prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: When was the paper published?

Read the following text and answer briefly.

Context 1: Paper Info

Title: Interpretable reduced-order modeling with time-scale separation Interpretable reduced-order modeling with time-scale separation
Publish Date: 7 March 2023
Author List: Sebastian Kaltenbach (from CSE-Lab, ETH Zurich, Harvard SEAS), Phaedon-Stelios Koutsourelakis (from CSE-Lab, ETH Zurich, Harvard SEAS), Petros Koumoutsakos (from CSE-Lab, ETH Zurich, Harvard SEAS), Harvard Seas (from CSE-Lab, ETH Zurich, Harvard SEAS)

Figure

FIG  5  Comparison between the phase-space of the reference solution (left) and the phase-space of the predictions
FIG  7  Comparison between predictions and reference solutions for a new initial condition fort = 1 25, 3 75, 7 5, 12 5, 20, 30  (from left to right and top to down) We note that with longer prediction time the uncertainty bounds increases Despite the chaotic nature of the KS equation, the predictive posterior mean is close to the reference solution for t ≤ 12 5

abstract

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering  However, finding solutions for these PDEs can be computationally expensive, making model-order reduction crucial  We propose such a data-driven scheme that automates the identification of the time-scales involved and, can produce stable predictions forward in time as well as under different initial conditions not included in the training data 
To this end, we combine a non-linear autoencoder architecture with a time-continuous model for the latent dynamics in the complex space  It readily allows for the inclusion of sparse and irregularly sampled training data  The learned, latent dynamics are interpretable and reveal the different temporal scales involved 
We show that this data-driven scheme can automatically learn the independent processes that decompose a system of linear ODEs along the eigenvectors of the system's matrix  Apart from this, we demonstrate the applicability of the proposed framework in a hidden Markov Model and the (discretized) Kuramoto-Shivashinsky (KS) equation 
Additionally, we propose a probabilistic version, which captures predictive uncertainties and further improves upon the results of the deterministic framework 

INTRODUCTION

High-fidelity simulations of critical phenomena such as ocean dynamics and epidemics have become essential for decision-making  They are based on physically-motivated PDEs expressing system dynamics that span multiple spatiotemporal scales and which necessitate cumbersome computations   In recent years there is increased attention to the development of data-driven models that can accelerate the solution of these PDEs as well as reveal salient, lower-dimensional features that control the long-term evolution 
In most cases, data-driven reduced-order models are not interpretable  In particular, models based on neural networks despite good predictive capabilities , they offer a black-box description of the system dynamics  A possible remedy is applying a symbolic regression to the learned neural network representation , but this adds additional computational cost due to the two-step procedure 
A number of frameworks such as SINDy allows to learn interpretable dynamics but it relies on the a-priori availability of lower-dimensional descriptors and of time-derivatives which can be very noisy for both simulation and experimental data  Other frameworks are tailored to specific problems such as molecular dynamics  
Here, we present a framework that only needs the value of the observables, and not their derivatives, as training data and is capable of identifying interpretable latent dynamics  The deployment of interpretable latent dynamics ensures that conservation of important properties of that are reflected in the reduced-order model  
The present method is related to approaches based on the Koopman-operator extended Dynamic Mode Decomposition (eDMD) but uses continuous complex-valued latent space dynamics and only requires one scalar variable per latent dimension to describe the latent space dynamics  Therefore we do not have to enforce any parametrizations on the Koopman matrix  
The time-continuous formulation moreover allows to incorporate sparse and irregularly sampled training data and fast generation of predictions after the training phase  By using a complex-valued latent space we can also incorporate harmonic effects and reduce the number of latent variables needed  Linear and non-linear autoencoders are used to map the observed, high-dimensional time-series to the lower-dimensional, latent representation and we identify simultaneously the autoencoder as well as the latent dynamics by optimizing a combined loss function 
Hence the to tasks of dimensionality reduction and discovery of the reduced dynamics are unified while other frameworks treat the two parts separately   Apart from using an architecture based on autoencoders to identify the latent space, projection-based methods could also be employed   We are also proposing a probabilistic version of our algorithm ) that makes use of probabilistic Slow Feature Analysis  
This allows for a latent representation that arart from being time-continuous, can quantify the predictive uncertainty and hierarchically decompose the dynamics into their pertinent scales while promoting the discovery of slow processes that control the system's evolution over long time horizons  The rest of the paper is structured as follows: We introduce the methodological framework as well as algorithmic details in section II 
Particular focus is paid on the interpretability of the inferred lower-dimensional dynamics  In section III we present three numerical illustrations, i e  a system of linear ODEs, a hidden Markov Model and the discretized KS-equation  We then present in section IV the probabilistic extension of the framework and apply it to the KS-equation 
We conclude with a summary and a short discussion about possible next steps  We introduce the autoencoders deployed in this work, followed by the interpretable latent space dynamic and discuss the training process  We consider data from high-dimensional time series x n ∈ R f with n = 1,    , T   We remark that the intervals between the different states do not need to be uniformly spaced 

Autoencoder

A core assumption of the method is that each high-dimensional state x n can be compressed to a lower-dimensional representation z n ∈ C c with c << f   We identify this lower-dimensional representation by an autoencoder consisiting of a parameterized encoder and decoder  The encoder maps the high-dimensional representation to the latent space as:
The latent space is complex-valued  The decoder reconstructs the high-dimensional representation based on the latent variables as: We denote the parameters of the encoder as well as the decoder by θ  As discussed later in Section II C, both set of parameters are optimized simultaneously during training and therefore there is no need for differentiating them 

Interpretable Latent Space Dynamics

We employ a propagator in the latent space to capture the reduced-order dynamics of the system  In contrast to other time-extended variational autoencoder frameworks, our representation uses complex valued latent variables  In addition the latent variables are treated independently  The latter feature enables us to have an interpretable latent dynamics as well as a model that is especially suitable for being trained in the Small Data regime due to the small number of required parameters 
This is in contrast to temporal propagators such as LSTMs   For each dimension i of the latent variable z we are using the following continuous ODE in the complex plane: By solving this ODE, we can define the operator: Interpretable reduced-order modeling with time-scale separation Here, λ is a vector containing all the individual λ's and ∆t n indicates the time-step between the latent states 
The symbol is used to indicate a component-wise multiplication  We remark that the latent variables and the parameter governing the temporal evolution are complex numbers and their role in describing the system dynamics is similar to that of an eigenvalue  The real part is associated with growth and decay whereas the imaginary part is representing the periodic component 
This approach has similarities with the Koopman-operator based methods and the extended dynamic mode decomposition   In contrast to the methods mentioned before we are using a continuous formulation in the latent space that allows us to incorporate scarce and irregularly sampled training data and directly rely on complex numbers in the latent space 

Training and Predictions

We optimize a loss function that combines both a reconstruction loss as well as a loss associated with the error of our learned propagator in the latent space: (5) We note that we could directly incorporate mini-batch training by only taking the summation over a subset of the N available training data 
For new predictions of unseen states, we use the encoder to generate a latent representations which is then advanced in time by the learned propagator  At a designated time step we are using the decoder to reconstruct the high-dimensional solution  We applied our algorithm to three systems  First, we show that the algorithm is capable of exactly reproducing the solution of a linear ODE and to identify its eigenvalues 
Afterwards we are applying the framework to a high-dimensional process generated by a complex latent dynamics, which is correctly identified  As a final test case, we are applying the algorithm to a Kuramoto Shivashinski (KS) equation  Interpretable reduced-order modeling with time-scale separation

Linear ODE

We are considering a two-dimensional ODE system for x = y 1 y 2 : Based on the obtained training data we run our algorithm using a linear encoder and decoder structure as well as two latent variables z  The loss function was optimized using the Adam algorithm   As we consider a linear ODE we can analytically compute the eigenvalues involved and compare it with the parameters λ identified by our algorithm 
We observe in Figure that the algorithm was able to recover the correct values, i e  the eigenvalues 7 and 3 of the given linear ODE  The system does not have a periodic component and the two imaginary parts correctly go to zero, whereas the real parts converge to the reference value  Moreover we are also able to identify for the linear mapping between our latent variables z and the training data a matrix consisting of a multiple of the eigenvectors (1,1) and (1,-1) and thus the correct solution 
This example was chosen to show that the algorithm is able to quickly identify the exact solution of a linear ODE in terms of its linearly independent components 

Hidden multiscale dynamics

We consider eight-dimensional synthetic time series data produced by an underlying twodimensional complex valued process  In particular, the data points x are generated by first solving for the temporal evolution for the two complex-valued processes p 1 and p 2 and than mapping to the eight-dimensional space by using a randomly sampled linear mapping W  
One of the two processes used to generate the data is chosen to be much slower than the other one and both processes have a periodic component  dp 2 dt = (−0 9 + 1 5i)p 2 (8) As training data we consider 40 time series with 150 data points each, obtained by simulating the described processes for a maximum of t = 15 s and then sampling from the obtained data points 
Hence the training data consists of: • 40 time-series • with each consisting 150 observations of the x at a uniform time-step ∆t = 0 0025 The autoencoder obtained consists of one linear layer for both the decoder as well as the encoder  The model is trained for 5000 iterations using the Adam optimizer and a learning rate of 10 −3  
The results for the convergence of the parameters λ 1 and λ 2 can be found in Figure   We note that the process which is slower decaying and thus more responsible for the long-term evolution of the system has a higher convergence rate than the faster process  With the obtained parameters λ as well as the trained autoencoder, we compute predictions based on the last time step used for training, i e  we apply the encoder to obtain our latent representation and than use the latent dynamics to advance the latent representation in time 
Afterwards, we employ the decoder to reconstruct the full high-dimensional system  The results can be found in Figure and show very good agreement between predictions and reference data  This example shows that our model is successfully able to carry out dimensionality reduction and moreover indicates that the convergence rate between latent processes can be different 
The latter is relevant when training models as for accurate predictions all latent processes and their dynamics should be converged 

Kuramoto-Sivashinsky

Finally, we applied our algorithm to the KS equation and aim to identify a reduced-order model for the solution u(y, t): We employed periodic boundary conditions, µ = 1 and a domain size y ∈ [0, 22]  For this domain-size, the KS-equation exhibits a structurally stable chaotic attractor as discussed in The black lines divides the area for which training data was given from the area without raining data 
;   The equation is discretized in space using a discretization step of 22 64 resulting in a state vector x of dimension 64 and a nonlinear system of coupled ODEs  This is solved using a stiff fourth-order solver  We employed a non-linear encoder and decoder with four fully-connected layers each and ReLU-activation functions as well as Dropout Layers between the fully-connected layers 
We trained the model for 200000 iterations using Adam and a learning rate of 5 • 10 4 and assuming a five-dimensional latent space  We obtained the λ's in Figure   Four latent variables have λ's close to zero and thus a slow temporal dynamic that is responsible for the long-term evolution whereas one latent variable is quickly decaying 
Based on the obtained parameters, we do predictions based on an unseen initial condition not contained in the training data  We are able to reconstruct the correct phase space based on our predictions despite only using a very limited amount of training data  The results for the phase space can be seen in Figure  
Although the small-scale fluctuations in the temporal dynamics are not well captured, the model identifies the correct manifold which has a good accuracy compared to the reference solution  All phase-spaces were obtained by using a finite-difference operator on the data or predictions  These results are in accordance Interpretable reduced-order modeling with time-scale separation with whose LSTM-based temporal dynamic model was also able to find the correct phase space but not to track the actual dynamics for long-term predictions 
Our model is not able to account for noise in the temporal evolution and thus dealing with chaotic, small-scale fluctuations is challenging  We believe that a probabilistic version of our algorithm could be advantageous here  This section contains a fully probabilistic formulation for the deterministic model discussed before 
We replace the Autoencoder with a Variational Autoencoder and the ODE in the latent space with a SDE  The loss function which we optimize is the Evidence-Lower Bound (ELBO) 

Model Structure

We postulate the following relations for our probabilistic model using an Ornstein-Uhlenbeck (OU) for each dimension i of the latent space and a Wiener process W t in the latent space: We again assume that the latent variables z t are complex-valued and a priori independent  Complex variables were chosen as their evolution includes a harmonic components which are observed in many physical systems 
We assume an initial conditions z 0,i ∼ CN (0, σ 2 0,i )  The total parameters associated with the latent space dynamics of our model are thus {σ 2 0,i , σ 2 i , λ i } c i=1 and will be denoted by θ together with all parameters responsible for the decoder mapping G (see next section)  These parameters along with the state variables z t have to be inferred from the data x t  
Based on probabilistic Slow Feature Analysis (SFA) , we set σ 2 i = 2; (λ j ) and σ 2 0,i = 1  As a consequence, a priori, the latent dynamics are stationary  A derivation and reasoning for this choice can be found in Appendix A  Hence the only independent parameters are the λ i , the imaginary part of which can account for periodic effects in the latent dynamics 

Variational Autoencoder

We employ a variational autoencoder to account for a probabilistic mappings from the lower-dimensional representation z n to the high-dimensional system x n   In particular we are employing a probabilistic decoder The encoder is used to infer the state variables z based on the given data and thus defined in the inference and learning section 

Inference and Learning

Given the probabilistic relations , our goal is to infer the latent variables z 0:T as well as all model parameters θ  We follow a hybrid Bayesian approach in which the posterior of the state variables is approximated using amortized Variational Inference and Maximum-A-Posteriori (MAP) point-estimates for θ are computed 
The application of Bayes' rule for each data sequence x 0:T leads to the following posterior: where p(θ) denotes the prior on the model parameters  In the context of variational inference, we use the following factorization of the approximate posterior i e  we infer only the mean µ and variance σ for each state variable based on the given data points 
This conditional density used for inference is the encoder-counterpart to the probabilistic decoder defined in the section before  It can be readily shown that the optimal parameter values are found by maximizing the Evidence Lower Bound (ELBO) F(q φ (z 0:T ), θ) which is derived in Appendix B  We compute Monte Carlo estimates of the gradient of the ELBO with respect to φ and θ with the help of the reparametrization trick and carry out stochastic optimization with the ADAM algorithm  

Results for the probabilistic extension

We applied our probabilistic version to the KS-equation  We used the same settings as for the deterministic approach but considered up to 10 complex latent variables  The obtained λ's are in Figure   The probabilistic model allows us to quantify the uncertainty in predictions  In Figure predictions for various time-steps and the respective uncertainty bounds are shown for an unseen initial condition 
Due to the chaotic nature of the KS-equation and the small amount of training data, the underlying linear dynamic of our model is only able to capture the full dynamics for a limited time horizon  Fortunately, due to the probabilistic approach the model is capable of capturing chaotic fluctuations with increasingly wide uncertainty bounds 
We also computed the phase space representation for the KS-equation based on the predictions obtained by our model and compare it with the reference solution  The probabilistic model identifies the correct manifold with a better accuracy than the deterministic model  As some of the small-scale fluctuations are accounted as noise, the resulting manifold is more concentrated at the origin and the obtained values are slightly smaller than the reference manifold although their shape is very similar 
Context 3: \section{Introduction}

The publicly available XMM-Newton slew data covers to date around 35\%
of the sky  The soft band (0 2$-$2 keV) sensitivity limit of the slews
(6$\times10^{-13}$\,ergs cm$^{-2}$ s$^{-1}$) is close to that of the
ROSAT All-Sky Survey (RASS; Voges et al \ 1999), and in the medium
(2$-$12 keV) band, the slew data goes significantly deeper
(4$\times10^{-12}$\,ergs cm$^{-2}$ s$^{-1}$) than all other previous
large area surveys  Over 7700 individual sources have so far been
detected to a positional accuracy of 8\arcsec   For details on the
the construction and
characteristics of the first released XMM-Newton slew survey
catalogue, see Saxton et al  (2008)  For details of the initial
science results from the slew survey, see Read et al  (2006) 

The comparison of XMM-Newton slew data with the RASS is now giving,
for the first time, the opportunity to find exotic, extreme
high-variability X-ray bursting objects, e g  tidal disruption
candidates (Esquej et al  2007), and also Galactic novae, flare stars,
and flaring white dwarfs, plus eclipsing binaries, AGN and blazars  It
is only with such a large-area survey as the XMM-Newton Slew Survey,
that transient events as these have a chance of being caught 

One such rare event, XMMSL1~J060636 2-694933, which we here show to be
a new Classical Nova, was discovered in an XMM-Newton slew from 18th
July 2006 at a very high count rate of 23 3\,ct s$^{-1}$ (EPIC-pn:
0 2$-$2\,keV)  

Classical novae (see Bode \& Evans 2008 for a review) occur in
interacting binary systems consisting of a white dwarf primary star
and a lower-mass secondary star  The nova itself is a cataclysmic
nuclear explosion caused by the accretion of material (via Roche Lobe
overflow or wind accretion) from the secondary star onto the surface
of the white dwarf; here the pressure and temperature at the base of
the accreted material becomes sufficient to trigger a thermonuclear
runaway  A recent review of the thermonuclear processes powering
classical novae can be found in Starrfield et al \ (2008)   The
accreted material is partially expelled, obscuring the X-ray emission
from the surface of the white dwarf  At later stages, the ejected
material expands further and becomes optically thin, revealing the
nuclear burning on the surface of the white dwarf   This emission
peaks in the soft X-ray regime and it is known as the super-soft
source (SSS) state (Krautter 2008)  Models of the classical nova SSS
state can be found in Tuchman \& Truran (1998) and Sala \& Hernanz
(2005) 

Though many classical novae have been observed in X-rays in their SSS
states (Ness et al \ (2007) for example discuss several examples observed with
Swift), it is in the optical band, early in their outbursts, that
classical novae are almost always discovered  This is because they are
intrinsically optically bright and easily found in inexpensive
wide-area shallow surveys   XMMSL1~J060636 2-694933 is very unusual
therefore in that it has been discovered, as we shall see, later in
its evolution, in the SSS X-ray state 

In this paper we describe the XMM-Newton slew observations
(Section~2), and the follow-up X-ray observations by the Swift XRT
(Section~3) and XMM-Newton (Section~4)  Multiwavelength observations
with Swift-UVOT, Magellan and ASAS are described in Section~5  We then
present a discussion of the results (Section~6), and conclusions 



\begin{table*}[t]
  \caption[]
  {Details of the four XMM-Newton Slew observations and the single (Rev \,1378) 
    dedicated XMM-Newton pointed observation  XMM-Newton revolution, date and observation ID 
    are tabulated, together with the 0 2$-$2 0\,keV X-ray properties of XMMSL1~J060636 2-694933;  
    position, background-subtracted counts, exposure, count-rate, and detection likelihood  For the 
    Rev \,1378 dedicated observation, these properties are given for all the EPIC cameras combined   
    For the slew observations, only the EPIC-pn values are given  In the first two slews the source 
    was not detected, and upper limits are shown in the table }
  \centering
\begin{tabular}{lccccrrrr}
\hline
Rev  & Date & Obs \,ID & RA(J2000)   & Dec(J2000) & Counts         & Exposure & Count rate  & Lik  \\ 
     & (UT) &        &     &            &                & (s) & (s$^{-1}$)  &      \\ \hline 
 351 (slew) & 07/11/01 &  9035100003  &        &               & $<$3 6     & 8 8 & $<$0 41 & $<$$\sim$8      \\
 750 (slew) & 12/01/04 &  9075000003  &        &               & $<$3 2     & 17 3 & $<$0 18 & $<$$\sim$8      \\  
1210 (slew )& 18/07/06 &  9121000003  & 06:06:36 2 & -69:49:33 & 228 8$\pm$14 1 & 9 8 & 23 4$\pm$1 4 & 1777 1   \\ 
1246 (slew) & 28/09/06 &  9121460003  & 06:06:36 5 & -69:49:38 &  12 9$\pm$2 4  & 3 4 &  3 8$\pm$0 7 &   54 7   \\
\vspace{-3 5mm}\\
\hline 
1378 (pointed) & 19/06/07 &  0510010501  & 06:06:36 5 & -69:49:37 & 1511 0$\pm$44 8 & 8940 0 &  0 20$\pm$0 01 & 4630 4          \\
\hline
\end{tabular}
\label{slewtable}
\end{table*}

\section{XMM-Newton slew observations}

XMMSL1~J060636 2-694933 was discovered in XMM-Newton slew 9121000003
from revolution 1210 on 18th July 2006  Details of the standard
XMM-Newton slew data reduction and analysis used, plus the
source-searching and catalogue cross-correlation etc , are presented
in Saxton et al   (2008) 

The source passed through the EPIC-pn detector in 14\,s, at a small
off-axis angle, such that an effective vignetting-corrected soft band
(0 2$-$2\,keV) exposure time of 9 8\,s was achieved   A total of 229
source counts lie within a radius of 20\arcsec, yielding a (EPIC-pn:
0 2$-$2\,keV) count rate of 23 4\,ct s$^{-1}$ 

The source is seen to have no cross-correlation identifications in the
RASS, and no other multiwavelength candidates within 30\arcsec\ in
Simbad\footnote{http://simbad u-strasbg fr/simbad/},
NED\footnote{http://nedwww ipac caltech edu/index html}, and
HEASARC\footnote{http://heasarc gsfc nasa gov/}  The position of the
source in the sky is such that it lies apparently at the outer eastern
edge of the LMC 

XMM-Newton has slewed over this region of sky a number of times, and
though nothing was detected in previous slews from 7th November 2001
and 12th January 2004, the source was seen again on 28th September
2006 (rev \,1246, 72 days after the rev \,1210 discovery), at the same
position, but at a reduced flux level (3 8\,ct s$^{-1}$; EPIC-pn:
0 2$-$2\,keV)   i e  it had reduced in flux by a factor of $\approx$6
in 72 days  XMM-Newton has not slewed over this area of sky since
rev \,1246  Details of the relevant XMM-Newton slews, together with
the (0 2$-$2\,keV) EPIC-pn source position, detected source counts,
count rate and detection likelihood are given in
Table~\ref{slewtable} 

The fact that XMMSL1 J060636 2-694933 is detected in the total-band
(0 2$-$12\,keV) and the soft-band (0 2$-$2\,keV), whilst effectively
zero counts are seen in the hard-band (2$-$12\,keV), is immediately
indicative of the source being very soft  

The moderately high count rate indicates that the spectrum is affected
by pile-up (the on-axis limit is 6\,ct s$^{-1}$ for EPIC-pn full-frame
mode
\footnote{http://xmm esac esa int/external/xmm\_user\_support/documentation
  /uhb\_2 5/index html})  This distorts the spectrum and makes
quantitative spectral analysis of the slew data difficult  We
minimized these effects by following the standard procedure, i e 
ignoring the central part of the Point Spread Function (PSF), and
extracted an event spectrum (containing single and double events) of
the source from within an annulus of 5\arcsec$-$30\arcsec\ radius,
centred on the source position  Unresolved problems associated with
the motion of sources across the detector still exist within slew
data, and approximations currently have to be made when calculating
the associated effective area and detector response matrix files  In
order to perform qualitative spectral analysis, an effective area file
was generated by averaging the individual core-removed effective area
files at 9 different positions along the detector track made by the
source  This accounts for the removal of the piled-up core, and takes
the vignetting and PSF variations into account to a good
approximation   Individual BACKSCAL values have been set by hand, as
have the EXPOSURE values, estimated by calculating the distance
travelled by the source in detector coordinates and finding the time
taken to do this, given a 90\,deg\,hr$^{-1}$ slew speed, then
subtracting the appropriate fractions for chip gaps and bad pixels 
For the response matrix, we used the equivalent canned detector
response matrix for the vignetting-weighted average source position,
for single plus double events and for full-frame mode:
epn\_ff20\_sdY6\_v6 9 rmf  A background spectrum was extracted from a
much larger circular region close to the source and at a similar
off-axis angle 

To fit the slew spectral data, and indeed all the high-energy spectra
in the present paper, the
XSPEC\footnote{http://heasarc gsfc nasa gov/docs/xanadu/xspec/}
spectral fitting package has been used  As $\chi^2$ minimization is
not valid when fitting spectra of low statistical quality, for the
fitting of the slew spectrum (and all the spectral fitting in the
present paper), C-statistics have been used  To take into account the
absorbing column along the line of sight, the {\em wabs} model with
the {\em wilm} cosmic abundance table (Wilms et al \ 2000) has been
used throughout the paper  All the errors quoted in the present paper
are 90\% confidence intervals, unless otherwise stated 

The rev \,1210 slew spectrum shows that the source is very soft, and
appears consistent with a 63$_{-10}^{+12}$\,eV black body, absorbed by
a hydrogen column density of
8 2$_{-4 1}^{+5 4}\times10^{20}$\,cm$^{-2}$  The fit is good, with a
P-statistic value of 0 11, obtained via the XSPEC {\em goodness}
command for this fit, based on 5000 random simulations  The best-fit
hydrogen column is equal to the full Galactic hydrogen column in the
direction of the source (8 0$\pm{1 1}\times10^{20}$\,cm$^{-2}$; Dickey
\& Lockman, 1990, calculated via the FTOOL {\em
  nh}\footnote{http://heasarc gsfc nasa gov/lheasoft/ftools/fhelp/nh txt}) 
The slew spectrum, plus the best fit simple black body model and the
deviations from the model, are shown in Fig \,\ref{slewspec}  The
observed count rate corresponds to a (0 2$-$2\,keV) flux, corrected
for the removal of the saturated PSF core, of
4 8$^{+2 7}_{-1 6}\times10^{-11}$\,ergs cm$^{-2}$ s$^{-1}$ (an
increase in flux over the RASS upper limit, assuming the same spectral
model, by a factor of more than 500) 

Simple power-law, thermal Bremmstrahlung, and other optically thin hot
plasma models are unable to fit the spectrum adequately well   Given
that we later are able to identify the source as a nova (Section~5 2),
then the black-body model will likely be a good approximation 
Furthermore, as we have obtained here a moderate number of slew
counts, the more physically realistic, though more complex atmosphere
model for CO white dwarfs of MacDonald \& Vennes (1991), provided by
K \,Page (private communication), was attempted   This model, used
e g  to model the nova V1974 Cyg (Balman et al \ 1998), yielded a
marginal fit (and not formally a more statistically significant fit;
P-statistic = 0 03, based on 5000 random simulations), with an
effective temperature of 70$^{+8}_{-6}$\,eV, an $N_{\rm H}$ of
3 7$^{+3 2}_{-2 5}$$\times$$10^{20}$\,cm$^{-2}$, and a PSF-corrected
(0 2$-$2\,keV) flux of 4 5$^{+1 3}_{-1 8}\times10^{-11}$\,ergs
cm$^{-2}$ s$^{-1}$  Note that a smaller $N_{\rm H}$ (though perhaps
still consistent with the full Galactic hydrogen column) is now
obtained using the white dwarf atmosphere model  (Note that the
MacDonald \& Vennes (1991) ONe white dwarf atmosphere model was also
attempted, but yielded a marginally worse fit than the CO white dwarf
atmosphere model; only the CO atmosphere model has been used in the
subsequent analysis) 

It is well known (e g  Krautter et al \ 1996) that, because of the
energy-dependent opacity in the white dwarf atmosphere, fits to super
soft source novae spectra with black body models give larger fluxes
and lower temperatures than atmosphere models fit to the same spectra,
and this is seen in the present case  Thus the black body model
requires a larger $N_{\rm H}$ to fit the same data than the atmosphere
model, as is seen  

The model normalizations, corrected for the removal
of the saturated PSF core, can be used to derive an approximate
distance to the source   If we assume a typical emitting region for
the white dwarf atmosphere to be of spherical radius 10$^{9}$\,cm,
then, for the black body model, this distance turns out to be
20$^{+31}_{-10}$\,kpc  The effects discussed above however can lead to
usage of the black body model giving rise to an underestimation of the
distance   For the white dwarf atmosphere model, a larger distance of
71$^{+27}_{-23}$\,kpc is obtained  Both estimates are consistent with
the distance to the LMC ($\sim$50\,kpc, see Section~6), and assuming a
distance of 50\,kpc, the black body derived flux corresponds to a
(pile-up corrected) 0 2$-$2\,keV X-ray luminosity of
1 4$^{+0 8}_{-0 5}\times10^{37}$\,ergs s$^{-1}$ 


\begin{figure}
\centering
\includegraphics[bb=100 20 575 700,clip,width=6 0cm,angle=270]{12082f1 ps}
\caption{XMM-Newton Slew spectrum of XMMSL1 J060636 2-694933 from
  XMM-Newton revolution 1210   The data points (crosses; adjacent data
  bins having been grouped together for the plot to have a significance of at least
  3) have been fitted with a black body model (kT=63\,eV; see text) 
  The solid line shows the best fit to the spectrum  The ratio of the
  data to the best fit model is shown in the lower panel }
\label{slewspec}
\end{figure}


\section{Swift XRT X-ray observations}

We requested and received a prompt observation with Swift of this
source before it moved out of the Swift visibility window in April
2007  We received over 14\,ksec of Swift-XRT time in 7
separate observations and the details of these observations are listed
in Table~\ref{xrttable}  All of the observations were in photon
counting mode and none of the observations showed any times of
significant high-BG flux  In none of the observations did the source
position coincide with any of the dead (micrometeorite-induced)
detector columns  The analysis has been performed using HEASOFT
v6 1 2  The individual XRT observations were astrometrically-corrected
and then stacked to ascertain a best Swift-XRT position $-$ this was
found to be 06 06 37 00 -69 49 33 9 (with a 90\% error radius of
4 0\arcsec)  Source counts were then extracted from each observation
from a circle of radius of 40\arcsec\ at this position  Background
counts were extracted from each observation from large-radius
off-source circles close to the source position  Source counts and
count rates for the individual XRT observations are given in
Table~\ref{xrttable} 


\begin{table}
  \caption[]{Details of the Swift-XRT observations (observation ID, observation date and 
    cleaned exposure time) are tabulated, together with the total (0 2$-$2 0\,keV) background-subtracted 
    counts and count rate from XMMSL1 J060636 2-694933 (see text) }
  \centering
\begin{tabular}{ccrrr}
\hline
ID          & Date     & Exp  & Counts       & Count rate       \\ 
            &   (UT)   &  (s) &              & (s$^{-1}$)        \\ \hline 
00030895001 & 28/02/07 & 1955 & 23 9$\pm$5 1 & 0 0122$\pm$0 0026  \\
00030895002 & 07/03/07 & 1796 & 15 8$\pm$4 2 & 0 0088$\pm$0 0024 \\
00030895003 & 08/03/07 & 1651 & 10 9$\pm$3 6 & 0



ground_truth: The paper was published on 7 March 2023.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What did Justice Kennedy argue about Quill in Direct Marketing Ass'n v. Brohl?

Read the following text and answer briefly.

Context 2: South Dakota v  Wayfair, Inc  - Harvard Law Review
Fourth Circuit Invalidates Maryland Statute Regulating Price Gouging in the Sale of Generic Drugs 
South Dakota Supreme Court Holds Unconstitutional State Law Requiring Internet Retailers Without In-State Physical Presence to Remit Sales Tax 
Judicial junk, the Court has long thought, is easier to scrap when the erroneous precedent cannot be fixed by Congress, as in constitutional cases 1× 1  See Burnet v  Coronado Oil & Gas Co , 285 U S  393, 405–10 (1932) (Brandeis, J , dissenting); Lee Epstein, William M  Landes & Adam Liptak, The Decision to Depart (or Not) from Constitutional Precedent: An Empirical Study of the Roberts Court, 90 N Y U  L  Rev  1115, 1116 (2015) (“[Justice Brandeis’s] dissenting opinion       now has the status of black letter law ”)  On the flip side, whenever a bad precedent can be corrected by Congress, stare decisis applies with “special force ”2× 2  See Patterson v  McLean Credit Union, 491 U S  164, 172–73 (1989)  The Court, following Justice Brandeis, usually articulates the rule as distinguishing between “constitutional” and “statutory” precedents  See, e g , id  But the distinction is occasionally said to be between “constitutional” and “nonconstitutional cases ” See, e g , Glidden Co  v  Zdanok, 370 U S  530, 543 (1962) (plurality opinion)  Nomenclature aside, the Court has — until now — adhered to Justice Brandeis’s key insight that the important factor is whether or not the mistake may be legislatively corrected  Last Term, in South Dakota v  Wayfair, Inc ,3× 3  138 S  Ct  2080 (2018)  the Court tinkered with this thinking in overruling an outdated dormant commerce clause precedent  Dormant commerce clause decisions technically produce constitutional holdings, but Congress may override them at will 4× 4  See Prudential Ins  Co  v  Benjamin, 328 U S  408, 421–27 (1946)  Under the usual logic of stare decisis, it should take special force to dislodge such precedents  But Wayfair applied the weakened stare decisis of constitutional cases, asserting that the Court must “address a false constitutional premise         whether or not Congress can or will act ”5× 5  Wayfair, 138 S  Ct  at 2096–97 
Emerging from Wayfair is an odd and ominous development in stare decisis doctrine  Odd, because it turns on a formal classification instead of on Congress’s practical ability to fix the problem  Ominous, because the Court’s logic leads far past the dormant commerce clause  Wayfair grants only feeble stare decisis to precedents that set a “constitutional default rule,”6× 6  Id  at 2096 (“While       Congress has the authority to change the physical presence rule, Congress cannot change the constitutional default rule ”)  meaning constitutional decisions that allow for legislative adjustment or override  This new stare decisis analysis makes other precedents setting constitutional default rules more vulnerable — including, perhaps, mainstays of criminal procedure like Miranda v  Arizona7× 7  384 U S  436 (1966)  and Mapp v  Ohio 8× 8  367 U S  643 (1961) 
Since its 1967 decision in National Bellas Hess, Inc  v  Department of Revenue,9× 9  386 U S  753 (1967)  the Court has held that, under the “dormant” or “negative” implication of the Commerce Clause,10× 10  The dormant or negative commerce clause is a judicial derivation from the Commerce Clause “prohibiting States from discriminating against or imposing excessive burdens on interstate commerce without congressional approval,” which “strikes at one of the chief evils that led to the adoption of the Constitution, namely, state tariffs and other laws that burdened interstate commerce ” Comptroller of the Treasury of Md  v  Wynne, 135 S  Ct  1787, 1794 (2015)  states may not compel remote sellers with no physical presence in the state to collect and remit sales taxes 11× 11  See Bellas Hess, 386 U S  at 759–60  In Quill Corp  v  North Dakota,12× 12  504 U S  298 (1992)  the Court refused to overrule the “bright-line, physical-presence requirement” of Bellas Hess, leaning heavily on stare decisis 13× 13  Id  at 317–18  Three Justices joined a concurrence explaining that their decision rested solely “on the basis of stare decisis ” Id  at 320 (Scalia, J , concurring in part and concurring in the judgment)  So the physical presence test remained the law of the land while the internet conquered the earth  Justice Kennedy had joined the Quill majority and Justice Scalia’s concurring opinion emphasizing stare decisis, but by 2015 he had second thoughts  Writing separately in Direct Marketing Ass’n v  Brohl,14× 14  135 S  Ct  1124 (2015)  Justice Kennedy acknowledged that “[t]he Internet has caused far-reaching systemic and structural changes in the economy” and therefore “Quill now harms States to a degree far greater than could have been anticipated earlier ”15× 15  Id  at 1135 (Kennedy, J , concurring)  He concluded with the wish that “[t]he legal system should find an appropriate case for this Court to reexamine Quill and Bellas Hess ”16× 16  Id 
Seldom has a concurring opinion signed by a lone Justice prompted a state to officially declare an emergency  Yet in 2016, in response to Justice Kennedy’s overture, the South Dakota legislature passed a law, S B  106, “to provide for the collection of sales taxes from certain remote sellers       and to declare an emergency ”17× 17  2016 S D  Sess  Laws ch  70 pmbl  217 (codified at S D  Codified Laws § 10-64 (2017))  It required every remote seller to collect and remit sales tax if the seller’s business in South Dakota comprised either a “gross revenue” greater than $100,000 or at least 200 “separate transactions” within one calendar year 18× 18  Id  § 1  Significantly, the law did not apply retroactively 19× 19  Id  § 5  The “emergency” declaration was necessary to give the law immediate effect, for the purpose of “permitting the most expeditious possible review of the constitutionality of this law” by the U S  Supreme Court 20× 20  Id  § 8(8)  As Justice Alito put it, the “South Dakota law [was] obviously a test case ”21× 21  Transcript of Oral Argument at 27, Wayfair, 138 S  Ct  2080 (No  17-494), https://www supremecourt gov/oral_arguments/argument_transcripts/2017/17-494_7lho pdf [https://perma cc/8HYH-VU8N] 
Expeditiously, a group of remote sellers challenged the law  After being sued by South Dakota for refusing to register for the newly required sales tax license, Wayfair, Inc , Overstock com, Inc , and Newegg, Inc  moved for summary judgment in South Dakota circuit court on the grounds that S B  106 was unconstitutional under Quill and Bellas Hess — a point South Dakota conceded, indicating that it was seeking review by the U S  Supreme Court to overturn Quill 22× 22  State v  Wayfair Inc , 2017 SD 56, ¶¶ 9–11, 901 N W 2d 754, 759–60  Accordingly, the South Dakota circuit court granted the motion for summary judgment and South Dakota appealed to the state’s highest court 23× 23  Id  ¶ 12, 901 N W 2d at 760  The South Dakota Supreme Court unanimously affirmed, recognizing that South Dakota’s “arguments on the merits” may be “persuasive” but “Quill remains the controlling precedent ”24× 24  Id  ¶ 18, 901 N W 2d at 761  See generally Recent Case, State v  Wayfair Inc , 2017 SD 56, 901 N W 2d 754 (S D  2017), 131 Harv  L  Rev  2089 (2018) 
The U S  Supreme Court vacated and remanded 25× 25  Wayfair, 138 S  Ct  at 2100  Writing for the Court one last time, Justice Kennedy26× 26  Justices Thomas, Ginsburg, Alito, and Gorsuch joined Justice Kennedy’s opinion  pilloried Quill’s physical presence rule as “arbitrary, formalistic,” “anachronistic,” and “unfair and unjust” to both states and brick-and-mortar retailers 27× 27  Wayfair, 138 S  Ct  at 2092, 2095  After all, the rationale of Quill was that remote sellers lacked a sufficiently “substantial nexus” with the state to justify imposing a duty of tax collection 28× 28  Quill Corp  v  North Dakota, 504 U S  298, 311 (1992) (quoting Complete Auto Transit, Inc  v  Brady, 430 U S  274, 279 (1977))  This was wrong even in the mail-order catalog days of 1967 and 1992, but “the Internet revolution has made [Quill’s] earlier error all the more egregious and harmful ”29× 29  Wayfair, 138 S  Ct  at 2097; see also id  at 2092  The rule deprived the states of billions of dollars, since they could not force remote sellers to collect the tax and consumers hardly ever paid it on their own 30× 30  Id  at 2088 (“[C]onsumer compliance rates are notoriously low ”)  Quill “serve[d] as a judicially created tax shelter” for remote retailers who do a great deal of business online 31× 31  Id  at 2094 
Satisfied that Bellas Hess and Quill were wrongly decided, the Court then jumped the hurdle of stare decisis  The Quill Court had feared upsetting reliance interests 32× 32  Quill, 504 U S  at 317 (“Bellas Hess       has engendered substantial reliance and has become part of the basic framework of a sizable industry ”)  Wayfair shrugged off this concern, noting that “stare decisis accommodates only ‘legitimate reliance interest[s]’”; by contrast, reliance on the physical presence rule was largely due to consumers evading their use-tax obligations 33× 33  Wayfair, 138 S  Ct  at 2098 (alteration in original) (quoting United States v  Ross, 456 U S  798, 824 (1982))  Quill had also appealed to Congress’s ultimate authority over interstate commerce as a reason to abide by a precedent, even if wrongly decided 34× 34  See Quill, 504 U S  at 318–19; id  at 320 (Scalia, J , concurring in part and concurring in the judgment) (“Congress       can change the rule of Bellas Hess by simply saying so ”)  But Wayfair denied that Congress’s ability to change the law was a proper consideration:
While it can be conceded that Congress has the authority to change the physical presence rule, Congress cannot change the constitutional default rule  It is inconsistent with the Court’s proper role to ask Congress to address a false constitutional premise of this Court’s own creation  Courts have acted as the front line of review in this limited sphere; and hence it is important that their principles be accurate and logical, whether or not Congress can or will act in response 35× 35  Wayfair, 138 S  Ct  at 2096–97 
Having dispensed with the physical presence rule, the Court remanded the case to the South Dakota courts to determine in the first instance “whether some other principle in the Court’s Commerce Clause doctrine might invalidate the Act ”36× 36  Id  at 2099  But the Court listed “several features [of South Dakota law] that appear[ed] designed to prevent discrimination against or undue burdens upon interstate commerce ” Id 
Justices Thomas and Gorsuch each filed concurring opinions  Justice Thomas wistfully likened himself to Justice White — who voted for Bellas Hess but against Quill a quarter-century later — and confessed that he “should have joined [Justice White’s dissenting] opinion ”37× 37  Id  at 2100 (Thomas, J , concurring)  Justice Thomas added that the “Court’s entire negative Commerce Clause jurisprudence” is wrong and should be abandoned 38× 38  Id  Justice Gorsuch also wrote separately to express skepticism of the Court’s dormant commerce clause jurisprudence, raising “questions for another day” of whether the doctrine “can be squared with the text of the Commerce Clause, justified by stare decisis, or defended as misbranded products of federalism or antidiscrimination imperatives flowing from Article IV’s Privileges and Immunities Clause ”39× 39  Id  at 2100–01 (Gorsuch, J , concurring) 
Chief Justice Roberts dissented 40× 40  Justices Breyer, Sotomayor, and Kagan joined the Chief Justice’s dissent  Surprisingly, the dissenting Justices “agree[d] that Bellas Hess was wrongly decided, for many of the reasons given by the Court ”41× 41  Wayfair, 138 S  Ct  at 2101 (Roberts, C J , dissenting)  The dispute between the majority and the dissent turned entirely on the principles and application of stare decisis  Chief Justice Roberts argued that whether or how to reverse Quill should be left to Congress, which “has the flexibility to address these questions in a wide variety of ways” and “can focus directly on current policy concerns rather than past legal mistakes ”42× 42  Id  at 2104  He also pointed to the “baffling” burdens of compliance with the idiosyncratic tax codes of “[o]ver 10,000 jurisdictions,” particularly for small businesses, and doubted that new “software” — the majority’s proposed solution to this mess43× 43  Id  at 2098 (majority opinion) (“Eventually, software that is available at a reasonable cost may make it easier for small businesses to cope with these problems ”)  — would soon solve the problem 44× 44  Id  at 2103–04 (Roberts, C J , dissenting)  In Bellas Hess, the Court reasoned that the dormant commerce clause protects interstate business from being “entangle[d]       in a virtual welter of complicated obligations to local jurisdictions ” Nat’l Bellas Hess, Inc  v  Dep’t of Revenue, 386 U S  753, 759–60 (1967)  The dissent replied that the Court “vastly underestimate[d] the skill of contemporary man and his machines ” Id  at 766 (Fortas, J , dissenting)  The dispute in Wayfair over whether software is up to the task effectively reprised the old debate from Bellas Hess, only this time couched as part of the stare decisis inquiry’s concern for reliance interests rather than as a matter of dormant commerce clause doctrine  While Wayfair acknowledged that “[c]omplex state tax systems could have the effect of discriminating against interstate commerce,” 138 S  Ct  at 2099, the Court remarked that “[t]he physical presence rule is a poor proxy” for an inquiry into any actual burdens imposed on interstate commerce, id  at 2093 
Chief Justice Roberts emphasized that a “heightened form of stare decisis”45× 45  Wayfair, 138 S  Ct  at 2102 (Roberts, C J , dissenting)  applies when “Congress       can, if it wishes, override this Court’s decisions with contrary legislation ”46× 46  Id  at 2101 (first citing Michigan v  Bay Mills Indian Cmty , 134 S  Ct  2024, 2036 (2014) (tribal sovereign immunity); then citing Kimble v  Marvel Entm’t, LLC, 135 S  Ct  2401, 2409 (2015) (statutory interpretation); and then citing Halliburton Co  v  Erica P  John Fund, Inc , 134 S  Ct  2398, 2411 (2014) (judicially created doctrine implementing a judicially created cause of action))  In Quill, the Chief Justice noted, the Court had taken to heart that “Congress may be better qualified” and “has the ultimate power to resolve” the question47× 47  Id  at 2102 (quoting Quill Corp  v  North Dakota, 504 U S  279, 318 (1992))  while Justice Scalia had “recogniz[ed] that stare decisis has ‘special force’ in the dormant Commerce Clause context due to Congress’s ‘final say over regulation of interstate commerce ’”48× 48  Id  (quoting Quill, 504 U S  at 320 (Scalia, J , concurring in part and concurring in the judgment))  Moreover, “[i]f stare decisis applied with special force in Quill, it should be an even greater impediment” afterward since Quill effectively “tossed [the ball] into Congress’s court ”49× 49  Id  (alteration in original) (quoting Kimble, 135 S  Ct  at 2409); cf  Bay Mills, 134 S  Ct  at 2039 n 12 (“When we inform Congress that it has primary responsibility over a sphere of law, and invite Congress to consider a specific issue within that sphere, we cannot deem irrelevant how Congress responds ”)  Because the Court invited Congress to act and then “suddenly chang[ed] the ground rules, the Court may have waylaid Congress’s consideration of the issue ”50× 50  Wayfair, 138 S  Ct  at 2102–03 (Roberts, C J , dissenting) 
In Wayfair, the Court applied the flimsier form of stare decisis to a precedent that could have been overruled by Congress  It did so in the context of a dormant commerce clause case, but Wayfair’s logic extends to all constitutional default rules — that is, constitutional decisions that Congress remains free to change  Not only does Wayfair deviate from the Court’s decades-old stare decisis analysis, it also imperils other precedents that set constitutional default rules 
The Court’s reasoning in Wayfair departs from its prior stare decisis analysis  In 1932, Justice Brandeis posited that stare decisis must bend “in cases involving the Federal Constitution, where correction through legislative action is practically impossible ”51× 51  Burnet v  Coronado Oil & Gas Co , 285 U S  393, 406–07 (1932) (Brandeis, J , dissenting)  The Court has long since adopted his argument,52× 52  See, e g , Smith v  Allwright, 321 U S  649, 665 (1944)  as well as its corollary — that stare decisis commands “special force in the area of statutory interpretation” where “Congress remains free to alter what [the Court has] done ”53× 53  Patterson v  McLean Credit Union, 491 U S  164, 172–73 (1989)  For normative evaluations of heightened stare decisis for statutory precedents, see generally Einer Elhauge, Statutory Default Rules: How to Interpret Unclear Legislation 211–23 (2008); and William N  Eskridge, Jr , Overruling Statutory Precedents, 76 Geo  L J  1361, 1364–1409 (1988)  Justice Brandeis’s logic demands that dormant commerce clause cases, where Congress is free to act, be granted the weightier stare decisis 54× 54  Scholars have noted the curious fact that Justice Brandeis included many dormant commerce clause cases as examples of overruled constitutional precedents  See, e g , Earl M  Maltz, Commentary, Some Thoughts on the Death of Stare Decisis in Constitutional Law, 1980 Wis  L  Rev  467, 468–469, 469 n 11  One explanation for this is that Justice Brandeis sought the authority of Chief Justice Taney’s dictum that the Court’s “opinion upon the construction of the Constitution is always open to discussion” — which referred to the dormant commerce clause  See Burnet, 285 U S  at 408 n 3 (Brandeis, J , dissenting) (quoting The Passenger Cases, 48 U S  (7 How ) 283, 470 (1849) (Taney, C J , dissenting))  In Chief Justice Taney’s time, it was thought that Congress could not override the Court’s dormant commerce clause decisions, see Cooley v  Bd  of Wardens, 53 U S  (12 How ) 299, 321 (1852), so the context of Chief Justice Taney’s dictum does not conflict with Justice Brandeis’s theory of stare decisis  The Court applied this reasoning in Quill, as Chief Justice Roberts underscored 55× 55  Wayfair, 138 S  Ct  at 2102 (Roberts, C J , dissenting) 
Yet the Wayfair majority refused to consider Congress’s authority to legislate as a relevant factor for stare decisis 56× 56  Even Justice Kennedy’s earlier opinion in Direct Marketing contemplated judicially overruling Quill, conspicuously neglecting a possible legislative solution  See supra p  278  The Court even insisted that to do so “is inconsistent with the Court’s proper role,” since Quill embodied “a false constitutional premise of th[e] Court’s own creation ”57× 57  Wayfair, 138 S  Ct  at 2096 (emphasis added)  This refusal breaks from the practical Brandeisian wisdom that has guided the Court’s treatment of precedent for the better part of a century  The point is not that stare decisis should have ultimately propped up Bellas Hess yet again, as Wayfair’s dissenting Justices maintained  After all, a realistic approach that is alert to each branch’s institutional capacities might have led to the conclusion that Congress was actually ill-equipped to overrule Quill  In this vein, the Court could have sensibly pointed out that Congress is unlikely to stick its neck out with a tax hike (or a look-alike) from which only the states would benefit 58× 58  For two practical arguments to this effect, see Brian Galle, Essay, Kill Quill, Keep the Dormant Commerce Clause: History’s Lessons on Congressional Control of State Taxation, 70 Stan  L  Rev  Online 158, 160–62 (2018), https://review law stanford edu/wp-content/uploads/sites/3/2018/03/70-Stan -L -Rev -Online-158-Galle pdf [https://perma cc/22YP-P4V5]; Edward A  Zelinsky, The Political Process Argument for Overruling Quill, 82 Brook  L  Rev  1177, 1191–92 (2017)  Indeed, South Dakota advanced such practical arguments in its brief 59× 59  See Petitioner’s Brief at 54, Wayfair, 138 S  Ct  2080 (No  17-494) (“Congress has little incentive to act here because it would be (or appear to be) authorizing new or greater tax collections from its constituents, while receiving none of the revenue in return ”)  More generally, the Court might have discussed the limits of the states’ influence in the federal system as a reason not to wait for congressional intervention, a topic it has debated on other occasions 60× 60  See Richard H  Pildes, Institutional Formalism and Realism in Constitutional and Public Law, 2013 Sup  Ct  Rev  1, 30–32; see also Galle, supra note 58, at 159 (“Congress is not a trustworthy guardian of state fiscal power, making continuing judicial involvement a more appealing prospect ”)  Or it could have argued that new facts on the ground — namely, the blast of e-commerce that hit like a comet after Quill — overpowered stare decisis of any force, special or plain 61× 61  Two recent studies of stare decisis highlighted the physical presence rule as exemplifying a precedent that may reasonably be overruled due to changed facts  See Bryan A  Garner et al , The Law of Judicial Precedent 364–65 (2016); Randy J  Kozel, Settled Versus Right: A Theory of Precedent 112–13 (2017)  It should be noted that the authors of The Law of Judicial Precedent classify the physical presence rule as a constitutional precedent for stare decisis purposes, thus anticipating the Court’s misstep in Wayfair  Garner et al , supra, at 354–65  Because even statutory precedents may sometimes be overruled,62× 62  See Patterson v  McLean Credit Union, 491 U S  164, 173–74 (1989) (discussing justifications for overruling statutory precedents)  Contra Lawrence C  Marshall, “Let Congress Do It”: The Case for an Absolute Rule of Statutory Stare Decisis, 88 Mich  L  Rev  177 (1989)  the Court could have killed Quill without first planting its constitutional kiss of death 63× 63  Cf  Thomas R  Lee, Stare Decisis in Historical Perspective: From the Founding Era to the Rehnquist Court, 52 Vand  L  Rev  647, 704 (1999) (“Justice Brandeis’       memorable prose has since become a mandatory part of the burial rite for any constitutional precedent ”) 
The Court resisted such arguments  Instead, Wayfair reasoned that Congress’s total ability to correct an erroneous decision counts for nothing when the Court gets the Constitution wrong  That such a theory sprouts from a case like Wayfair, which repudiated a “formalistic distinction,”64× 64  Wayfair, 138 S  Ct  at 2092  is ironic  Wayfair’s stare decisis analysis resorts to the formalism of making constitutional a “magic” word65× 65  See Transcript of Oral Argument, supra note 21, at 12  rather than asking whether Congress can step in 
Moreover, the Court’s new thinking on stare decisis threatens other constitutional default rules  Wayfair now stands for the proposition that a “constitutional default rule” — a term the Court apparently lifted from South Dakota’s reply brief on the merits66× 66  Reply Brief at 22, Wayfair, 138 S  Ct  2080 (No  17-494) (“Congress is polarized, which makes it critical       to get the constitutional default rule right ”)  — gets only weakened stare decisis  To appreciate why this holding matters, it is worth exploring the concept and scope of constitutional default rules  Contract theory describes default rules as legal rules that the parties may “contract around ”67× 67  See, e g , Ian Ayres & Robert Gertner, Filling Gaps in Incomplete Contracts: An Economic Theory of Default Rules, 99 Yale L J  87, 87 (1989)  Although “constitutional default rule” could be read broadly to include a variety of actors and contracting mechanisms,68× 68  See John Ferejohn & Barry Friedman, Toward a Political Theory of Constitutional Default Rules, 33 Fla  St  U  L  Rev  825, 826 (2006) (“When we speak of default rules in constitutional law, we typically are talking about specifications of ways the government can act (or modify its behavior) to get around a constitutional prohibition ”)  the Court’s use of the term for purposes of stare decisis may be narrowly defined as judicial precedents of constitutional law that “are ultimately subject to congressional control ”69× 69  Gillian E  Metzger, Congress, Article IV, and Interstate Relations, 120 Harv  L  Rev  1468, 1525 (2007) (describing judicially enforceable “constitutional default rules imposing obligations on the states in the name of union [that] are ultimately subject to congressional control”)  The dormant commerce clause is a paradigmatic constitutional default rule because what the Court does today Congress may undo tomorrow  Justice Scalia declared this fact “[t]he clearest sign that the negative Commerce Clause is a judicial fraud,” for “[h]ow could congressional consent lift a constitutional prohibition?”70× 70  Comptroller of the Treasury of Md  v  Wynne, 135 S  Ct  1787, 1808 (2015) (Scalia, J , dissenting)  But that’s what a constitutional default rule is  The Court has allowed Congress to overturn its dormant commerce clause cases since 1891 71× 71  See In re Rahrer, 140 U S  545, 560–62 (1891) 
Dormant commerce clause cases are not the only constitutional default rules  Professor Laurence Tribe’s treatise identifies two others 72× 72  1 Laurence H  Tribe, American Constitutional Law § 6-35 (3d ed  2000)  And in a groundbreaking article, Professor Henry Monaghan revealed “a substructure of substantive, procedural, and remedial rules” forming “a constitutional common law subject to amendment, modification, or even reversal by Congress ”73× 73  Henry P  Monaghan, The Supreme Court, 1974 Term — Foreword: Constitutional Common Law, 89 Harv  L  Rev  1, 2–3 (1975); see also Susan R  Klein, Identifying and (Re)Formulating Prophylactic Rules, Safe Harbors, and Incidental Rights in Constitutional Criminal Procedure, 99 Mich  L  Rev  1030 (2001) (further developing Monaghan’s theory in criminal procedure context)  What follows is a list of six lines of cases beyond the dormant commerce clause that may be fairly described as constitutional default rules  The first two are drawn from Tribe’s treatise while the next four are found in Monaghan’s article:
(1) State Taxation of Federal Instrumentalities: States may not tax instrumentalities of the federal government74× 74  McCulloch v  Maryland, 17 U S  (4 Wheat ) 316, 436 (1819)  — unless Congress consents 75× 75  See, e g , Helvering v  Gerhardt, 304 U S  405, 411 n 1 (1938) (“Congress may curtail an immunity which might otherwise be implied or enlarge it beyond the point where, Congress being silent, the Court would set its limits ” (citations omitted))  One court has described such judicial decisions as setting a “constitutional default rule ” United States v  Delaware, 958 F 2d 555, 560 n 9 (3d Cir  1992) (“[W]e must decide the constitutional default rule for this type of tax, fully aware that Congress could decide at any time to reverse our decision statutorily ”)  (2) Article I, Section 10 Cases: Article I, Section 10 provides that certain prohibitions on the states may be waived by Congress 76× 76  See U S  Const  art  I, § 10, cls  2–3  The Court has taken note of this when considering whether to overrule, for instance, an Import-Export Clause precedent 77× 77  See Hooven & Allison Co  v  Evatt, 324 U S  652, 668 (1945) (“In view of the fact that the Constitution gives Congress authority to consent to state taxation of imports and hence to lay down its own test for determining when the immunity ends, we see no convincing practical reason for abandoning the test which has been applied for more than a century        ”), overruled on other grounds by Limbach v  Hooven & Allison Co , 466 U S  353 (1984)  In Michelin Tire Corp  v  Wages, 423 U S  276 (1976), the Court left open the question whether “Congress may authorize, under the Import-Export Clause, an exaction that it could not directly impose under the Tax Clause ” Id  at 301 n 13  Metzger, however, argues that the Import-Export Clause is free of other clauses’ limits on congressional power  See Metzger, supra note 69, at 1500 & n 120  (3) Bivens Cases: In Bivens v  Six Unknown Named Agents of Federal Bureau of Narcotics,78× 78  403 U S  388 (1971)  the Court held that a violation of the Fourth Amendment gives rise to a right to sue for damages 79× 79  Id  at 397  But the Court has also held that “[s]uch a cause of action may be defeated       when       Congress has provided an alternative remedy which it explicitly declared to be a substitute for recovery directly under the Constitution and viewed as equally effective ”80× 80  Carlson v  Green, 446 U S  14, 18–19 (1980)  (4) Miranda Cases: The Miranda Court famously “encourage[d]” Congress and the states to explore alternative “procedures which are at least as effective in apprising accused persons of their right of silence and in assuring a continuous opportunity to exercise it ”81× 81  Miranda v  Arizona, 384 U S  436, 467 (1966)  In Dickerson v  United States, 530 U S  428 (2000), the Court struck down a congressional attempt to effectively abolish Miranda, holding that “Miranda announced a constitutional rule that Congress may not supersede legislatively ” Id  at 444  But Dickerson also stood by Miranda’s “invitation for legislative action” to replace Miranda with an adequate substitute  Id  at 440; see also Michael C  Dorf & Barry Friedman, Shared Constitutional Interpretation, 2000 Sup  Ct  Rev  61 (discussing legislative alternatives to Miranda)  (5) The Police Lineup Case: In United States v  Wade,82× 82  388 U S  218 (1967)  the Court created an exclusionary rule for evidence obtained from a police lineup in violation of the Sixth Amendment right to counsel but acknowledged that it could be replaced by “[l]egislative or other regulations       which eliminate the risks of abuse ”83× 83  Id  at 239  (6) The Exclusionary Rule Cases: Mapp v  Ohio made the Fourth Amendment “exclusionary rule” binding on the states,84× 84  367 U S  643, 655 (1961)  yet Congress is thought to have the power to replace it 85× 85  See Bivens v  Six Unknown Named Agents of Fed  Bureau of Narcotics, 403 U S  388, 422–24 (1971) (Burger, C J , dissenting) (inviting Congress to replace the Fourth Amendment exclusionary rule); Harold J  Krent, How to Move Beyond the Exclusionary Rule: Structuring Judicial Response to Legislative Reform Efforts, 26 Pepp  L  Rev  855, 864–71 (1999) 
All of the above are arguably constitutional default rules set by the Court that remain, to one degree or another, open to congressional revision  The list could be longer or shorter, depending on which default rules the Court will view as constitutional86× 86  A shorter list could be produced by whittling away at the constitutional status of the cases identified by Monaghan  While the Court has held that Miranda is a constitutional decision, Dickerson, 530 U S  at 444, some of the other cases may be viewed as nonconstitutional  See, e g , Collins v  Virginia, 138 S  Ct  1663, 1675–80 (2018) (Thomas, J , concurring) (arguing that Mapp is “nonconstitutional,” id  at 1678 n 5); Richard H  Fallon, Jr  et al , Hart and Wechsler’s The Federal Courts and the Federal System 775–77 (7th ed  2015) (discussing whether Bivens is constitutionally required)  Conversely, a longer list might include any constitutional right that can be waived by a party  See, e g , Daniel A  Farber, Another View of the Quagmire: Unconstitutional Conditions and Contract Theory, 33 Fla  St  U  L  Rev  913, 918 (2006) (describing the Eleventh Amendment as “just a contractual default rule that the states are free to barter away”)  Such a list might also include various constitutionally inspired judicial presumptions  See, e g , Jack Goldsmith & John F  Manning, The President’s Completion Power, 115 Yale L J  2280, 2299 (2006) (describing the Chevron presumption of delegated interpretive power to administrative agencies as “a constitutionally inspired default rule”); Nicholas Quinn Rosenkranz, Federal Rules of Statutory Interpretation, 115 Harv  L  Rev  2085, 2097–98 (2002) (describing clear statement rules as “constitutional default rules” reversible by Congress)  Many other decisions could likely be characterized as constitutional default rules; the list above is only an initial stab  and on how it will answer open questions about congressional authority over certain constitutional provisions 87× 87  See, e g , Thomas v  Wash  Gas Light Co , 448 U S  261, 272 n 18 (1980) (plurality opinion) (leaving unresolved whether Congress may limit constitutional full faith and credit obligations); White v  Mass  Council of Constr  Emp’rs, Inc , 460 U S  204, 215 n 1 (1983) (Blackmun, J , concurring in part and dissenting in part) (leaving unresolved “whether Congress may authorize       what otherwise would be a violation” of the Privileges and Immunities Clause); 1 Tribe, supra note 72, § 6-35, at 1243–44 (arguing that Congress cannot override judicial constructions of the Privileges and Immunities Clause); Metzger, supra note 69, at 1486–89 (arguing the opposite)  But the takeaway is clear: weaker stare decisis for constitutional default rules  Pre-Wayfair, one would have thought that stare decisis applies with special force to such precedents, given congressional power to set them straight  Not anymore  Why? Because it is improper to “ask Congress to address a false constitutional premise of th[e] Court’s own creation ”88× 88  Wayfair, 138 S  Ct  at 2096  The Latin for Wayfair’s doctrine is not stare decisis, which should reflect a realistic, working relationship between the legislative and judicial branches  It is mea culpa 
In its zeal to update the Constitution for “the Cyber Age,”89× 89  Id  at 2097  the Court deleted Congress from stare decisis doctrine in constitutional cases  The Court had better options  It could have left Quill on Congress’s doorstep, as the dissent argued  Or it could have justified overruling Quill notwithstanding the special force of stare decisis  Instead, the Court reasoned that it doesn’t matter whether Congress is willing and able to do the job: a constitutional mess calls for a judicial clean-up crew  For constitutional default rules — a category of decisions embracing the dormant commerce clause and sweeping far beyond — Wayfair’s new theory of stare decisis makes the Court’s precedents less sticky and Congress less relevant 
Context 3: 0066$\pm$0 0022 \\
00030895004 & 08/03/07 & 2547 & 20 6$\pm$4 8 & 0 0081$\pm$0 0019 \\
00030895005 & 10/03/07 & 2550 & 29 5$\pm$5 7 & 0 0116$\pm$0 0022 \\
00030895006 & 20/03/07 &  552 &  8 6$\pm$3 2 & 0 0156$\pm$0 0057 \\
00030895007 & 22/03/07 & 3391 & 24 4$\pm$5 4 & 0 0072$\pm$0 0016 \\
\hline
\end{tabular}
\label{xrttable}
\end{table}

The observation naturally fell into three time-separated groups, those
of obs \,1, obs \,2-5 and obs \,6-7  A similar analysis applied to
these groups (where the statistics are improved) gives rise to source
counts and count rates of 76 7$\pm$9 3\,counts and
0 0090$\pm$0 0011\,ct~s$^{-1}$ (for obs \,2-5), and
33 0$\pm$6 2\,counts and 0 0084$\pm$0 0016\,ct~s$^{-1}$ (for
obs \,6-7)  (Analysis of all the data together yields
133 6$\pm$12 3\,counts and 0 0092$\pm$0 0009\,ct~s$^{-1}$)  

A spectrum was extracted from all the Swift-XRT data from a 40\arcsec\
radius circle, using grades 0$-$12, centred on the Swift-XRT position 
A background spectrum was extracted again from all the Swift-XRT data,
from large-radius off-source circles close to the source position  An
ARF file was created using {\em xrtmkarf} and the appropriate RMF
(swxpc0to12\_20010101v008 rmf) from the Swift-XRT Calibration Database
was obtained 

Standard spectral models were again fit to the spectral data using
XSPEC  Again, C-statistics were used, as was the {\em wabs} absorption
model with the {\em wilm} cosmic abundance table  It was again 
obvious that only a very soft spectrum would be appropriate for the
data, and the only simple model that was able to fit the data
adequately was a black-body model of temperature
$kT$=$59^{+14}_{-10}$\,eV, with an absorbing hydrogen column of
9 5$^{+5 0}_{-3 9}$$\times$$10^{20}$\,cm$^{-2}$  No sufficiently constrained parameters could
be obtained using the CO white dwarf atmosphere model (MacDonald \&
Vennes 1991)  The Swift-XRT spectrum, together with the best-fit black
body model is shown in Fig \,\ref{xrtspec}  The corresponding
(0 2$-$2 0\,keV) flux is 2 7$^{+0 7}_{-1 2}\times10^{-13}$\,ergs
cm$^{-2}$ s$^{-1}$ (i e  a reduction by more than a factor 100 from
the XMM-Newton slew discovery flux), and the X-ray luminosity, for the
assumed distance of 50\,kpc, is 8 0$^{+2 2}_{-3 5}\times10^{34}$\,ergs
s$^{-1}$ 

\begin{figure}
\centering
\includegraphics[bb=100 15 580 710,clip,width=6 0cm,angle=270]{12082f2 ps}
\caption{Swift-XRT spectrum from XMMSL1 J060636 2-694933  The data
  points (crosses; adjacent data bins having been grouped together for
  the plot to have a significance of at least 3) have been fitted with
  a black body model (kT=59\,eV; see text)  The source has faded by a
  factor of $>100$ since the XMM-Newton revolution 1210 slew
  discovery  The solid line show the best fit to the spectra   The
  ratio of the data to the best fit model is shown in the lower panel 
}
\label{xrtspec}
\end{figure}

A cautious estimate of the size of the emitting region can be obtained
from the model normalization; the assumed distance of 50\,kpc yields a
maximum radius of 4 5$\times$10$^{8}$\,cm (the fit normalization is
essentially unconstrained at the lower bound)   Though great care
should be taken in interpreting this result, as the black body model
is possibly overestimating the luminosity, this obtained radius is
still consistent with that of moderately massive ($>$1 1$M_{\odot}$)
white dwarfs (Hamada \& Salpeter 1961), i e \,the whole white dwarf
surface may still be emitting at 59\,eV 

\section{Dedicated XMM-Newton observations}

We were granted an XMM-Newton Target of Opportunity (ToO) observation,
once the source became again visible to XMM-Newton, and a 10\,ks
XMM-Newton EPIC observation was made on 19th June 2007 (see
Table~\ref{slewtable})  All the XMM-Newton EPIC data, i e   the data
from the two MOS cameras and the single pn camera, were taken in
full-frame mode with the thin filter in place   These data from the
three EPIC instruments have been reprocessed using the standard
procedures in XMM-Newton SAS (Science Analysis System) $-$ v 7 1 0 
Periods of high-background, of which there were very few, were
filtered out of each dataset by creating a high-energy 10$-$15\,keV
lightcurve of single events over the entire field of view, and
selecting times when this lightcurve peaked above 0 75\,ct s$^{-1}$
(for pn) or 0 25\,ct s$^{-1}$ (for MOS)  This resulted in
$\approx$9 4(8 0)\,ks of low-background MOS(pn) data  Details of this dedicated
XMM-Newton observation, together with source position, and
(0 2$-$2\,keV) all-EPIC combined (pn, MOS1, MOS2) detected source
counts, count rate and detection likelihood are given in
Table~\ref{slewtable} 

Source spectra, containing single and double events, were extracted
from the datasets from circles (none of the data were now piled up)
centred on the source position  An extraction radius, estimated from
where the radial surface brightness profile was seen to fall to the
surrounding background level, was set to 30\arcsec  Background spectra
were extracted from each cleaned dataset from a 40\arcsec$-$80\arcsec\
annulus centred on the source position  Point sources seen to
contaminate these larger-area background spectra were removed from the
background spectra to a radius of 60\arcsec  ARF files were created
for the source spectra, and were checked to confirm that the correct
extraction area calculations had been performed  Finally RMF response
files were generated 
 
Standard spectral models were again fit to the spectral data using
XSPEC  Once again it was obvious that only a very soft model would fit the data; the only
simple model that was able to fit the data well (a P-statistic = 0 17,
based on 5000 random simulations) was a black-body model of
temperature $kT$=70$^{+3}_{-4}$\,eV, with an absorbing hydrogen column
of 6 9$^{+1 0}_{-1 6}\times10^{20}$\,cm$^{-2}$  The spectrum, together with this best-fit
model are shown in Fig \,\ref{xmmspec}  The corresponding
(0 2$-$2 0\,keV) flux is only marginally less than the Swift-XRT value
at 2 2$^{+0 8}_{-0 9}\times10^{-13}$\,ergs cm$^{-2}$ s$^{-1}$ and the
X-ray luminosity (for the assumed distance of 50\,kpc) is
6 7$^{+2 5}_{-2 8}\times10^{34}$\,ergs s$^{-1}$ 

\begin{figure}
\centering
\includegraphics[bb=110 15 570 705,clip,width=6 0cm,angle=270]{12082f3 ps}
\caption{XMM-Newton ToO spectrum from XMMSL1 J060636 2-694933  The
  data points (crosses; adjacent data bins having been grouped
  together for the plot to have a significance of at least 3)) have
  been fitted again with a black body model (kT=70\,eV) (see text) 
  EPIC-pn data is shown in black, with EPIC-MOS1 in red and EPIC-MOS2
  in green  The solid lines show the best fit to the spectra   The
  ratios of the data to the best fit model are shown in the lower
  panel }
\label{xmmspec}
\end{figure}

Given that, in this XMM-Newton ToO observation, we had obtained a
larger number of counts ($\raisebox{-1mm}{$\stackrel{>}{\sim}$}$1500 over the 3 EPIC cameras), the
physically more realistic CO white dwarf atmosphere model (MacDonald \&
Vennes 1991) was also attempted  This yielded a marginal fit (and formally
a no more statistically significant fit; P-statistic = 0 04, based on
5000 random simulations), with an effective temperature of
73$^{+3}_{-2}$\,eV, and an $N_{\rm H}$ of
3 4$^{+0 8}_{-0 8}$$\times$$10^{20}$\,cm$^{-2}$  Again, usage of the black body model results
in a larger fitted $N_{\rm H}$ and a lower fitted temperature than
with the atmosphere model  


As before, the model normalization can be used to obtain a cautious
estimate of the size of the emitting region  For the assumed distance
of 50\,kpc, then the black body model returns an emitting region
radius of only 1 3$\pm$0 2$\times$10$^{8}$\,cm   Again care should be
taken, as this may be an overestimation, the black body model having
perhaps overestimated the luminosity  For the white dwarf atmosphere
model, a smaller radius of 0 4$\pm$0 1$\times$10$^{8}$\,cm is
obtained  Note further that the assumption of a larger distance (see
Section~6) would result in a proportionally larger emitting radius 
The range in allowed radius therefore is quite large, and it is not
impossible for for the whole of the white dwarf surface to be emitting
at 70\,eV  If this is the case, then the white dwarf would have to be
at the high end of the mass range ($>$1 2$M_{\odot}$; Hamada \&
Salpeter 1961)  It may be the case then that we are at this point at,
or close to the end of the SSS phase, where the effective temperature
has reached a maximum (Sala \& Hernanz 2005), as is tentatively seen
in the spectral fitting results, and where the photospheric radius has
reached a minimum, close to the white dwarf radius 


\subsection{X-ray variability}

The full (XMM-Newton slew plus Swift-XRT plus XMM-Newton ToO) X-ray
lightcurve of XMMSL1 J060636 2-694933 is shown in
Fig \,\ref{lightcurve}  The calculated (0 2$-$2 0\,keV) flux values
are shown plotted against the number of days since the rev \,1210
XMM-Newton Slew discovery  The first two data points are the
rev \,1210 and the rev \,1246 XMM-Newton Slew observations  Then the
three nested Swift-XRT points are shown and finally the XMM-Newton ToO
observation  The level of RASS upper limit is shown to the bottom
left  The (0 2$-$2 0\,keV) X-ray flux is seen to have dropped by more
than two orders of magnitude in 230 days since the discovery, but is
then seen to have levelled off for the next 120 days, at a level still
$\approx$3 times that of the RASS  Finally, no evidence for any
short-term variability (using time bins down to 100\,s) is seen in the
highest statistic continuous X-ray lightcurve (the $\approx$8 0\,ksec
background-filtered EPIC-pn lightcurve) obtained from the 19/06/07
XMM-Newton observation 

\begin{figure}
\centering
\includegraphics[bb=60 60 550 454,clip,width=8 7cm]{12082f4 ps}
\caption{The full X-ray lightcurve of XMMSL1 J060636 2-694933  Plotted
  are the calculated (0 2$-$2 0\,keV) flux values versus time  The
  first point is the rev \,1210 XMM-Newton Slew observation, then the
  rev \,1246 XMM-Newton Slew observation  The three nested Swift-XRT points
  are shown next and finally the XMM-Newton ToO observation  The RASS upper
  limit is shown bottom left  }
\label{lightcurve}
\end{figure}


\section{Multi-wavelength Follow-up}

\subsection{Swift UVOT}

For the Feb/Mar 2007 Swift observations, we arranged for both the
Swift UVOT-B filter and the UVOT-UVW2 filters to be used in an
approximate exposure time ratio of 1:5, thus ensuring roughly equal
numbers of counts in the two bands (though there is a spectral type
dependency here)  Swift UVOT images in these two filters of the area
of sky around XMMSL1 J060636 2-694933 are shown in Fig \,\ref{uvot} 

Prior to the Swift UVOT observations, a `best-guess' to the possible
candidate optical/IR counterpart would have been the USNO-A2 0 source
0150-04066298 (B~mag: 17 4, R~mag: 16 1), seen 4\arcsec\ south of the
XMM-Newton slew position  The UVOT images however immediately showed
that the optically fainter source at position RA, Dec (J2000) = 06 06
36 4, -69 49 34 3 (error radius: ~0 5\arcsec) was a very strong UVW2
source and very blue, and was very likely the true counterpart to
XMMSL1~J060636 2-694933  (The UVW2 filter spans approximately
800\AA\,, centred at $\approx$1900\AA)

\begin{figure}
\centering
\includegraphics[bb=-82 210 695 585,clip,width=8 7cm]{12082f5 ps}
\caption{Swift UVOT images of the field around XMMSL1 J060636 2-694933 from observation
  00030895002  Left shows the UVOT B-filter and right shows the the
  UVOT UVW2-filter  The large circle is a 20\arcsec\ radius circle around
  the XMM-Newton Slew position  The small circle in the UVW2 image around the
  bright source is reproduced in the B image, indicating that a faint
  optical source is also visible at this position }
\label{uvot}
\end{figure}

The Swift UVOT pipeline processed data were analysed using the UVOT
photometry package {\em uvotsource} released with
FTOOLs\footnote{http://heasarc nasa gov/lheasoft/ftools/ftools\_menu html} 
This package performs aperture photometry on pre-specified source and
background regions, accounting for photometric- (via PSF fitting) and
coincidence loss- effects using the UVOT calibration files  Source
counts were extracted using a 5\arcsec\ radius aperture centred on the
source, while for the background we used a 10\arcsec\ radius aperture
located in a nearby source-free region   We used a larger background
aperture to effectively smooth over the modulo-8 fixed pattern noise
present in UVOT observations and to improve the statistics of the
background counts  Source counts were converted to UVOT UV-magnitudes
using the UVW2 zero-point calibration released with version~2 8 (Build
22) of the CALDB  The source is seen (see Fig \,\ref{uvotlc}) to be
roughly constant over the short duration of the Swift observations,
with a suggestion of a decline towards the end  This is in keeping
with the general form of the X-ray lightcurve (Fig \,\ref{lightcurve})
at this time 

\begin{figure}
\centering
\includegraphics[bb=80 70 535 380,clip,width=8 7cm]{12082f6 ps}
\caption{Variation of the UVW2 magnitude of the bright UV source
  during the Swift observations  The same time axis as
  Fig \,\ref{lightcurve} has been used to aid comparison, and a zoom
  is also shown  The UVW2 filter was only employed during observations
  00030895002, 00030895004, 00030895005, 00030895006 \& 00030895007
  (hence the points span the dates 07/03/07 to 22/03/07)  The errors here are 1-$\sigma$  }
\label{uvotlc}
\end{figure}

It is possible to include the UVOT-detected flux with the XRT spectrum
described in Section~3  UVOT files, created using {\em uvot2pha} for
the five observations (00030895002, 00030895004, 00030895005,
00030895006 \& 00030895007) where the UVW2 filter was employed, were
incorporated into {\em xspec}, along with the appropriate response
file (swuw2\_20041120v104 rsp) from the Swift-XRT Calibration
Database  We attempted to fit a single black-body spectrum to the
Swift-XRT+UV data (again using C-statistics, the {\em wabs} absorption
model and the {\em wilm} cosmic abundance table, plus the inclusion of
the {\em xspec-redden} component to model the absorption in the UV
band)  The best fit however, with a much lower temperature of
$kT$=$36^{+3}_{-4}$\,eV, is a very poor fit to the data; we obtain a
{\em goodness} P-statistic value of 0 00, based on 5000 random
simulations  This notwithstanding, a flux in the UVW2
(1 57$-$7 77\,eV) band of 3 5$\pm{0 2}\times10^{-13}$\,ergs cm$^{-2}$
s$^{-1}$ can be obtained, corresponding to a UVW2 luminosity, for the
assumed distance of 50\,kpc, of 1 0$\pm{0 1}\times10^{35}$\,ergs
s$^{-1}$ 

The very poor single black-body fit above, plus the large change in
fitted temperature is strongly suggestive that a model other than, or
in addition to the XRT-derived kT=59\,eV black body model (Section~3)
should be used to describe the UVW2 data  As we have no UV data other
than in the UVW2 filter, all that can be done is to apply the
XRT-derived black body model to the UVW2+XRT data, and in doing this,
a large flux excess with respect to the XRT-derived black body model
is seen in the UVW2 band  This is shown in Fig \ref{xrtuvotspec}  This
excess in UV emission (most of the $10^{35}$\,ergs s$^{-1}$ discussed
above) is likely due to a combination of residual post-nova nuclear
burning on the surface of the white dwarf, plus accretion in the disk,
including from emission lines



ground_truth: Quill harmed states more than anticipated due to the Internet.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: What is the maximum radius of the emitting region for the black body model?

Read the following text and answer briefly.

Context 3:  The situation is likely to be rather
complex, depending on the structure of both the ejecta and the
accretion disk, and is beyond the scope of the present work, where we
only have sparse UV data   For a review of the UV emission from
classical novae, see Shore (2008) 


\begin{figure}
\centering
\includegraphics[bb=100 15 580 710,clip,width=6 0cm,angle=270]{12082f7 ps}
\caption{Swift-XRT spectrum (black) from XMMSL1 J060636 2-694933, plus
  the best-fit black-body model to this spectrum (Section~3; Fig \,2),
  but extending into the UV to the Swift-UVOT UVW2 flux points (coloured)
  (see text)  The data points are plotted such that adjacent data
  bins have been grouped together to have a significance of at least
  3  The solid line show the best fit to the Swift-XRT spectrum  The
  ratio of the data to the best fit model is shown in the lower
  panel }
\label{xrtuvotspec}
\end{figure}


\subsection{Magellan optical observations}

On Nov ~13, 14, and 15, 2007, XMMSL1~J060636 2--694933 was observed
with the Low--Dispersion Survey Spectrograph 3 (LDSS3) mounted on the
Magellan Clay telescope  Images were obtained through the Sloan
$g^\prime$, $r^\prime$ and $i^\prime$ filters  On Nov ~15, 2007
conditions were photometric and the Landolt field RU 149A was observed
to flux calibrate the data in the $g^\prime$, $r^\prime$ and
$i^\prime$--bands   The Landolt (1992) magnitudes of the standards
were converted to Sloan magnitudes using the transformations presented
in Smith et al \ (2002)  All the images were debiased and flatfielded
using dome flatfield frames  We applied aperture photometry on each of
the images using DAOPHOT in \textsc{IRAF}\footnote{\textsc {iraf} is
  distributed by the National Optical Astronomy Observatories} to
compute the instrumental magnitudes of the stars  Differential
photometry of the optical counterpart to XMMSL1~J060636 2-694933
(marked by an arrow in Fig ~\ref{magellan}) was performed with respect
to the field star (marked with a `c' in Fig ~\ref{magellan})  This was the
brightest isolated and unsaturated star common to all frames   The
calibrated brightness of this comparison star is $g'= 18 42 \pm 0 04$,
$r'= 17 85 \pm 0 06$ and $i'=17 58 \pm 0 07$ 

\begin{figure}
\centering
\includegraphics[bb=35 215 575 575,clip,width=8 7cm]{12082f8 ps}
\caption{Magellan Clay LDSS3 finder chart  The counterpart to
  XMMSL1~J060636 2-694933 (and the bright Swift-UVOT UVW2-filter
  source; Figs \ref{uvot}\&\ref{uvotlc}) is marked with an arrow  The comparison star is
  shown marked with a 'c' }
\label{magellan}
\end{figure}

In addition to the imaging observations described above, we have
obtained spectroscopic observations on Nov ~13, 14, and 15, 2007 using
the VPH All grism, which has 660 lines per mm, and employing a
1\arcsec\ wide slit  This set-up provides a mean dispersion of 2\AA\,
per pixel  For a slit width of 1 arcsecond and a mean seeing close to
1\arcsec, the mean spectral resolution is $\approx$10\AA  On Nov ~13, 2007
we took 4 exposures of 450\,s each, on Nov ~14, 2007 we took 2
exposures of 900\,s each, and on Nov ~15, 2007 we took one 1200\,s
exposure with the slit at the parallactic angle  The spectra were bias
and flatfield corrected, and extracted in \textsc{IRAF}  The
instrumental response was corrected using the spectrophotometric flux
calibrators LTT 3218 (Nov ~13), H600 (Nov ~14) and LTT 9293 (Nov ~15) 
Significant differences in the flux around H$\alpha$ are apparent with
the flux being 50\% higher during the Nov ~15, 2007 with respect to
the Nov ~13, 2007 observations  Since there is no evidence for
brightening in the $r^\prime$ images we attribute the difference to
the fact that the source was not observed at the parallactic angle on
Nov ~13 and 14, 2007  We exported the one dimensional spectra to the
spectral analysis software package \textsc{molly} for further
analysis 

\begin{figure}
\centering
\includegraphics[bb=70 30 600 800,clip,width=6 8cm,angle=270]{12082f9 ps}
\caption{Magellan Clay averaged optical spectrum of the optical source
  associated with XMMSL1 J060636 2-694933  The flux scaling is
  approximate  The prominent strong emission lines are marked (see
  text)  }
\label{optspec}
\end{figure}

We have averaged all spectra (see Fig ~\ref{optspec})  We find several
strong emission lines  The strongest of these emission lines are best
interpreted as due to [OIII] 4958 9\AA\, and 5006 9\AA\,, He~II at
4685 8\AA\, and a blend of the H$\alpha$ plus the [NII] at 6548 1\AA\,
and 6583 4\AA\,, lines found often in novae (Williams 1992)  In this
case the main [OIII] lines appear redshifted by approximately 2000\,km
s$^{-1}$  We interprete this as due to clumpy outflows in the nova
shell  The integrated light from different outflowing parts can also
explain the substructure that is present in the [OIII] lines  The
outflow velocities that we obtain for the H$\alpha$ and H$\beta$ lines
is $\approx$350\,km s$^{-1}$, hence less than that for the [OIII]
lines   Note that, if XMMSL1~J060636 2-694933 does reside within the
LMC, then the systematic line-of-sight recession velocity of the LMC,
262$\pm$3 4\,km~s$^{-1}$ (van der Marel et al \ 2002), should be taken
into account; i e \,a good fraction of the observed H$\alpha$ and H$\beta$
recession would then be due to the recession of the LMC itself 

\subsection{Long-term Optical light curve}

Analysis of archival robotic optical survey data from 3-minute CCD
exposures (pixel size 14\arcsec 8), obtained with a 70\,mm (200\,mm
focal length) f/2 8 telephoto lens in the course of the All Sky
Automated Survey (ASAS; Pojmanski 2002) show that the visual magnitude
of this source rose from m$_{V}\raisebox{-1mm}{$\stackrel{>}{\sim}$}$14 to m$_{V}$$\approx$12 between
Sep ~18, 2005 and Sep ~30, 2005, and then declined rapidly thereafter (see
Fig \ref{optlc})  ASAS did not detect any significant emission from
the source after around November 2005, the source having dimmed below
the limiting magnitude of ASAS 

The decline from the brightest data point ($\approx$2 2 magnitudes in
10 days, then a further $\sim$1 3 magnitudes in 46 days) suggests that
this is a nova of the 'very fast' speed class (Warner 1995, Downes
et al \ 2001)  We estimate that the time that the light curve takes to
decline 2 magnitudes below maximum observed brightness is
8$\pm$2\,days (see Section~6) 

\begin{figure}
\centering
\includegraphics[bb=30 78 453 549,clip,width=7 8cm,angle=270]{12082f10 ps}
\caption{All Sky Automated Survey V-band magnitudes of the optical counterpart 
to XMMSL1~J060636 2-694933, during outburst (late September 2005) and afterwards }
\label{optlc}
\end{figure}



\section{Discussion}

The optical spectrum, showing lines of [OIII] 4958 9\AA\, and
5006 9\AA\,, He~II at 4685 8\AA\, and a blend of the H$\alpha$ plus
[NII] at 6548 1\AA\, and 6583 4\AA\, suggests that
XMMSL1~J060636 2-694933 was a nova, observed (in Nov 2007) in the late
A$_{0}$ auroral phase  The fact that the observed [OIII] lines are not
in the more usual, optically thin 3:1 ratio, can be explained in terms
of a clumpy outflow scenario, whereby individual clumps of both
rest-frame and redward-shifted material are observed, and the
superposition of these account for the observed [OIII] ratio (note
further that density enhancements can change observed [OIII] ratios to
more like $\sim$1:1)  Clumps of material are often seen in nova ejecta
(e g  Shara et al \ 1997), and outflows of speeds around 2000\,km
s$^{-1}$ are not uncommon in novae (e g  in nova LMC 1991; Schwartz
et al \ 2001) 

XMMSL1~J060636 2-694933 was likely at its onset (in Oct 2005) a very
fast, Fe~{\sc ii} nova (Section~3 and Williams et al \ 1991; Williams
et al \ 1994)  An accurate classification now however is not possible,
so late after maximum brightness  The soft ($kT_{\rm
  eff}$$\approx$60--70\,eV) X-ray spectrum indicates that the nova was
in a super-soft source (SSS) state (Krautter 2008) during its
discovery (in July 2006), and throughout its X-ray decline (by more
than two orders of magnitude) in the observations of Sept 2006, March
2007 and June 2007   Such a state originates from nuclear burning on
the surface of the white dwarf, and measurements of the intensity,
duration, and temperature can be used to estimate the distance to the
nova and the mass of the white dwarf (e g  Balman et al \ 1998; Lanz
et al \ 2005)  Indeed, we believe (Section~4) that the white dwarf
within XMMSL1~J060636 2-694933 may be quite massive
($>$1 2$M_{\odot}$) 

As discussed earlier, classical novae are almost always discovered
optically in the early phases of their outbursts 
XMMSL1~J060636 2-694933 is very unusual therefore in that it has been
discovered first in X-rays  As such, it is useful to compare it with
XMMSL1~J070542 7-381442 (also known as V598 Pup; Read et al \ 2008),
another nova recently discovered (in X-rays) in the XMM-Newton slew
survey  With a peak $m_{V}$ of $\ltsim12$, XMMSL1~J060636 2-694933 is
not a particularly bright nova (c f  V598 Pup, which reached an
m$_{V}$ of $\raisebox{-1mm}{$\stackrel{<}{\sim}$}$4), and so it is not surprising that it went
unnoticed, only being discovered in X-rays during the later (here
291\,days after the outburst), optically thin nebular phase, when
classical novae are typically observed as soft X-ray sources  Though
this delay should be taken as a upper limit, it is long when compared
to V598 Pup ($\raisebox{-1mm}{$\stackrel{<}{\sim}$}$127 days), but may instead be more similar to the
delays of $\sim$200 days seen in V1974 Cyg (Krautter et al \ 1996),
$\sim$6 months of V382 Vel (Orio et al \ 2002), and 6$-$8 months of
V1494 Aql (Drake et al \ 2003)  In their X-ray monitoring of optical
novae in M31, Pietsch et al \ (2007) detect 11 out of 34 novae in
X-rays within a year after their optical outbursts  Seven novae are
seen to be X-ray bright, several (3$-$9) years after outburst, and
three novae showed very short X-ray outbursts, starting within
50\,days of outburst, but lasting only two to three months 
XMMSL1~J060636 2-694933 therefore is not particularly unusual 

A method to estimate the distance to the nova is to use the relation
between the absolute magnitude at maximum brightness and the time that
the light curve takes to decline 2 magnitudes below maximum
brightness, $t_{2}$ (Della Valle \& Livio 1995)  We have no
information over the 12 days between the data point of maximum
brightness and the lower limit prior to this (Fig \,\ref{optlc}), and
therefore we have no exact outburst date, nor exact apparent
magnitude at outburst   Assuming for the moment though that we have
caught the outburst exactly in the Sep ~30, 2005 observation, then we
can estimate (Sect ~5 3) $t_{2}$ to be 8$\pm$2\,days, and using this,
we can estimate (Della Valle \& Livio 1995) the absolute magnitude at
maximum brightness $M_{V}$ to be --8 7$\pm$0 6  An absolute magnitude
of $M_{V}$=--8 7 implies a peak luminosity $\sim$7 times the Eddington
luminosity for a 1\,$M_{\odot}$ white dwarf  This is quite typical of
novae 

With $A_{V}$=0 39$^{+0 05}_{-0 09}$ (90\% error), as derived (Predehl
\& Schmitt 1995) from $N_{\rm
  H}$=6 9$^{+1 0}_{-1 6}\times10^{20}$\,cm$^{-2}$ (from the highest
statistic spectral fit; the XMM-Newton ToO observation), and with
$M_{V}$=--8 7$\pm$0 6, and a peak $m_{V}$ of 12 0, we can derive a
distance to XMMSL1~J060636 2-694933 of 115$^{+43}_{-30}$\,kpc   As
discussed above however, we are unsure as to the exact outburst date
and the maximum brightness at outburst  Our assumed peak $m_{V}$ of
12 0 is almost certainly an underestimation  Although we have no
information in the 12 days prior to Sep ~30, 2005, a simple linear
extrapolation of the early October lightcurve back prior to Sep ~30,
2005 suggests that the actual peak $m_{V}$ was somewhere between 9 and
12  The corresponding distance estimates are then between 29 and
115\,kpc (with a mid-point $m_{V}$=10 5 value yielding a distance
estimate of 58\,kpc)  Many methods have been used to estimate the
distance to the LMC (e g   Kovacs 2000, Nelson et al \ 2000), but a
value of around 50\,kpc appears to be quite robust  Our distance
estimate is certainly consistent with that of the LMC, though the
errors are quite large   It does appear to be the case however, that
our distance estimate places the source far outside of our own Galaxy 
This, together with the source's position on the sky (at the eastern
edge of the LMC) and the sizable ($\sim$Galactic) X-ray hydrogen
column densities obtained from the spectral fits, suggest strongly
that XMMSL1~J060636 2-694933 lies within the LMC itself   Note further
that the (pile-up corrected) spectral model normalizations to the
initial Slew discovery data (Sect ~2) also imply an approximate
distance to XMMSL1~J060636 2-694933 of $\sim$50\,kpc 

The source had, at the time of the slew detection, an absorbed
(0 2$-$2\,keV) X-ray flux of 4 8$^{+2 7}_{-1 6}\times10^{-11}$\,ergs
cm$^{-2}$ s$^{-1}$, corresponding to a 0 2$-$2\,keV X-ray luminosity
(at 50\,kpc) of 1 4$^{+0 8}_{-0 5}\times10^{37}$\,ergs s$^{-1}$ 
Assuming instead for the moment a distance more like 100\,kpc (though
this is thought to be well beyond the LMC, e g  Kovacs 2000), then the
(0 2$-$2\,keV) X-ray luminosity of
5 7$^{+3 0}_{-1 9}\times$$10^{37}$\,erg s$^{-1}$ obtained is at the high end of the X-ray luminosities of
classical SSS-phase novae discussed e g \,in Orio et al \ (2002) and
Ness et al \ (2007)  As discussed though, we have very likely missed
the outburst peak, and as such, our more probable assumed distance of
50\,kpc gives rise to a more typical SSS-phase X-ray luminosity   The
luminosities of 7$-$8$\times$$10^{34}$\,erg s$^{-1}$, obtained during
the Swift and pointed XMM-Newton observations, are more typical of
novae at later times, when the emission can also sometimes be
described by a thermal plasma, rather than a black-body type spectrum,
or a more mixed spectrum, due to the complex structure of the ejecta
and the accretion disk (Krautter 2008, Shore 2008) 


\section{Conclusions}

A bright X-ray source, XMMSL1~J060636 2-694933, was detected in an
XMM-Newton slew on 18 July 2006 at a position where no previous X-ray
source had been seen  The XMM-Newton slew data, plus follow-up dedicated
XMM-Newton and Swift observations, plus optical imaging and
spectroscopic data acquired with the Magellan Clay telescope and 
All-Sky Automated Survey (ASAS) data were used to classify the new object
as a nova, and to examine its properties  The primary conclusions are
as follows:

  \begin{itemize}

  \item The soft X-ray spectrum indicates that the nova was in a
    super-soft source (SSS) state at its discovery in July 2007
    (XMM-Newton slew) and through its X-ray decline (by over two
    orders of magnitude) in September 2006 (XMM-Newton slew), March
    2007 (Swift) and June 2007 (XMM-Newton) 

  \item The Magellan optical spectrum (Nov 2007) of the source
    indicates that it was very likely then a nova in the late
    A$_{0}$ auroral phase 

  \item The very fast optical decline (ASAS) during the nova's onset
    (Oct 2005), indicates that the initial nova was likely of speed class
    'very fast' 

  \item The very fast speed, together with the absolute magnitude at
    maximum brightness and the X-ray absorption, give rise to a
    distance to the source far beyond our own Galaxy  The large
    distance, together with the source's position in the sky, at the
    eastern edge of the LMC, and the spectral information from the
    X-ray data, are very suggestive that the nova is situated within
    the LMC itself 

  \item Analysis of XMM-Newton slew data is continuing to provide a
    powerful means of finding new X-ray transient objects 

\end{itemize}

\begin{acknowledgements}

  The XMM-Newton project is an ESA Science Mission with instruments
  and contributions directly funded by ESA Member States and the USA
  (NASA)  The XMM-Newton project is supported by the Bundesministerium
  f\"ur Wirtschaft und Technologie/Deutsches Zentrum f\"ur Luft- und
  Raumfahrt (BMWI/DLR, FKZ 50 OX 0001), the Max-Planck Society and the
  Heidenhain-Stiftung  AMR and PE acknowledge the support of STFC
  funding, and PGJ of the Netherlands Organisation for Scientific
  Research  The ASAS project is supported by the N2030731/1328 grant
  from the MNiSzW  We thank the referee (G \,Sala) for very useful
  comments and several references that have improved the paper
  notably  We thank Kim Page for providing the white dwarf atmosphere
  model, and we thank her and Graham Wynn for useful discussions  The
  use of the spectral analysis software package \textsc{molly} written
  by Tom Marsh is also acknowledged  MM acknowledges support by a
  Miller Institute Research Fellowship during the time in which part
  of the work was completed 

\end{acknowledgements}





ground_truth: 4.5x10^8 cm.