\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage[round]{natbib}
\let\cite\citep




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[english]{babel}










\begin{document}

\title{Working Title: LMC X-1 with NuSTAR}



\author[1]{Brian Grefenstette}%
\affil[1]{California Institute of Technology (Caltech)}%


\vspace{-1em}



  
  \date{June 13, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Story board for this paper:

(1) NuSTAR observed LMC X-1 three times. Once on its own (40 ks), once
with XMM (60 ks), and once again on its own (40 ks).

(2) NuSTAR sees lots of variability in the source, with the
diskbb-related component apparently varying a lot during an observation,
while the \textgreater{}15 keV emission varies from epoch-to-epoch.

(3) During the XMM / NuSTAR observation we saw various ``flares'' here
meaning flux increasing by factors of 2x in both XMM and NuSTAR. For one
of these we see some evident of spectral evolution through the flare.

(4) In all three epochs, the epoch-integrated spectrum shows that the
source is in a different state compared to what Jack Steiner saw when
they measured the spin using Suzaku. We see a softer power-law component
in all three states (more like 3) compared to the 2.5 that Jack saw.~

~~~~Note: In general we haven't had great success in modeling the
Fe-line with a reflection model because the statistics are too poor.
This being said, there seem to be a lot more models out there (if not
public, at least accessible if you know the right people\ldots{})

Results:

(5) From these data, we can't confirm the spin measured by Suzaku. The
RXTE analysis explicitly assumes that the source always has a power-law
index of 2.5 in order to get the spin measurements. Given that we've
looked at it three times and have seen a softer non-thermal component I
need to make a probabilistic statement against the RXTE analysis (Gao
~et al, I'll link the paper in here).

(6) Let's compare the source explicitly to Cyg X-1. These are both wind
fed systems, so why is their behavior so different? What's special about
LMC X-1 (or Cyg X-1, for that matter) that allows one source to undergo
state transitions and the other not to. Something to do with the angular
momentum of the stellar wind for the LMC X-1 companion truncating the
disk?

(7) How can we interpret the spectral evolution of the flare? It looks
like the harder emission goes first, then the softer emission responds.
This implies that there is some energy transfer in the disk, but the
timescales are pretty small. Can we use this to measure the viscous
timescale of the disk? How else can we interpret this?

\par\null%
\end{abstract}%



\sloppy


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

One of the outstanding problems in modern astrophysics 



Only two parameters are needed to completely describe the physics of a black hole: its mass and its spin. This is true for both stellar mass black holes as well as for the supermassive black holes that reside in the centers of most galaxies. While these two parameters are fundamental to our understanding of black holes, accurately measuring the spin of a black hole is a challenge in modern astrophysics Many of the spins of black hole systems are only measurable when the system goes into outburst and the luminosity increases to nearly the Eddington limit from quiescence ($\sim$10$^{-6}$ Eddington). While these outbursting systems are becoming more common, with dozens of systems now observed, the mass transfer is presumably cataclysmic and we do not know whether the observed phenomenology describes the average accretion onto the black hole (e.g. is the angular momentum of the accretion disk aligned with the spin of the black hole?).




Unlike it's near-twin in Cyg X-1, which shows state transitions between a canonical ``hard state" (characerized by something) to a ``soft state" (characterised by something else), LMC X-1 has only even been seen in the ``soft state" \cite{Nowak_2001}. This implies that LMC X-1 is an ideal laboratory that we can use to study the variations in near steady-state accretion onto the black hole from its companion, which is an $\approx$ 30 M$_{\odot}$ O7 companion \citep{Cowley_1995}.

While LMC X-1 is usually described as primarily being in a ``high soft" state, it does show variations in the strength of the power-law component and in the Fe line region. The dominant source of variability is in change in the slope and strength of the power law components \citep[e.g., ][]{Gou:2009hv}. This can be used to identify at least three apparent states: (1) a thermally dominated state with a a weak power-law component with a slope of $\sim$3.0; (2) a thermally dominated state with a stronger power-law component where the slope remains at $\sim$3.0; and (3) a state where the power-law transitions to a harder index of $\sim$2.5 and a relativistically broadened iron line is seen \citep{Steiner:2012ja}. Similarly, \cite{Koyama_2015} showed that even within the \textit{Suzaku} observation used by \cite{Steiner:2012ja} the power-law components can vary dramatically.






Since it's discovery by \textit{Uhuru} \citep{Leong_1971}, LMC X-1 has been an oddity in black hole binaries. Unlike many stellar mass black binaries, which undergo a variety of emission states (see \citealt{McClintock_2013} for a review), the $\approx$ 10 M$_{\odot}$ black hole in LMC X-1 \citep{Orosz_2009} is persistently emitting \citep{Nowak_2001, Gou_2009} with a spectrum characterized by emission from an multi-color accretion disk along with emission from a non-thermal tail of high-energy (E$>$ 20 keV) X-rays.




\section*{A summary of Historical Observations}

Mostly to drive thoughts for later, this will get re-written into something coherent eventually.

\subsection*{X-ray Observations}

\subsubsection*{Discovery with Uhuru}

Discovery by \textit{Uhuru} \citep{Leong_1971} in 2--7 keV bandpass, already have a power-law with $\Gamma$ = -3.3 $\pm$ 0.7 or bremss with kT = 10 MK.

\subsubsection*{Ginga}

Ginga saw QPO of 0.0751 $\pm$ 0.0009 Hz \cite{Ebisawa_1989} with a soft thermal component (0.7 keV) and a non-thermal power-law tail with $\Gamma$ = 2. Energy range was 1.2 -- 37 keV. QPOs seen over 1.2--15.7 keV bandpass. Also saw an ionized iron line component (E$_{line}$ of 6.9 $\pm$ 0.2 keV). QPOs also appear to be transient.

Observations from the Broad Band X-ray Telescope (BBXT) saw a $\Gamma$ = 2.1 power-law with disk emission (kT = 0.8 keV). But limited to 0.3 -- 12 keV. They claim emission lines at 5.1 and 7.3 keV. No QPOs were seen.

\subsubsection*{Beppo_SAX}



\subsubsection*{RXTE}

Early Rossi X-ray Timing Experiment (RXTE) observations (0.25 -- 10 keV) show a disk (kT = 1.0 keV) and a soft non-thermal power-law ($\Gamma$ = 3.65) \citep{Wilms_1999}. Longer PCA observations (2 -- 15.9 keV) show indicate that the (5.9 -- 15.9 keV ) / (2 -- 5.9 keV) hardness ratio drives the (5.9 -- 15.9 keV) count rate \citep{Schmidtke_1999}. No QPOs were found. Extremely hard found. Extremely hard power-law component ($\Gamma$ = 1.45 \textbf{!?!??!? and wildly inconsistent with Figure 4 in the same paper...may have been a typo?}). 

More complete treatment of PCA data from 3.6 -- 22 keV found a thermal component (roughly 0.9 keV) with a soft power-law ($\Gamma$ around 3) along with a broad iron line. No iron ``edge" and again no QPO \cite{Nowak_2001}.

An analysis of many PCA pointings was used to measure the thermal component, the power-law emission, and their relative contributions \cite{Gou_2009}. Choosing observations (with exposures of between 5 and 10 ks) that are in the ``thermally dominated state" showing a lack of QPOs and that the disk is contributing $>$75\% of the 2--20 keV emission and assuming that the power-law emission $\Gamma$ = 2.5, \cite{Gou_2009} used the \texttt{KERBB2} disk model to measure the spin of the black hole ($a^{*}$ = 0.92 $\pm$ 0.05). \textbf{There's a lot of discussion in that paper justifying their choices. There's also more of a discussion about possible contamination from PSR B0540-69, which I'll discuss later}.

An additional approach was to subdivide the exiting observations to search for short-term variability using slices that correspond to 1-orbit intervals \cite{Ruhlen_2011}. Keeping the power-law (here using \texttt{simpl}) fixed at $\Gamma$=2.65, the 3--16 keV fits give you the behavior of the disk temperature and luminosity as well as the fraction of photons that are up-scattered in the \texttt{simpl} component to give you the non-thermal tail. The sub-observation variations and trends seem to indicate here that the disk itself is not changing (because the viscous time-scales for the disk are more like 5e4 -- 4s6 seconds), but rather the disk is surrounding by a marginally optically thick, ionized corona. The idea here is that since the scattering fraction is lowest when the accretion disk is hottest, that what's going on is that the inner region off the accretion disk is sometimes obscured by optically thick hot electrons (so you only see the cooler parts of the accretion disk). The corona is therefor sensitive to changes in the accretion rate (i.e. clumps) while the thermal component is fixed and stable and changes on much slower timescales. \textbf{This is an interesting thing for us to test with NuSTAR and XMM}.

Finally, a long baseline analysis of ASM data found a 3.9 day orbital variation in the LMC X-1 lightcurve \cite{Levine_2011}. This is mostly seen at low energies (1.5 - 5.0 keV). Can be attributed to variations in the nH column throughout the orbit. But was not identified in any of the previous RXTE observations using PCA data (maybe not sensitive enough at low enough energies?). \textbf{Also, was present after a 100 day smoothing timescale was introduced onto the data, presumably to smooth out the variations that we see above}.









~

\par\null

\subsection*{X-ray Source Position and Identification of the Companion}

Refined X-ray source positions by Uhuru \cite{Giacconi_1974}, Copernicus \cite{Rapley_1974}, SAS-3 \cite{Epstein_1977}, HEAO-1 \cite{Johnston_1978}, and Eistein \cite{Long_1981}. With the Rosat localization using the High Resolution Imager \cite{Cowley_1995} and IEU UV \cite{Hutchings_1983} and observations, we know that the optical companion is ``Star 32" which is an O7 star with a companion of roughly 4 days \cite{Hutchings_1983}.

\subsection*{Orbital Characteristics and Mass}

Periodicity in the RXTE lightcurve 


There are two optical sources near the Einstein position, though 




\section*{The paper starts here!!}


\section*{Introduction}

Only two parameters are needed to completely describe the physics of a black hole: its mass and its spin. This is true for both stellar mass black holes as well as for the supermassive black holes that reside in the centers of most galaxies. While these two parameters are fundamental to our understanding of black holes, accurately measuring the spin of a black hole is a challenge in modern astrophysics (see \citealt{McClintock_2013} for a recent review). Many of the spins of black hole systems are only measurable when the system goes into outburst and the luminosity increases to nearly the Eddington limit from quiescence ($\sim$10$^{-6}$ Eddington). While these outbursting systems are becoming more common, with dozens of systems now observed, the mass transfer is presumably cataclysmic and we do not know whether the observed phenomenology describes the average accretion onto the black hole (e.g. is the angular momentum of the accretion disk aligned with the spin of the black hole?).

The emission spectrum of black holes in the X-ray band is generally dominated by a "soft" thermal component from an the accretion disk with a temperature of $\sim$1 keV along with a power-law component that extends above 10 keV which is assumed to result from Compton up-scattering of photons in an optically thin hot corona around the black hole. A third ``Compton reflection" component is responsible for the broad Fe line features seen in most black hole binary spectra and arises when the coronal hard X-rays ``reflect" off of the optically thick accretion disk. These three components carry information about the accretion disk, including the location of the innermost stable circular orbit, which in general drives the shape of the Fe emission line in the reflection spectrum, as well as the location of the coronal hard X-ray source.

Persistently accreting systems, in contrast, allow us to study a steady-state accretion mode. Two persistent wind-fend black hole binaries with giant companions are close enough for detailed spectral analysis: Cyg X-1 and LMC X-1. In these systems the luminosity is relatively constant at $\sim$10\% of the Eddington rate and so we can study the growth of black holes through persistent, but moderate, mass accretion.

Based on optical studies of the companion star, we know that the physical characteristics of the two persistently accreting sysems are rather similar. From radial velocitiy studies we know that the Cyg X-1 binary system is composed of a black hole with a mass of 14.8 $\pm$ 1.0 M$_{\odot}$ and an O star companion with a mass of 19.2 $\pm$ 1.9 M$_{\odot}$ \citep{Orosz:2011}, while the LMC X-1 system has a black hole mass of 10.91 $\pm$ 1.41 M$_{\odot}$ and an O star companion with a mass of 31.79 $\pm$ 3.48 M$_{\odot}$. The periods of the two systems ($\sim$5.6 days for Cyg X-1 and $\sim$ 3.9 days fo LMC X-1) result in orbital separations of the black hole and donor star that are roughly similar at $\sim$0.31 and $\sim$0.35 AU.

However, the X-ray behavior of the two systems is remarkably different. Cyg X-1 has the characteristics of a black hole in the "low/hard" state, when the emission from the corona dominates the spectrum, with excusions into the "high/soft" state when the emission from the accretion disk dominates the spectrum (see e.g. \cite{Tomsick2014a} and references therein). This contrasts with LMC X-1, which has persistently been seen in a a soft state \citep[e.g.][]{Nowak:2001ex} where both a thermal component and a soft ($\Gamma$ $>$ 2.5) power-law are present.



\cite{Steiner:2012ja} showed that the strength of the broad Fe line has a dependence on the reflection fraction
in the power law continuum. They were not, however, able to spectrally resolve the line and try to determine
whether there are changes in the line shape that may be associated with the changing non-thermal coronal emission.
The previous high spectral resolution observations with \xmm\ \citep{Alam_2014} saw an order of magnitude variability in
the strength of the iron line compare to what was observed by \suzaku\. However, the \xmm\ data were relatively short (40 ks)
and so sampled a fraction of the orbit similar to what we have observed thus far, while the \suzaku\ data integrated over almost
an entire orbital period ($\sim$ 3.9 days). 



While LMC X-1 is usually described as primarily being in a ``high soft" state, it does show variations in the strength of the power-law component and in the Fe line region. The dominant source of variability is in change in the slope and strength of the power law components \citep[e.g., ][]{Gou:2009hv}. This can be used to identify at least three apparent states: (1) a thermally dominated state with a a weak power-law component with a slope of $\sim$3.0; (2) a thermally dominated state with a stronger power-law component where the slope remains at $\sim$3.0; and (3) a state where the power-law transitions to a harder index of $\sim$2.5 and a relativistically broadened iron line is seen \citep{Steiner:2012ja}. Similarly, \cite{Koyama_2015} showed that even within the \suzaku\ observation used by \cite{Steiner:2012ja} the power-law components can vary dramatically.

\selectlanguage{english}
\FloatBarrier
\bibliographystyle{plainnat}
\bibliography{bibliography/converted_to_latex.bib%
}

\end{document}

