Palace stated that Kohler no longer participates in the work of the MSC, adding that he fully complied with the law. "Mr Kohler will provide all the documents needed to show that his behavior respected the rule of law at all times," Elysee Palace said.
In May 2017 Emmanuelle Macron took office as President of France. Then Kohler was appointed secretary general of the Elysee Palace. Previously, he worked in the Directorate of the Tax Service of France and the International Monetary Fund.
Kohler served as director of the Cabinet of the Minister of Economy and Finance in the government of François Hollande, the predecessor of Macron.
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Baldwin Bombers Youth Football
The Baldwin Bombers is a travel youth football organization established in 1966, servicing kids from ages 5 to 13. We currently play in the Nassau County Youth Football League.
We are a USA Football Heads Up Certified organization, that services the children of Baldwin, Oceanside, Freeport, Rockville Centre, South Hempstead and other surrounding areas. All of our coaches are Heads Up Certified and use their training to provide a safe environment that enhances the teaching of the game of football, and to instill the values of teamwork, cooperation and sportsmanship.
Some notable former players include U.S. Skier and Olympic Silver Medalist Devin Logan UFC Champion Chris Weidman and current NFL players Greg Van Roten and Stephen Bowen.
We encourage active participation by all parents. If you are interested in volunteering, please let us know.
WHO CAN PLAY
We are open to all athletes ages 5 to 13, from Baldwin and any other town WITHOUT a NCYFL team membership. There are eight age divisions, one for each age.
NEW WEIGHT CLASSES (Starting 2013)
AGE ROSTER* / GAME WEIGHT
5-6 Year Olds Special Rules Apply (Contact Your Head Coach)
7 Year Olds 85 / 95 lbs
8 Year Olds 95 / 105 lbs
9 Year Olds 105 / 115 lbs
10 Year Olds 115 / 125 lbs
13 Year Olds No weight limit
* - Roster Wt. is the maximum weight allowed to make the Team's Roster at the League's official weigh-in for our organization (usually around the last week of Aug., unless an early weigh-in is requested. See your Head Coach for details).
If a player's weight exceeds their age division's maximum Roster Weight, they are permitted to "play up" one age division only.
Cash, Check, CC are accepted. All players must be registered to practice & play.
Registration Does Not Include a New Helmet
Full Refunds will be provided prior to the first practice.
50% Refund will be provided after August 1st up to August 15th
No refund will be provided after August 15th
If equipment that we provided to your child is not returned by February 1st of the year following the season, you will be billed $100.
TO OUR ALUMNI.....
Do you have an old picture or story about your days playing with the Bombers or as a parent to a Bombers player?
Please share it with us by sending it to [email protected].
Remember.......Once a Bomber, Always a Bomber!
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text:
A Better Day A-Coming with Robin & Linda Williams
July 8, 2021 Written by missjill
Robin & Linda Williams
Send A Message of Hope In Song: A BETTER DAY A-COMING
New album out on July 30, 2021
"… vocally and instrumentally, the Williamses combine impeccable musical discipline with a bare simplicity and an utter lack of pretension." – The New York Times
A Better Day A-Coming, the 24th album from Robin & Linda Williams, uses the prism of the past to convey a message just as suited to the present. This album was recorded from August 2019 to August 2020 in their living room with its 10-foot ceilings and plaster walls and their good friend Kevin McNoldy assisting as engineer and co-producer. A Better Day A-Coming will be released on July 30, 2021, with tour dates as a duo and with their longtime friend Garrison Keillor.
This album marks the culmination of a series of active transitions since their last release in 2013; a re-structuring of their personal and professional lives, coming to a head with their leaving their Shenandoah Valley, Virginia farmhouse where they'd lived for 42 years and moving to town. After more than 25 years, they dropped their road band and returned to their roots to working as a duo. Simultaneously, the adage that "no one gets by forever without the aid of medical professionals" became a reality.
Though their forward momentum of life on the road began to be interrupted, their creative juices suffered no such interference, and the songs kept flowing. While off the road, they used this period to write and start this new project. During the first session, the couple laid down the primary tracks and had bassist Mark Schatz and multi-instrumentalist David McLaughlin come by the house for the second. The digital files were then sent to Richie Dworsky (Hammond B3 organ), Kevin Maul (dobro, pedal steel), and Patrick McAvinue (fiddle) to add their parts via remote.
Then came the Covid19 Pandemic of 2020 and months of seclusion, which put the brakes on the couple. But Robin and Linda look back at those months of isolation as "the gift of time." "With no road work taking us away from home and no time crunch pressuring us, we could focus on the songs and tweak the mixes and sequencing to the point of really enjoying what we heard. Now we can't wait for others to hear it as well," Robin and Linda explained.
After the hundreds of thousands of miles they've traveled, after the thousands of nights they have performed -plus the hundreds of songs they have recorded over a more than 40-year career, one thing's for sure, Robin and Linda Williams honestly and authentically present their music. With them, it's all about the song, whether it's one they've written or chosen from another source. Songs on A Better Day A-Coming cover topics of history, small-town gossip, big city living, and all the characters met along the way. A couple of covers of note, "Tower Of Song" from Leonard Cohen, "Leaving Home" an old Charlie Poole favorite, and one from Scott Miller, "Someday Sometime."
No Depression magazine praises Robin and Linda Williams for creating "music that is both comfortable and thoughtful – a rare combination that explains why and how the Williamses are able to keep on an even keel while musical trends come and go. They don't play at being country – they are country."
The Williamses have built their career like an old house, with a firm foundation, thick walls to withstand the weather, and a lot of love and affection, and it shows. "We think the release of this recording brings a transitional period to an end. We are comfortable in our new home, we are healthy, and we are having fun playing as a duo. But the CD is also a transition all its own which leads us forward to A Better Day A-Coming."
WITH THE GHOSTS OF LEVON HELM AND JIM DICKINSON LOOKING ON:
Daryl Wayne Dasher – Honky Tonk Ways – New album out September 10, 2021


text:
Blotter for Saturday, January 25 through Sunday, January 26
SAT., JAN. 25
Adam M. Roach, 22, of Toledo, was arrested for theft and cited for abuse of harmful intoxicants and criminal damaging within the 100 block of W. Gypsy Lane Rd. He was lodged in the Wood County Justice Center.
Brice S. Imwalle, 22, of Bowling Green; and Grant E. Klosterman, 21, of Bowling Green, were both cited for disorderly conduct/nuisance party within the 300 block of N. Enterprise St. Joshua D. Meyer, 19, of Russia, Ohio, was cited for disorderly conduct/public urination.
SUN., JAN. 26
Christopher Robert Novak, 19, of Bowling Green; Timothy Glenn Ohlemacher, 18, of Sandusky, Ohio; and Nathanael D. Viereck, 18, of Bowling Green, were all cited for open container and underage possession of alcohol near Lot 6 downtown. Gabriel Tienzhu Colwell, 19, of Richmond Heights, Ohio, was cited for underage/under the influence of alcohol.
Logan Alexander Walker, 21, of Petersburg, Virginia, was arrested for criminal trespass and disorderly conduct/unable to care for self within the 400 block of Frazee Ave. He was lodged in the Wood County Justice Center.
Eric D. Barga, 22, of Bowling Green, was cited for disorderly conduct/public urination within the 200 block of N. Prospect St.
Ranon L. Chapman, 21, of Bowling Green, was cited for drug paraphernalia within the 400 block of Frazee Ave.
Mario A. Mockus, 20, of Bowling Green, was cited for disorderly conduct/public urination within the 100 block of E. Court St.
Shawn Gregory Fulford, 19, of Bowling Green; and Gerardo Cacho Samonte Jr., of Bowling Green, were both cited for disorderly conduct/public urination within the 500 block of E. Wooster St.
Niall J. McNamara, 19, of Bowling Green, was cited for disorderly conduct/public urination within the 300 block of N. Main St.
Complainant reported that sometime during the night an unknown person stole her debit card, $10 in cash and lip gloss within the 100 block of N. Main St.
Complainant reported an unknown person had punched out the driver side light of their vehicle within the 200 block of E. Merry Ave. Damage is estimated at $250.
Complainant reported the theft of his laundry within the 700 block of S. Main St.


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//     FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
//     AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
//     LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
//     OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
//     THE SOFTWARE.
// </copyright>
// --------------------------------------------------------------------------------------------

namespace Effort.DataLoaders
{
    using System;

    /// <summary>
    ///     Defines functionality for converting arbitrary values to a specified type.
    /// </summary>
    internal interface IValueConverter
    {
        /// <summary>
        ///     Converts the specified value to comply with the expected type.
        /// </summary>
        /// <param name="value"> The current value. </param>
        /// <param name="type"> The expected type. </param>
        /// <returns> The expected value. </returns>
        object ConvertValue(object value, Type type);
    }
}

redpajama_set_name: RedPajamaGithub


text:
Q: Getting input without a linebreak I'm writing a program which will be doing manipulation of matrices. I want the user to be able to enter data into a matrix by typing it in one row at a time. So it will first ask for the value in row: 1, column: 1. The user will type in the appropriate value, and then press enter, after which he will type in the value for row: 1, column: 2.
This is the trick: I want the console to not enter a new line when the user presses enter. Instead, I want it to simply insert a tab character. Is this possible?
Thanks so much.

A: Yes, it's possible. You'll need to use a console/terminal library, though. Ncurses for *nix, wincon (part of the Windows API; you can just #include windows.h to use it)... There are a lot of choices out there.
The actual algorithm will simply be checking the characters that are sent as key events/using the getkey() equivalents of the various libraries, outputting the inputted characters to the console if the key pressed is not ENTER but would still cause a character to be echoed to the screen (i.e. function keys, caps lock, shift, etc. wouldn't cause any echoing to the console or terminal window) and then outputting \t if the key pressed is indeed ENTER.

A: Set the cursor position back up to the previous line. In Windows, you can use SetConsoleCursorPosition().

A: It's not exactly what you wanted, but you could get the same effect by using getline to obtain the row input all on one line, and then use std::stringstream to parse out the values.
 std::string row;
 getline(cin,row);
 std::stringstream ss(row);
 int j=0,i=currentrow;  //put this in a loop over your rows
 int input; //or float, double, whatever
 while(ss >> input)
 {
      mat[i][j] = input;
      j++;
 }

redpajama_set_name: RedPajamaStackExchange


text:
Vicksburg ist der Name mehrerer Städte in den Vereinigten Staaten

 Vicksburg (Arizona)
 Vicksburg (Colorado)
 Vicksburg (Florida)
 Vicksburg (Indiana)
 Vicksburg (Kentucky)
 Vicksburg (Michigan)
 Vicksburg (Mississippi)
 Vicksburg (Pennsylvania)
 Vicksburg Junction (Arizona)

Feldzüge und Schlachten:
 Erster Vicksburg-Feldzug, ein Feldzug des amerikanischen Bürgerkrieges, 2. November 1862 bis 29. März 1863
 Zweiter Vicksburg-Feldzug,  ein Feldzug des amerikanischen Bürgerkrieges, 29. März bis 4. Juli 1863
 Schlacht um Vicksburg, eine Schlacht des amerikanischen Bürgerkrieges, 19. Mai bis 4. Juli 1863

Siehe auch:
 Vicksburg (Schiff), ein Passagierschiff der Dominion Line (1872)
 Vicksburg Bridge, Straßenbrücke der Interstate 20 über den Mississippi (1973)
 Old Vicksburg Bridge, kombinierte Eisenbahn- und ehemalige Straßenbrücke über den Mississippi (1930)

redpajama_set_name: RedPajamaWikipedia


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DEVELOPMENT MANAGER: Faction Projects Inc.
An office and retail development housing multiple public and private uses. The City of Revelstoke and Faction Projects worked collaboratively to facilitate this development, with the developer executing the delivery process and assuming the associated risks and responsibilities in exchange for the strata sale of approximately 50% of the development to the City of Revelstoke. The building addresses the need for visibility and presence and expresses the progressive nature of Revelstoke with a nod to the City's past.


text:
Celeste O'Connor Height, Weight, Age, Body Statistics, Biography, Facts
November 22, 2021 Cornytube Biographies 0
Celeste O'Connor Quick Info
Date of Birth December 2, 1998
Celeste O'Connor is a Kenyan-born American actor who has been cast in movies such as Irreplaceable You, Wetlands, Selah and the Spades, Ghostbusters: Afterlife, and Freaky.
Celeste O'Connor
Celeste O'Connor as seen in an Instagram post in November 2020 (Celeste O'Connor / Instagram)
Kenyan, American
Celeste O'Connor studied at Notre Dame Preparatory School and studied the violin and singing at Peabody Preparatory.
They then got enrolled at Johns Hopkins University as a public health and pre-medicine major. Celeste has also taken courses in Islamic studies.
Siblings – Celeste has a younger brother.
Celeste O'Connor has been signed with Authentic Talent and Literary Management, Talent Management Company, Brooklyn, New York, United States.
Celeste O'Connor as seen while taking a mirror selfie (Celeste O'Connor / Instagram)
50 kg or 110 lbs
Celeste O'Connor is of Kikuyu Kenyan descent.
They came out as non-binary in 2020.
Pouty lips
Celeste O'Connor in 2018 (Celeste O'Connor / Instagram)
Celeste O'Connor Facts
Celeste uses they/them pronouns.
Alongside their brother, Celeste grew up in Baltimore, Maryland.
They have been interested in the social determinants of health including food security, housing insecurity, and education.
They were cast as Teen Abbie in the 2018 romantic comedy-drama film Irreplaceable You. It was released by Netflix on February 16, 2018.
Alongside Lovie Simone, Jharrel Jerome, Gina Torres, and Jesse Williams, Celeste co-starred as Paloma Davis in the 2019 American drama film Selah and the Spades.
Celeste O'Connor has been an advocate for improving diversity and representation in the entertainment industry.
In 2020, they appeared as Nyla Chones, Millie's best friend, in the slasher comedy film Freaky. Their co-stars for the project included Vince Vaughn, Kathryn Newton, Katie Finneran, and Alan Ruck.
Celeste brought to life the character of Lucky Domingo, Trevor's co-worker and love interest, in the 2021 supernatural comedy film Ghostbusters: Afterlife, the sequel to Ghostbusters (1984) and Ghostbusters II (1989). The film stars Carrie Coon, Finn Wolfhard, Mckenna Grace, and Paul Rudd.
READ ALSO: Net Worth, Darrell Ward, Husband, Family, Wiki
Featured Image by Celeste O'Connor / Instagram
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AMDEF 2010: Celebrate a culture of the Arts.
AMDEF is Seattle's most influential annual spring arts exposition. This is an EXPLOSIVE event combining a variety of talent from the Northwest Art, Music, Dance, Entertainment, and Fashion communities. The eclectic nature of this event draws crowds from all genres, generating an exhilarating sense of forward movement within the Art Culture.
- Headlining! Truckasaurus, Mash Hall, CyberSutra, Ayron Jones, Shift Records.
- CyberSutra to debut Video Release of "Bad Self," performed and choreographed by Guilty Obsessions Burlesque.
- Fashion Designer Lina Zeineddine to debut new line.
- Joseph Madeo flying in to release new line of clothing, "Ether."
- Main Stage Event hosted by Nathaniel Luke of Chance Fashion and Deevious Decadence.
- Noel Austin performing during the release of his new fashion line, DNA.
Truckasaurus, Mash Hall, CyberSutra, Ayron Jones, Shift Records, (Lukki, Dubtek, Sublo, Bleed.) DJ's Martini and Punish. MC's Dough and Outrageous.
Lina Zeineddine, Joseph Madeo, Poirier Couture, Lisa Vian Hunter, Morgan Carson, Leile Smith, DNA, Sam St Michael, Natalia Makova.
Guilty Obsessions Burlesque, Super Sonic Theater, The Nines Improv Comedy, Ignition Fire Dance, Skin Deep Belly Dance, Noel Austin and the Pure Cirkus Freak's, Michele Frances, Pantera Blacksmith, Endor.
Artifakt Art, Jay Mason, Dana Peugh, Aaron Grosshauns.
Hang out with the talent! Access to the VIP lounge will only be granted to talent and staff during the event. VIP ticket's come with access to the VIP lounge and a bracelet for drink discounts.
Contact Ryan@ActiveEntertainmentsp.com for sponsorship or media information and further event details.
Related links to AMDEF Fashion Designers, Talent, and Sponsors.
Support a culture of the arts at Seattle's most influential annual spring arts exposition, AMDEF 2010.


1)Add three more powerful bow.
2)Add three more interesting scenes.
3) Optimizing the game to feel the real shooting experience.
The first Archer comes to your phone now!
Smooth game play, amazing graphics and awesome vivid sound, Archer gives you an epic sports experience just like in the wild.
Pull your bow down. Aim the arrow at the target by moving your hand on the screen. Confirm the target distance and wind. Watch out the moving target. Take off your finger to shot the arrow.
Three addictive modes here: Single Mode, VS Mode and Training Mode.
Challenge yourself with the Single Mode, enjoy the most crazy and thrilling sports feeling. Endless levels as well as incremental difficulties, witch gives you fantastic challenges. 10 point time bonus gives you a good chance to get higher scores. Try your best to hit the further level!
Not enough archer experience? Train yourself with the Training Mode and improve yourself to be a qualified archer athlete!
Any feedback please mail us, because we can't reply on comments. Thanks very much for all your support in our games!
AE Archer is completely free to play but some in-game items such as coins or diamonds will require payment. In-app purchases range from $1.99 to $99.99. You can control in-app purchases by enabling Wallet PIN. Wallet PIN can be found in your Windows Phone settings.
If you like archer games, you shouldn't miss this game.
Keep your nerve and aim your target. Let's begin the fantastic shooting!