text:
\section{Introduction}

Molecular clouds are birthplaces of stars that form the visible backbones of galaxies.
Therefore, it is important to investigate the molecular gas mass, its distribution in galaxies and its physical properties to understand galaxy evolution.
Molecular gas in galaxies mainly consists of H$_2$ molecules.
However, H$_2$ molecules do not radiate line emissions in cold environments such as molecular clouds whose temperature is typically a few tens K, since H$_2$ is a homonuclear diatomic molecule (i.e., no dipole moment).
Molecular gas mass is usually estimated indirectly from observations of heteronuclear diatomic molecules such as $^{12}$CO and its isotopologues since they are the second most abundant molecules after H$_2$ in the interstellar medium.
Therefore, $^{12}$CO$(J=1-0)$ line ($^{12}$CO, hereafter) has been commonly used to observe molecular gas in external galaxies as well as the Galactic objects.

It has been observationally shown that the $^{12}$CO line luminosity correlates with the molecular gas mass estimated in several different ways, such as virial techniques, dust emission, extinction mapping and gamma-ray observation (\cite{Bolatto+2013} and references therein).
The correlation between $^{12}$CO luminosity and molecular gas mass is explained theoretically under the assumptions that 1) molecular clouds are virialized, 2) the mass of clouds are dominated by H$_{2}$, 3) the clouds follow the size-line width relation and 4) they have a constant temperature (\cite{Bolatto+2013} and references therein).
According to the observational evidence and the theoretical explanation above, the mass and distribution of molecular gas in nearby galaxies have been investigated with the observed $^{12}$CO maps by assuming a constant CO-to-H$_2$ conversion factor over a whole galaxy (e.g., BIMA SONG, \cite{Helfer+2003}; Nobeyama CO atlas, \cite{Kuno+2007}, hereafter K07; Heracles, \cite{Leroy+2009}).

For a more accurate estimation of the molecular gas mass, multiple CO-isotopologues should be used in a complementary manner.
The mass of virialized molecular clouds can be measured with $^{12}$CO and the higher opacity of $^{12}$CO allows us to trace the molecular gas with lower densities on the order of $10^2$ cm$^{-3}$.
On the other hand, the opacity of $^{12}$CO is too high to estimate the column density through the molecular cloud unlike more optically thin lines such as $^{13}$CO$(J=1-0)$ and C$^{18}$O$(J=1-0)$ ($^{13}$CO and C$^{18}$O, hereafter).
However, the line intensities of these CO-isotopologues are usually much weaker than that of $^{12}$CO (by factors of $\sim1/5-1/20$ for $^{13}$CO and \hspace{0.3em}\raisebox{0.4ex}{$<$}\hspace{-0.75em}\raisebox{-.7ex}{$\sim$}\hspace{0.3em}$1/20$ for C$^{18}$O, respectively) and require a lot of telescope time to be detected.
Therefore, $^{13}$CO or C$^{18}$O mapping observations toward nearby galaxies have been limited to only a handful of cases \citep{Huttemeister+2000,Paglione+2001,Tosaki+2002,Hirota+2010,Watanabe+2011}.

Some studies have investigated the relation between the physical states of molecular gas and galactic structures such as arms and bars from the CO multi-isotopologue observations (e.g. \cite{Huttemeister+2000,MeierTurner2004}).
\citet{Watanabe+2011} (hereafter W11) observed NGC~3627 in $^{13}$CO and showed high $^{12}$CO/$^{13}$CO intensity ratios in the bar region.
They concluded that the high $^{12}$CO/$^{13}$CO ratio indicates the existence of gravitationally unbound diffuse gas as a result of the strong streaming motion in the bar region.
Spiral arms are also likely to affect not only the dynamics of molecular clouds but also their internal physical conditions.
The molecular gas in spiral galaxies is expected to be accumulated at the arm region through galactic shocks (e.g. \cite{Fujimoto1968,Roberts1969,Egusa+2011}) and sheared out in interarm regions due to the differential rotation.
However there are only a few studies that focus on the physical states of molecular gas in interarm regions since even the $^{12}$CO emission is quite weak \citep{Tosaki+2002}.
To understand the effects of spiral arms on the molecular clouds, it is necessary to detect emissions of CO isotopologues in the first place and then investigate the physical states of molecular gas in the interarm region.

The aim of this paper is to detect weak $^{13}$CO emission and investigate the relationship between the galactic structures and properties of molecular gas by comparing $^{12}$CO and $^{13}$CO spectra in the characteristic regions of spiral galaxies.
We stacked $^{12}$CO and $^{13}$CO spectra of a nearby barred spiral galaxy, NGC~3627\footnote{
NGC~3627 is classified as SABb in the Third Reference Catalog of Bright Galaxies (RC3, \cite{deVaucouleurs+1991}) and has slightly asymmetric spiral arms.
This asymmetric feature of the spiral arms is thought to have arisen from a past interaction with a neighboring galaxy, NGC~3628 (\cite{Haynes+1979,Zhang+1993}).
}
obtained in previous studies (K07\nocite{Kuno+2007} and W11\nocite{Watanabe+2011}) after shifting the velocity axis so that the zero of the $^{13}$CO spectra corresponds to the local mean $^{12}$CO velocity.
This stacking method was originally proposed by \citet{Schruba+2011} where the local mean velocity of HI is adopted as the zero velocity of $^{12}$CO spectra in the outer region of galaxies.
This allows us to improve the signal-to-noise ratios (S/N) of the spectra.
Then we discuss the physical properties of molecular gas in the interarm region by comparing the $^{12}$CO and $^{13}$CO spectra.

The structure of this paper is as follows:
The data and method are explained in section \ref{DandA}.
We show the results of the stacking analysis of the $^{12}$CO and $^{13}$CO spectra in the different regions of NGC~3627 in section \ref{Results}.
We compare the $^{12}$CO with $^{13}$CO stacked spectra in section \ref{Analyses} and discuss the physical properties of the molecular gas in the different regions of NGC~3627 in section \ref{Discussion}.
Finally, we summarize this study in section \ref{Summary}.

\section{Data \& stacking technique}\label{DandA}

We first summarize the data we used and the stacking method in the following sub-sections.

\subsection{Data}

\begin{table*}
\caption{Summary of the $^{12}$CO and $^{13}$CO observations.}
\begin{center}
\begin{tabular}{lcc}
\hline
&$^{12}$CO&$^{13}$CO\\
\hline
\hline
Date & April in 2004 & May in 2007 and April in 2008\\
Telescope & the 45-m telescope at NRO & the 45-m telescope at NRO\\
$\eta_{\rm mb}$ & 0.4 & 0.31\\
Receiver & BEARS & BEARS\\
Backend & digital spectrometers & digital spectrometers\\
Band width (MHz) & 512 & 512\\
Grid spacing & $10''.3$ & $10''.3$\\
r.m.s. (mK, $T_{\rm mb}$) & $40-100$ & $6-16$\\
Velocity resolution (km s$^{-1}$) & 5 & 20\\
Reference & \cite{Kuno+2007} (K07) & \cite{Watanabe+2011} (W11)\\
\hline
\end{tabular}
\end{center}
\label{tab-1}
\end{table*}%

$^{12}$CO and $^{13}$CO mapping data of NGC~3627 were both obtained with the 25-BEam Array Receiver System (BEARS) which is a 25 $(5\times5)$ beam SIS receiver mounted on the 45-m radio telescope at the Nobeyama Radio Observatory (NRO) (K07\nocite{Kuno+2007}; W11\nocite{Watanabe+2011}).
The rest-frame frequencies of $^{12}$CO and $^{13}$CO are adopted as $115.27120$ GHz and $110.20135$ GHz, respectively.
For the backend, 25 digital spectrometers \citep{Sorai+2000} were used with a total bandwidth of 512 MHz and frequency resolution of 605 kHz centered on the frequency corresponding to the local standard of rest (LSR) receding velocity.
We adopted $16''$ as a half-power beam width (HPBW) of both data in the same way as W11\nocite{Watanabe+2011}, which corresponds to $\sim$ 800 pc assuming a distance of 11.1 Mpc to NGC~3627 \citep{Saha+1999}\footnote{To be exact, the beam sizes at the frequency of $^{12}$CO and $^{13}$CO are $\sim16''$ and $\sim17''$, respectively but no correction is applied since the error due to this is expected to be small, especially for the spatially extended sources ($\sim10\%$ even for a point source, W11\nocite{Watanabe+2011}).}.
The grid spacing of the map is $10''.3$ ($\sim550$ pc).
The typical r.m.s. noise temperatures (in $T_{\rm mb}$ scale) of $^{12}$CO and $^{13}$CO data are $40-100$ mK at 5 km s$^{-1}$ resolution and 6$-$16 mK at 20 km s$^{-1}$ resolution, respectively.
The profile maps of $^{12}$CO and $^{13}$CO are shown in figure \ref{fig:ProfileMap}.
The observations are summarized in table \ref{tab-1}.
More detailed information of the observations is described in the original studies, K07\nocite{Kuno+2007} for $^{12}$CO and W11\nocite{Watanabe+2011} for $^{13}$CO, respectively.

\subsection{Stacking analysis of $^{12}$CO and $^{13}$CO spectra with Velocity-axis Alignment (VA)}

Schruba et al.(2011, 2012\nocite{Schruba+2011,Schruba+2012}) improved the sensitivity for $^{12}$CO emission in outer regions of galaxies by up to about one order of magnitude over previous studies with the stacking method they invented.
One way to reduce the r.m.s. noise temperature is to stack the spectra from various regions in the galaxy.
However, because the systemic velocities of each part of the galaxy are different due to galactic rotation, simple stacking will result in a smeared spectrum and may not yield the highest S/N.
The method adopted by \citet{Schruba+2011} overcomes this problem by shifting the spectrum in the velocity axis so that they are aligned with the mean of the local HI velocity, before stacking the spectra.
The S/N of the integrated intensity increases by a factor of $\sqrt{\Delta V_{\rm emi}/\Delta V_{\rm emi, VA}}$, taking into account that the error of the integrated intensity can be expressed as $\Delta T \sqrt{\Delta V_{\rm emi} \Delta v}$, where $\Delta V_{\rm emi}$ is the velocity range to be integrated to calculate the integrated intensity of the spectra obtained with normal stacking, $\Delta V_{\rm emi, VA}$ is one with stacking after the velocity-axis alignment, $\Delta T$ is the r.m.s. noise temperature and $\Delta v$ is the velocity resolution of the data \citep{Schruba+2012}.
Here $\Delta V_{\rm emi, VA}$ is narrower than $\Delta V_{\rm emi}$ thanks to the velocity-axis alignment.
Another reason is the reduction of frequency-dependent noise produced by systematic effects of weather, receiver instabilities and standing waves occurring during the transmission of the signal.
These sources of additional noise are canceled out if the spectra are stacked after applying different velocity shifts for each pixel \citep{Schruba+2011}.

\citet{Schruba+2011} stacked $^{12}$CO spectra of the outer HI-dominated region after shifting the velocity axis so that the zero velocity of the $^{12}$CO spectra corresponds to the local mean HI velocity.
In this paper, we adopt an intensity weighted mean velocity of $^{12}$CO as a reference velocity for the velocity-axis alignment procedure and apply the stacking method of \citet{Schruba+2011} to improve the S/N of $^{13}$CO spectra as well as that of $^{12}$CO spectra.

First, the velocity field of NGC~3627 is estimated with the $^{12}$CO data.
The intensity-weighted mean velocity of each pixel of the $^{12}$CO map is given by,
\begin{equation}
\overline{v_{\rm ^{12}CO}} = \frac{\int v T_{\rm mb}(v) dv}{\int T_{\rm mb}(v) dv}.
\end{equation}
The obtained first-moment map is shown in figure \ref{fig:ProfileMap} (d).
Then the shifted velocity $v_{\rm VA}$ of each spectrum is defined as
\begin{equation}
v_{\rm VA} = v_{\rm LSR} - \overline{v_{\rm ^{12}CO}},
\end{equation}
where $v_{\rm LSR}$ is the original velocity of the spectrum.
Hereafter, we refer to this procedure as velocity-axis alignment (VA).

The averaged spectra of six different regions, 1) center, 2) bar, 3) bar-end, 4) offset\footnote{Offset region denotes an area where the emission runs off toward the leading side of the stellar bar (W11\nocite{Watanabe+2011}).}, 5) arm and 6) interarm were obtained by stacking the spectra after the VA procedure\footnote{
We integrated full velocity range for the calculation of the local mean velocities of the all regions but the offset region.
The mean velocities of the spectra in the offset region, which is shown as an orange region in figure \ref{fig:ProfileMap}, are estimated by the integration ranging from $487.5$ to $687.5$ km s$^{-1}$, since we could not obtain adequate value in case of the full range integration due to poor quality of the baseline.}.
The regions of 1) $-$ 4) were determined according to W11\nocite{Watanabe+2011}.
We visually defined 5) arm and 6) interarm regions by dividing the ``other'' region in W11\nocite{Watanabe+2011} according to optical and near infrared (NIR) images.
NIR image ($3.6$ $\mu$m) from the SIRTF Nearby Galaxies Survey (SINGS, \cite{Kennicutt+2003}) is shown in figure \ref{fig:ProfileMap}c.
Each area is illustrated in different colors in figures \ref{fig:ProfileMap}a and \ref{fig:ProfileMap}b in the following way, the center in red, bar in green, bar-end in blue, offset in orange, arm in purple and interarm regions in yellow.
Finally, we averaged the velocity-axis aligned spectra with equal weights and obtained a stacked spectrum in each region.

\begin{figure*}
\includegraphics[width=168mm]{profile_map-01.eps}
 \vspace{0cm}
 \caption{(a) $^{12}$CO and  (b) $^{13}$CO profile maps of NGC~3627 obtained with the 45-m telescope at NRO (K07\nocite{Kuno+2007}; W11\nocite{Watanabe+2011}). The mapping area is $3'.2\times3'.2$ centered on $(\alpha, \delta)_{\rm J2000} = (11^{\rm h}20^{\rm m} 15^{\rm s}.027, +12^\circ 59' 29''.58)$. The grid size of both data are $10''.3$ and $\sim550$ pc in a linear scale. The center, bar, bar-end, offset, arm and interarm regions are colored red, green, blue, orange, purple, and yellow, respectively. (c) Spitzer/IRAC $3.6$ $\mu$m image \citep{Kennicutt+2003}. (d) 1st-moment map of the $^{12}$CO emission.}
  \label{fig:ProfileMap}
\end{figure*}

\section{Results}\label{Results}

\begin{figure*}
\includegraphics[width=150mm]{Spectra_stacking-01.eps}

 \vspace{0cm}

 \caption{(a) $^{12}$CO stacked spectra without the velocity-axis alignment (VA), (b) $^{12}$CO stacked spectra with VA, (c) $^{13}$CO stacked spectra without VA and (d) $^{13}$CO stacked spectra with VA.
 The vertical axis of each spectrum is main-beam temperature in mK.
 The velocity resolution of $^{12}$CO and $^{13}$CO spectra is 20 km s$^{-1}$.
 The fitting results with a Gaussian for the stacked spectra with VA are also plotted with red lines on each spectrum.
 }
  \label{fig:StackedSpectra}
\end{figure*}

\begin{table*}
 \caption{The properties of the spectrum in each different region.}
 \label{tab-2}
 \begin{minipage}{\textwidth}
 \begin{center}
 \begin{tabular}{@{}lccccc}
  \hline
   Line& $^{12}$CO & $^{12}$CO & $^{13}$CO & $^{13}$CO\\
   VA procedure & no & yes & no & yes\\
  \hline
  \hline
Center &  &  &  &  &  \\
$I_{\rm CO}$ (K km s$^{-1}$)& $70.0\pm2.0$ (36)\footnotemark[$\ast$] & $70.6\pm2.2$ (32) & $3.37\pm0.53$ (6) & $3.59\pm0.38$ (10) \\
FWHM\footnotemark[$\ast\ast$] (km s$^{-1}$) & $225\pm11$ & $194\pm6$ & $209\pm36$ & $195\pm21$ \\
$T_{\rm peak}$ (mK) & $308\pm20$ (15) & $347\pm22$ (15) & $22.3\pm5.3$ (4) & $18.2\pm3.9$ (5) \\
  \hline
Bar &  &  &  &  &  \\
$I_{\rm CO}$ (K km s$^{-1}$)& $45.1\pm1.6$ (29) & $45.2\pm1.6$ (28) & $1.17\pm0.24$ (5) & $1.42\pm0.09$ (16)\\
FWHM (km s$^{-1}$) & $287\pm34$ & $147\pm7$ & -- & $126\pm14$ \\
$T_{\rm peak}$ (mK) & $241\pm17$ (14) & $323\pm19$ (17) & $8.28\pm2.64$ (3) & $13.4\pm1.1$ (12) \\
  \hline
Bar-end &  &  &  &  &  \\
$I_{\rm CO}$ (K km s$^{-1}$)& $45.5\pm1.3$ (36) & $46.6\pm0.6$ (74) & $3.54\pm0.22$ (16) & $3.56\pm0.11$ (33)\\
FWHM (km s$^{-1}$) & $87\pm5$, $126\pm14$\footnotemark[$\ast\ast\ast$] & $110\pm4$ & $112\pm9$, $76\pm14$ & $100\pm4$ \\
$T_{\rm peak}$ (mK) & $220\pm14$ (15), $215\pm14$ (15) & $400\pm9$ (44) & $18.1\pm2.5$ (7), $20.8\pm2.5$ (8) & $34.5\pm1.6$ (22) \\
  \hline
Offset &  &  &  &  &  \\
$I_{\rm CO}$ (K km s$^{-1}$)& $20.6\pm1.1$ (19) & $20.1\pm0.9$ (23) & $1.46\pm0.25$ (6) & $1.52\pm0.23$ (7)\\
FWHM (km s$^{-1}$) & $67\pm5$ & $67\pm3$ & $50\pm6$ & $54\pm7$ \\
$T_{\rm peak}$ (mK) & $276\pm20$ (14) & $279\pm16$ (17) & $28.7\pm4.5$ (6) & $26.9\pm4.4$ (6) \\
  \hline
Arm &  &  &  &  &  \\
$I_{\rm CO}$ (K km s$^{-1}$) & $29.5\pm1.0$ (31) & $28.6\pm0.6$ (51) & $2.24\pm0.27$ (8) & $2.01\pm0.11$ (19)\\
FWHM (km s$^{-1}$) & $206\pm11$ & $104\pm4$ & $168\pm16$ & $97\pm8$ \\
$T_{\rm peak}$ (mK) & $133\pm11$ (12) & $248\pm7$ (36) & $13.7\pm3.2$ (4) & $19.1\pm1.3$ (15) \\
  \hline
Interarm &  &  &  &  &  \\
$I_{\rm CO}$ (K km s$^{-1}$) & $22.4\pm0.9$ (25) & $20.4\pm1.0$ (20) & $1.02\pm0.27$ (4) & $0.824\pm0.118$ (7)\\
FWHM (km s$^{-1}$) & $268\pm23$ & $159\pm7$ & $170\pm55$ & $94\pm13$ \\
$T_{\rm peak}$ (mK) & $88\pm10$ (9) & $130\pm13$ (10) & $6.89\pm2.82$ (2) & $8.24\pm1.52$ (5) \\
  \hline
\end{tabular}
\end{center}
\footnotetext[$\ast$]{The signal-to-noise ratios of $I_{\rm CO}$ and $T_{\rm peak}$ are shown in the round bracket after each value.}
\footnotetext[$\ast\ast$]{The FWHM is estimated with Gaussian fitting.}
\footnotetext[$\ast\ast\ast$]{ For the stacking results without the VA procedure in the bar-end region, the FWHM and $T_{\rm peak}$ values of the two velocity components in the spectra are shown separately.}
\end{minipage}
\end{table*}

The stacked spectra with and without the VA procedure of $^{12}$CO and $^{13}$CO are shown in figure \ref{fig:StackedSpectra}.
The $^{12}\rm{CO}$ spectra are binned so that the velocity resolution matches that of the $^{13}\rm{CO}$ spectra (i.e., 20 km s$^{-1}$).
The smoothed $^{12}$CO spectra are employed for the following analysis.
The r.m.s. noise temperatures of the stacked $^{12}$CO and $^{13}$CO spectra per $20$ km s$^{-1}$
are typically reduced to $7-22$ mK and $1.1-4.4$ mK, respectively.
The error of the $T_{\rm peak}$ listed in table \ref{tab-2} is the r.m.s. noise temperature, which is calculated within a narrow velocity range outside the emission line.
This is because we must calculate the r.m.s. noise temperature within the baseline range in which the same number of data are stacked as the emission line range.
The number of the stacked data is getting small as the velocity offset from the line center is large.
In table \ref{tab-2}, some errors of $T_{\rm peak}$ and $I_{\rm CO}$ of the stacked spectra with VA are slightly larger than those of the stacked spectra without VA.
This may be partly attributed to the poor statistics in estimation of the r.m.s. noise temperature.

The increase of the peak temperature and the reduction of noise level by the stacking analysis after the VA procedure allow us to detect $^{13}$CO emission even from the interarm region with S/N of 5 where the emission was not detected in the spectrum of each pixel in the original data or in the stacked spectrum without the VA procedure (S/N $=2$).
The fitting results with a Gaussian for the stacked spectra after the VA procedure are also plotted with red lines on each spectrum in figure \ref{fig:StackedSpectra}.
The integrated intensity ($I_{\rm CO}$), full width at half maximum (FWHM) and the peak temperature ($T_{\rm peak}$) of $^{12}$CO and $^{13}$CO with and without the VA procedure in different regions of NGC~3627 are shown in table \ref{tab-2}.
Although the line profiles of the stacked spectra, especially the one without the VA procedure, do not look like a Gaussian, the FWHM and its error are determined by a Gaussian fitting and the fitting error, respectively.
If the FWHM is calculated literally as the width at the half of the peak intensity, the derived FWHM is more susceptible to the r.m.s. noise temperature than the one from global fitting.
In table \ref{tab-2}, we also separately present the FWHM and $T_{\rm peak}$ values of the two velocity components in the bar-end spectrum obtained without the VA procedure.

The validity of this method is examined by comparing the integrated intensity of the stacked spectra with and without the VA procedure.
Both spectra obtained with and without the VA procedure are the averaged spectra in each region.
Therefore, the integrated intensity estimated in both ways should be the same.
In table \ref{tab-2}, we see that the two $I_{^{12}\rm{CO}}$ values of each region are almost the same within the error, confirming the validity of the stacking method with the VA procedure.
Moreover the S/N of $I_{\rm CO}$ of each spectrum is improved by a factor of up to 3.2.

\section{Analyses}\label{Analyses}

\subsection{Surface density of molecular gas mass}

We estimate the surface density of molecular gas mass in the six regions of NGC~3627 from the $^{12}$CO and $^{13}$CO spectra.
$I_{\rm ^{12}CO}$ and $I_{\rm ^{13}CO}$ estimated from Gaussian fitting are used for the calculation hereafter, since the line profiles of the stacked spectra after the VA procedure are well fitted with a Gaussian (see figure \ref{fig:StackedSpectra})\footnote{
The $^{13}$CO emission line of the stacked spectra in the center region has a bluewards wing that is not seen in $^{12}$CO spectra with higher S/N than $^{13}$CO.
Therefore the wing is not expected to be a realistic feature but a wrong feature due to bad baselines of $^{13}$CO spectra.
The Gaussian fitting is not expected to be severely affected by this feature, because the FWHM of $^{13}$CO is consistent with the one of $^{12}$CO within the margin of error.
}.
The integrated intensities estimated with a Gaussian fitting agree with the values listed in table \ref{tab-2} within the margin of error.
The column density of H$_2$, $N_{\rm H_2}$ (cm$^{-2}$), for extragalactic objects is commonly estimated from $I_{\rm ^{12}CO}$ with a CO-to-H$_2$ conversion factor, $X_{\rm CO}$ (cm$^{-2}$ [K km $\rm s^{-1}$]$^{-1}$) under the premise that $^{12}$CO is optically thick.
If $^{12}$CO is optically thick, the brightness temperature is not mainly related to the column density of gas but to the excitation temperature of the $\tau_{\rm ^{12}CO}\sim1$ surface of the virialized molecular clouds \citep{Bolatto+2013}.
$N_{\rm H_2}$ is described as
\begin{equation}
N_{\rm H_2} = X_{\rm CO} I_{\rm ^{12}CO}.
\end{equation}

We can also estimate $N_{\rm H_2}$ from the column density of $^{13}$CO, $N_{\rm ^{13}CO}$ as long as the $^{13}$CO emission is optically thin.
Under the local thermal equilibrium (LTE) approximation, $N_{\rm ^{13}CO}$ can be calculated as
\begin{equation}
N_{\rm ^{13}CO} = \frac{3 k_{\rm B}}{4 \pi^3 \mu^2 \nu_{\rm ^{13}CO}}\exp{\left(-\frac{h\nu_{\rm ^{13}CO}J}{2 k_{\rm B} T_{\rm k}} \right)}\frac{I_{\rm ^{13}CO}}{1-\exp{\left(-\frac{h \nu_{\rm ^{13}CO}}{k_{\rm B} T_{\rm k}} \right)}}\ \ \ \rm{cm^{-2}},
\label{eq-4}
\end{equation}
where $k_{\rm B}$ is the Boltzmann constant, $\mu$ is the dipole moment of $0.11\times10^{-18}$ esu cm, $h$ is the Planck constant, $\nu_{\rm ^{13}CO}$ is the rest-frame frequency of $^{13}$CO, $J$ is the rotational quantum number of lower energy state and $T_{\rm k}$ is the kinetic temperature.
We obtain $(N_{\rm H_2}/{\rm cm}^{-2})=8.07\times10^{20} (I_{\rm ^{13}CO}/\rm{K\ km\ s}^{-1})$ by assuming an $N_{\rm H_2}/N_{\rm ^{13}CO}$ ratio of $7.5\times10^5$ \citep{Frerking+1982} and $T_{\rm k}=20$ K.

It is useful to estimate a lower limit of $N_{\rm H_2}$ by assuming that the $^{12}$CO line has a small optical depth ($\tau_{\rm ^{12}CO} \ll 1.0$).
The minimum H$_2$ column density is calculated in the same manner as equation (\ref{eq-4}) with $I_{\rm ^{12}CO}$.
We obtain $(N_{\rm H_2}/{\rm cm^{-2}})=9.88\times10^{18} (I_{\rm ^{12}CO}/\rm{K\ km\ s^{-1}})$ with $N_{\rm H_2}/N_{\rm ^{12}CO}$ ratio of $1.0\times10^4$ \citep{YoungScoville1991} and $T_{\rm k}=20$ K.
We utilize this conversion factor in the discussion in section \ref{Discussion}.

The surface density of the molecular gas, $\Sigma_{\rm mol}$ is calculated as,
\begin{equation}
\Sigma_{\rm mol}=1.36\times 2 \times m_{\rm H} N_{\rm H_2} \cos{(i)},
\end{equation}
where 1.36 is a factor to account for the contribution of He by mass, $m_{\rm H}$ is the mass of the hydrogen atom and $i$ is the inclination of NGC~3627 ($52^\circ$).
Then we can obtain the surface density of the molecular gas for the case of optically thick $^{12}$CO emission as,
\begin{equation}
\left( \frac{\Sigma_{\rm mol,12,thick}}{M_\odot\ \rm{pc^{-2}}} \right ) = 1.34\ \left( \frac{I_{\rm ^{12}CO}}{\rm K\ km\ s^{-1}} \right),
\label{eq:mol12thick}
\end{equation}
for the case of optically thin $^{13}$CO emission as,
\begin{equation}
\left( \frac{\Sigma_{\rm mol,13,thin}}{M_\odot\ \rm{pc^{-2}}} \right ) = 10.8\ \left( \frac{I_{\rm ^{13}CO}}{\rm K\ km\ s^{-1}} \right),
\label{eq:mol13thin}
\end{equation}
and for the case of optically thin $^{12}$CO emission as,
\begin{equation}
\left( \frac{\Sigma_{\rm mol,12,thin}}{M_\odot\ \rm{pc^{-2}}} \right ) = 0.133\ \left( \frac{I_{\rm ^{12}CO}}{\rm K\ km\ s^{-1}} \right),
\label{eq:mol12thin}
\end{equation}
where $\Sigma_{\rm mol,12,thick}$, $\Sigma_{\rm mol,13,thin}$ and $\Sigma_{\rm mol,12,thin}$ are the surface densities of molecular gas estimated from $^{12}$CO (optically thick), $^{13}$CO (optically thin) and $^{12}$CO (optically thin), respectively.
We adopt $X_{\rm CO}$ of $1\times10^{20}$ cm$^{-2}$ $[\rm K\ km\ s^{-1}]^{-1}$ \citep{NakaiKuno1995}.
The $\Sigma_{\rm mol,12,thick}$, $\Sigma_{\rm mol,13,thin}$, $\Sigma_{\rm mol,12,thin}$ and $\Sigma_{\rm mol,12,thick}/\Sigma_{\rm mol,13,thin}$ ratios in all the regions are shown in table \ref{tab-3}.

In table \ref{tab-3}, there is a wide variety in $\Sigma_{\rm mol,12,thick}/\Sigma_{\rm mol,13,thin}$ ratios among the six regions.
Here we focus on the relative difference of the $\Sigma_{\rm mol,12,thick}/\Sigma_{\rm mol,13,thin}$ ratios among different regions rather than the discrepancy between $\Sigma_{\rm mol,12,thick}$ and $\Sigma_{\rm mol,13,thin}$
in each region.
The errors of $\Sigma_{\rm mol}$ in table \ref{tab-3} are calculated only from the errors of the integrated intensities.
However, the $\Sigma_{\rm mol}$ values calculated here implicitly include the following assumptions;
1) the observed molecular clouds mainly consists of H$_2$ molecules, are virialized, follow the size-line width relation and have constant temperature and the $^{12}$CO emission from them is optically thick (for the constant CO-to-H$_2$ conversion factor),
2) the kinetic temperature and the abundance ratios of $^{13}$CO to H$_2$ are free parameters (for the LTE assumption).
In particular, the coefficient in equation (\ref{eq:mol13thin}) varies from 6.16 to 25.1 for $T_{\rm k}=10$ and $50$ K, respectively.

We estimate $T_{\rm k}$ from the comparison between $\Sigma_{\rm mol, 12, thick}$ and $\Sigma_{\rm mol, 13, thin}$ by assuming that both $^{12}$CO and $^{13}$CO emissions are radiated from the same region, the abundance ratios of $^{13}$CO to H$_2$ do not vary within the galaxy, and the estimated value of $\Sigma_{\rm mol, 12, thick}$ with $X_{\rm CO}$ is correct.
In table \ref{tab-3}, we can see that the $\Sigma_{\rm mol, 12, thick}/\Sigma_{\rm mol, 13, thin}$ ratios in the center, bar and interarm regions are $\sim3$ while those in the other regions are as small as $\sim1.6$.
We obtain $T_{\rm k}\sim50$ K for the center, $\sim90$ K for the bar, $\sim70$ K for the interarm, and $\sim30-40$ K for the other regions.
\citet{Galametz+2012} derived the dust temperature distribution of NGC~3627 with a grid size of $18''$, which corresponds to half of the effective spatial resolution of $36''$.
They found a radial temperature gradient declining from $\sim25$ K to $\sim17$ K from their SED fitting using the dust temperature and emissivity index as free parameters (figure 4 of \cite{Galametz+2012}).
In their plot, the highest temperature ($\sim25$ K) is found in the center and the bar-end regions and the lowest values are seen in the interarm region ($\sim17$ K).
In the center region, which contains nuclear starburst and active galactic nuclei \citep{Krips+2008}, the high $\Sigma_{\rm mol, 12, thick}/\Sigma_{\rm mol, 13, thin}$ ratio may be partly attributed to the high $T_{\rm k}$ although the averaged temperature of $\sim50$ K over the 800-pc beam is too high.
However, it is quite unlikely that the temperatures of the molecular gas in the bar and interarm regions are higher than the arm, bar-end and offset regions where stars are actively forming.
Therefore, the high $\Sigma_{\rm mol, 12, thick}/\Sigma_{\rm mol, 13, thin}$ ratios in the bar and the interarm regions are likely attributed to the overestimation of $\Sigma_{\rm mol, 12, thick}$ estimated with $I_{\rm ^{12}CO}$ and a constant CO-to-H$_2$ conversion factor.
We compare the $^{12}$CO and $^{13}$CO spectra of each region in the following subsections to physically explain the high $\Sigma_{\rm mol, 12, thick}/\Sigma_{\rm mol, 13, thin}$ ratios in the bar and interarm regions.

\begin{table*}
 \caption{The surface densities of molecular gas $\Sigma_{\rm mol}$ estimated under the assumption of optically thick $^{12}$CO (equation (\ref{eq:mol12thick})), optically thin $^{13}$CO (equation (\ref{eq:mol13thin})) and optically thin $^{12}$CO (equation (\ref{eq:mol12thin})).}
 \label{tab-3}
 \begin{minipage}{\textwidth}
 \begin{center}
 \begin{tabular}{@{}lcccccc}
  \hline
 & Center & Bar & Bar-end & Offset & Arm & Interarm\\
  \hline
  \hline
$\Sigma_{\rm mol,12,thick}$ ($M_\odot$ pc$^{-2})$& $93.7\pm3.7$ & $60.2\pm3.7$ & $63.4\pm3.0$ & $27.6\pm1.8$ & $36.0\pm1.8$ & $28.1\pm1.6$\\
$\Sigma_{\rm mol,13,thin}$\footnotemark[$\ast$] ($M_\odot$ pc$^{-2}$)& $38.4\pm5.5$ & $17.5\pm2.6$ & $39.5\pm2.3$ & $17.4\pm2.8$ & $20.5\pm2.3$ & $8.32\pm1.51$\\
$\Sigma_{\rm mol,12,thin}$\footnotemark[$\ast$] ($M_\odot$ pc$^{-2}$)& $9.30\pm0.37$ & $5.98\pm0.36$ & $6.29\pm0.30$ & $2.74\pm0.18$ & $3.58\pm0.18$ & $2.79\pm0.15$ \\
$\Sigma_{\rm mol,12,thick}/\Sigma_{\rm mol,13,thin}$\footnotemark[$\ast\ast$] & $2.4\pm0.4$ & $3.4\pm0.6$ & $1.6\pm0.1$ & $1.6\pm0.3$ & $1.8\pm0.2$ & $3.0\pm0.6$\\
  \hline
  \end{tabular}
\end{center}
\footnotetext[$\ast$]{$\Sigma_{\rm mol}$ is estimated with $T_{\rm k}=20$.}
\footnotetext[$\ast\ast$]{$\Sigma_{\rm mol,12,thick}/\Sigma_{\rm mol,13,thin}$ ratio is also shown.}
\end{minipage}
\end{table*}

\subsection{Integrated intensity, FWHM, and peak temperature ratios of the $^{12}$CO and $^{13}$CO spectra}\label{subsec-Discussion2}

We show the $I_{^{12}\rm{CO}}$/$I_{^{13}\rm{CO}}$, FWHM$_{^{12}\rm{CO}}$/FWHM$_{^{13}\rm{CO}}$ and $T_{\rm peak, ^{12}CO}/T_{\rm peak, ^{13}CO}$ ratios in table \ref{tab-4}.
We find for the first time that the $I_{^{12}\rm{CO}}$/$I_{^{13}\rm{CO}}$ ratio in the interarm region is almost twice as high as those in the bar-end, offset and arm regions.
The high ratios in the bar and center regions reported in W11\nocite{Watanabe+2011} are confirmed by the stacking analysis.
The $I_{^{12}\rm{CO}}$/$I_{^{13}\rm{CO}}$ ratios obtained in the bar-end, offset and arm regions are consistent with the values obtained in \citet{Paglione+2001} where they observed 17 nearby galaxies in $^{12}$CO and $^{13}$CO along the major axes and obtained the $I_{^{12}\rm{CO}}/I_{^{13}\rm{CO}}$ ratios of $4-22.8$ ($45''$ spatial resolution).
The bar region shows a higher value of $T_{\rm peak, ^{12}CO}/T_{\rm peak, ^{13}CO}=24.0$ than the other regions ($10-16$) and the center region shows an intermediate value between them ($19.1$).

It is noteworthy that the FWHM$_{^{12}\rm{CO}}$/FWHM$_{^{13}\rm{CO}}$ ratio in the interarm region is $1.7$ whereas the other regions have almost unity.
In other words, the line width of $^{12}$CO is larger than that of $^{13}$CO in the interarm region.
To investigate local effects on this trend, we separate the interarm region into Northeastern (NE) and Southwestern (SW) parts, produce the averaged spectra in each part, measure the FWHM ratios, and check whether this trend still holds or not.
Their FWHM estimated with Gaussian fitting are presented in table \ref{tab-5}.
Although the S/N (the peak temperature-to-noise ratio) of the data is not so high ($\sim4$), the trend that FWHM of $^{12}$CO is larger than that of $^{13}$CO still exists.
The FWHM ratios that are estimated with NE and SW interarm spectra separately are consistent with the interarm ratio of $\sim1.7$ within the margin of error.
Thus we conclude that the difference in FWHM between the $^{12}$CO and $^{13}$CO spectra is a characteristic feature in the interarm region of NGC~3627 rather than any local feature, which has nothing to do with the galactic structures.

\begin{table*}
 \caption{The $^{12}$CO$/$$^{13}$CO ratios of intensity, FWHM and $T_{\rm peak}$ estimated from Gaussian fitting in each region.}
 \label{tab-4}
 \begin{tabular}{@{}lcccccc}
  \hline
   & Center & Bar & Bar-end & Offset & Arm & Interarm\\
  \hline
  \hline
$I_{^{12}\rm{CO}}$/$I_{^{13}\rm{CO}}$ & $19.7\pm1.4$ & $31.8\pm3.9$ & $13.1\pm0.5$ & $13.3\pm1.4$ & $14.2\pm0.6$ & $24.7\pm2.8$\\
FWHM$_{^{12}\rm{CO}}$/FWHM$_{^{13}\rm{CO}}$ & $0.99\pm0.11$ & $1.17\pm0.14$ & $1.10\pm0.06$ & $1.24\pm0.17$ & $1.07\pm0.10$ & $1.69\pm0.24$\\
$T_{\rm peak, ^{12}CO}/T_{\rm peak, ^{13}CO}$ & $19.1\pm2.8$ & $24.0\pm3.8$ & $11.6\pm0.7$ & $10.4\pm1.0$ & $13.0\pm0.7$ & $15.8\pm2.4$ \\
  \hline
  \end{tabular}
\end{table*}

\begin{table*}
\caption{FWHM estimated with Gaussian fitting to the stacked spectra of the interarm region.}
\begin{center}
\begin{tabular}{lccc}
\hline
&FWHM$_{^{12}\rm{CO}}$&FWHM$_{^{13}\rm{CO}}$&FWHM$_{^{12}\rm{CO}}$/FWHM$_{^{13}\rm{CO}}$\\
& (km s$^{-1}$)&(km s$^{-1}$)&\\
\hline
\hline
All & $159\pm7$ & $94\pm13$ & $1.69\pm0.24$\\
Northern-East & $145\pm9$ & $66\pm12$ & $2.20\pm0.43$\\
Southern-West & $175\pm8$ & $123\pm16$ & $1.42\pm0.19$\\
\hline
\end{tabular}
\end{center}
\label{tab-5}
\end{table*}%

\subsubsection{The radial trends of $I_{\rm ^{12}CO}$/$I_{\rm ^{13}CO}$, FWHM$_{\rm ^{12}CO}$/FWHM$_{\rm ^{13}CO}$ and $T_{\rm peak, ^{12}CO}$/$T_{\rm peak, ^{13}CO}$}

Each region has a different mean galactocentric distance and therefore the variations in $I_{\rm ^{12}CO}$/$I_{\rm ^{13}CO}$, FWHM$_{\rm ^{12}CO}$/FWHM$_{\rm ^{13}CO}$ and $T_{\rm peak, ^{12}CO}$/$T_{\rm peak, ^{13}CO}$ found in the previous section may be attributed to a radial trend.
To investigate the radial gradient of $I_{\rm ^{12}CO}$/$I_{\rm ^{13}CO}$, FWHM$_{\rm ^{12}CO}$/FWHM$_{\rm ^{13}CO}$ and $T_{\rm peak, ^{12}CO}$/$T_{\rm peak, ^{13}CO}$, we produced the stacked spectra of $^{12}$CO and $^{13}$CO in five concentric annuli (r1$-$r5, from the galaxy center) with a width of $\sim1.1$ kpc in the galactic plane.
The fitting results with a Gaussian to the stacked spectra after the VA procedure of the five annuli are summarized in table \ref{tab-6}.
The radial profiles of the $I_{\rm ^{12}CO}$/$I_{\rm ^{13}CO}$, FWHM$_{\rm ^{12}CO}$/FWHM$_{\rm ^{13}CO}$ and $T_{\rm peak, ^{12}CO}$/$T_{\rm peak, ^{13}CO}$ ratios are shown in figure \ref{fig:RadialDistributions} with black lines.
In these plots, we also show the fraction of the number of pixels of each six morphologically defined regions included in a concentric annulus to the total number of pixels in each annulus.
The colors of these lines are the same as the six regions in figure \ref{fig:ProfileMap}.
Grey points and lines (``others'') represent the area which is not categorized in the (1)$-$(6) regions but included in the concentric annuli.

We find a radial gradient in the $T_{\rm peak, ^{12}CO}/T_{\rm peak, ^{13}CO}$ ratio plot (figure \ref{fig:RadialDistributions}a) and a weak gradient in the $I_{^{12}\rm{CO}}$/$I_{^{13}\rm{CO}}$ ratio plot (figure \ref{fig:RadialDistributions}c).
The radial gradient of $I_{^{12}\rm{CO}}$/$I_{^{13}\rm{CO}}$ reported in W11\nocite{Watanabe+2011} is confirmed with the data obtained with the stacking analysis.
The $T_{\rm peak, ^{12}CO}/T_{\rm peak, ^{13}CO}$ and the $I_{^{12}\rm{CO}}$/$I_{^{13}\rm{CO}}$ ratios tend to be higher at smaller galactocentric distance $D$ (kpc) while we found the highest values of both ratios in the bar and interarm regions outside r1.
In figure \ref{fig:RadialDistributions}b, we do not see any systematic radial gradient in the FWHM$_{^{12}\rm{CO}}$/FWHM$_{^{13}\rm{CO}}$ plot but there is a bump at r2$-$r4.
This radial range contains the interarm region and the highest contribution from the interarm region is found in r2$-$r3.
Additionally, the FWHM$_{^{12}\rm{CO}}$/FWHM$_{^{13}\rm{CO}}$ ratios at the bump ($\sim1.3$) are smaller than those of the interarm region ($\sim1.7$).
Hence, we conclude that the high FWHM$_{\rm ^{12}CO}$/FWHM$_{\rm ^{13}CO}$ ratios at r2$-$r4 are due to the inclusion of the interarm region.
Accordingly, the differences seen in the $I_{\rm ^{12}CO}$/$I_{\rm ^{13}CO}$, FWHM$_{\rm ^{12}CO}$/FWHM$_{\rm ^{13}CO}$ and $T_{\rm peak, ^{12}CO}$/$T_{\rm peak, ^{13}CO}$ ratios in the morphologically defined regions do not represent the radial trends of these ratios.

\begin{table*}
\caption{Gaussian fitting results of the stacked spectra after the VA procedure in different concentric radii.}
\begin{center}
\begin{tabular}{lccc}
\hline
Line & $^{12}$CO & $^{13}$CO & $^{12}$CO/$^{13}$CO\\
\hline
\hline
r1: $D=0-1.1$ (kpc)&&&\\
$I_{\rm CO}$ (K km s$^{-1}$) & $72.7\pm2.8$ & $3.07\pm43$ & $23.7\pm3.4$\\
FWHM (km s$^{-1}$) & $191\pm5$ & $184\pm20$ & $1.03\pm0.11$\\
$T_{\rm peak}$ (mK) & $357\pm9$ & $15.6\pm1.4$ & $22.8\pm2.2$\\
\hline
r2: $1.1-2.2$ (kpc)&&&\\
$I_{\rm CO}$ (K km s$^{-1}$) & $35.4\pm1.3$ & $1.76\pm0.20$ & $20.1\pm3.4$\\
FWHM (km s$^{-1}$) & $167\pm5$ & $149\pm13$ & $1.12\pm0.10$\\
$T_{\rm peak}$ (mK) & $199\pm5$ & $11.1\pm0.8$ & $17.9\pm1.4$\\
\hline
r3: $2.2-3.3$ (kpc)&&&\\
$I_{\rm CO}$ (K km s$^{-1}$) & $25.7\pm1.5$ & $1.25\pm0.11$ & $20.5\pm2.2$\\
FWHM (km s$^{-1}$) & $144\pm6$ & $108\pm7$ & $1.33\pm0.11$\\
$T_{\rm peak}$ (mK) & $167\pm6$ & $10.9\pm0.7$ & $15.3\pm1.1$\\
\hline
r4: $3.3-4.4$ (kpc)&&&\\
$I_{\rm CO}$ (K km s$^{-1}$) & $30.4\pm1.2$ & $1.80\pm0.11$ & $16.9\pm1.2$\\
FWHM (km s$^{-1}$) & $94.1\pm2.8$ & $70.7\pm3.1$ & $1.33\pm0.1$\\
$T_{\rm peak}$ (mK) & $304\pm8$ & $23.9\pm0.9$ & $12.7\pm0.6$\\
\hline
r5: $4.4-5.5$ (kpc)&&&\\
$I_{\rm CO}$ (K km s$^{-1}$) & $20.2\pm1.0$ & $1.56\pm0.09$ & $13.0\pm1.0$\\
FWHM (km s$^{-1}$) & $119\pm4$ & $118\pm5$ & $1.01\pm0.06$\\
$T_{\rm peak}$ (mK) & $160\pm5$ & $12.5\pm0.5$ & $12.8\pm0.7$\\
\hline
\end{tabular}
\end{center}
\label{tab-6}
\end{table*}%

\begin{figure*}
\includegraphics[width=170mm]{RadialDistribution-b-01.eps}

 \vspace{0cm}

 \caption{Radial distributions of a) $T_{\rm peak, ^{12}CO}/T_{\rm peak, ^{13}CO}$, b) FWHM$_{^{12}\rm{CO}}$/FWHM$_{^{13}\rm{CO}}$ and c) $I_{^{12}\rm{CO}}$/$I_{^{13}\rm{CO}}$.
 These ratios are shown as a black line in each graph.
 Red, green, blue, orange, purple, yellow, and grey lines represent the fraction of spectra of center, bar, bar-end, arm, interarm, offset regions and others included in each concentric annulus.
 The error bars of the three ratios (vertical axis) are estimated from the fitting error (1$\sigma$).
The horizontal bar of each point represents the radial range within which the stacked spectrum is calculated.
 }
  \label{fig:RadialDistributions}
\end{figure*}

\subsection{The intensity ratios of $T_{^{12}\rm{CO}}/T_{^{13}\rm{CO}}$ in the different regions}
\label{subsec:slope}

We compare the $^{12}\rm{CO}$ and $^{13}\rm{CO}$ spectra in each region in figure \ref{fig:SpectraComparison1213}.
Column (a) of this figure is $^{12}$CO and $^{13}$CO spectra multiplied by a fixed value of $10$ for the comparison of the heights of the $^{12}$CO and the $^{13}$CO emission lines in each different region.
Column (b) shows the $^{12}$CO and the rescaled $^{13}$CO spectra, which are matched at the peak of the $^{12}$CO.
This is done to compare the widths of the $^{12}$CO and the $^{13}$CO emission lines.
The emission ranges of the spectra are indicated as the unshaded regions and the baseline range are indicated as the shaded regions in the column (a) and (b).
Hereafter we refer to them as the ``emission'' and ``baseline'' ranges, respectively.
In column (c) of this figure, we plot the $T_{\rm mb}$ of $^{12}$CO versus $^{13}$CO for all the velocity channels in each region.
Grey and black points in this plot represent the data points of the ``baseline'' and ``emission'' ranges of the spectra.
The linear fitting results of the data within the ``emission'' range (black-filled circles) are also shown in red solid lines.
They are fitted so as to cross the origin.

Column (a) in figure \ref{fig:SpectraComparison1213} visually confirms that the $^{12}$CO spectra of the center, bar and interarm regions are still much higher than $10\times^{13}$CO, unlike those in the three other regions.
This difference is quantitatively expressed by different slopes of the fitting lines in column (c) in figure \ref{fig:SpectraComparison1213}.
The slope of 22.7 in the bar region is almost twice as high as those in the bar-end, offset and arm regions ($11-13$) and those in the center and interarm regions show the intermediate value ($17-18$) between them.

\begin{figure*}
\includegraphics[width=110mm]{hikaku1213-01.eps}

\vspace{+1.0cm}

 \caption{Comparison between the $^{12}$CO and $^{13}$CO spectra.
(a) $^{12}$CO and $10\times ^{13}$CO spectra for a comparison of $T_{\rm mb}$.
(b) $^{12}$CO and $^{13}$CO spectra multiplied by adequate values where the peak temperatures of $^{12}$CO and $^{13}$CO become comparable for a comparison of FWHM.
The ``emission'' range of spectra is indicated as an unshaded region and the ``baseline'' ranges are indicated as shaded regions.
(c) $T_{\rm ^{12}CO}-T_{\rm ^{13}CO}$ correlation plots.
Grey and black points in the plot represent the data points of ``baseline'' and ``emission'' range of the spectra.
The linear fitting results of data within the ``emission'' range (black points) are also shown as a black solid line.
The error bars represent the r.m.s. noise temperatures of the $^{12}$CO and $^{13}$CO spectra ($1\sigma$).
They are fitted so as to cross the origin.
A magnified figure of the dotted rectangle region on the plot of the interarm region is shown in figures \ref{fig:SpectraComparison1213Interarm}b and \ref{fig:SpectraComparison1213Interarm}c.
}
  \label{fig:SpectraComparison1213}
\end{figure*}

The most notable result in this study is that the width of the $^{12}$CO emission line is larger than that of $^{13}$CO in the interarm region whereas both lines in the other regions have comparable widths (column (b) in \ref{fig:SpectraComparison1213}).
We separate the ``emission'' range of the interarm spectra into the ``peak'' and the ``outskirt'' ranges that are indicated with blue and green horizontal lines in figure \ref{fig:SpectraComparison1213Interarm}a.
In figure \ref{fig:SpectraComparison1213Interarm}b, we show a magnified plot of the dotted rectangle region of figure \ref{fig:SpectraComparison1213}c.
Figure \ref{fig:SpectraComparison1213Interarm}c is the same as figure \ref{fig:SpectraComparison1213Interarm}b, but the data points of the ``peak'' and the ``outskirt'' ranges of the spectra are indicated as blue and green points, respectively.
The blue and green solid lines represent the linear fitting results of the data within the ``outskirt'' and the ``peak'' points.

In figure \ref{fig:SpectraComparison1213Interarm}c, there are distinct spectral features of 1) a large gradient ($26.4\pm5.3$) at $T_{\rm ^{13}CO}$\hspace{0.3em}\raisebox{0.4ex}{$<$}\hspace{-0.75em}\raisebox{-.7ex}{$\sim$}\hspace{0.3em}3 mK and 2) a small gradient ($7.2\pm1.9$) at $T_{\rm ^{13}CO}$\hspace{0.3em}\raisebox{0.4ex}{$>$}\hspace{-0.75em}\raisebox{-.7ex}{$\sim$}\hspace{0.3em}3 mK.
The two slopes are significantly different taking into account the error.
This result suggests that there are two gas components with different velocity widths and the component with a broader line width has the highest $T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ ratio of $26.4$ among all the regions.

\begin{figure*}
\includegraphics[width=150mm]{hikaku1213_interarm-01.eps}

 \caption{Comparison between the $^{12}$CO and $^{13}$CO spectra in the interarm region.
(a) $^{12}$CO and $^{13}$CO spectra multiplied by 15.
The ``baseline,'' ``peak,'' and ``outskirt'' ranges are indicated as shaded region, green and blue horizontal lines, respectively.
(b) A magnified figure of the dotted rectangle region in the original plot in figure \ref{fig:SpectraComparison1213}c.
(c) The same plot as (b).
But the data points are shown in different colors and symbols:
grey filled circles for ``baseline,'' blue filled circles for ``outskirt,'' and green open square for ``peak.''
The blue and green solid lines on this plot represent the fitting results of the data within the ``outskirt'' and ``peak'' ranges, respectively.
The error bars in (b) and (c) represent the r.m.s. noise temperatures of the $^{12}$CO and $^{13}$CO spectra ($1\sigma$).
}
  \label{fig:SpectraComparison1213Interarm}
\end{figure*}

\subsection{Brief summary of the analyses}

The surface densities of molecular gas were calculated with the $^{12}$CO and $^{13}$CO spectra in the six regions of NGC~3627.
We found that the bar and interarm regions have higher $\Sigma_{\rm ^{12}CO, thick}/\Sigma_{\rm ^{13}CO, thin}$, i.e., $I_{\rm ^{12}CO}/I_{\rm ^{13}CO}$ than the other regions.
The $I_{^{12}\rm{CO}}/I_{^{13}\rm{CO}}$ ratio in the bar region is high because the $T_{^{12}\rm{CO}}/T_{^{13}\rm{CO}}$ ratios are fairly high ($22.7$) within the velocity range of the emission line.
For the case of the interarm region, the high $I_{^{12}\rm{CO}}/I_{^{13}\rm{CO}}$ ratio is attributed to the broader line width of the $^{12}$CO spectra compared to the $^{13}$CO spectra.
The difference of the FWHM of $^{12}$CO and $^{13}$CO suggests the existence of two molecular gas components with different FWHM in the interarm region.
$T_{^{12}\rm{CO}}/T_{^{13}\rm{CO}}$ ratio of the gas component with broader FWHM in the interarm region is higher than the other regions.

\section{Discussion}\label{Discussion}

A new and the most important result of our study is that the $I_{\rm ^{12}CO}/I_{\rm ^{13}CO}$ in the interarm region is high due to broader FWHM$_{\rm ^{12}CO}$ than FWHM$_{\rm ^{13}CO}$.
The obtained spectra in this study are the emissions from an ensemble of giant molecular clouds (GMCs), giant molecular associations (GMAs) and/or the ambient components, since the typical sizes of those structures are \hspace{0.3em}\raisebox{0.4ex}{$<$}\hspace{-0.75em}\raisebox{-.7ex}{$\sim$}\hspace{0.3em}$40$ pc (GMCs) and $\sim200$ pc (GMAs), which are much smaller than the beam size of $\sim800$ pc.
Therefore, the observed FWHM of the $^{12}$CO and $^{13}$CO spectra are likely to represent not a random motion within a cloud but a random motion between clouds since the FWHM of the former (\hspace{0.3em}\raisebox{0.4ex}{$<$}\hspace{-0.75em}\raisebox{-.7ex}{$\sim$}\hspace{0.3em}$10$ km s$^{-1}$, \cite{Sanders+1985,Scoville+1987,Solomon+1987}) is much smaller than that of the latter.
If the molecular gas (or clouds) within a beam has almost the same $^{12}$CO to $^{13}$CO intensity ratio in each velocity channel, the FWHM of the spectra of the $^{12}$CO and $^{13}$CO lines are expected to be almost the same.
This  is the case for every region except for the interarm region.
The different FWHM between the $^{12}$CO and $^{13}$CO lines in the interarm region is hardly explained by the ensemble of molecular gas with uniform physical states within a beam.
We discuss the physical conditions of molecular gas in each region of NGC~3627 in the following subsections.

\subsection{Differences in the physical states of molecular gas among different regions}
\label{subsec:physicalstate}

The brightness temperature of line radiation, $T_{\rm B}(\nu)$, under the assumption of local thermal equilibrium (LTE), is described as
\begin{equation}
T_{\rm{B}}(\nu) = \Phi [ J_\nu (T_{\rm ex}) - J_\nu (T_{\rm bg}) ] [1 - \exp{(-\tau_\nu)}],
\end{equation}
where $\Phi$ is the beam-filling factor, $J_\nu (T)$ is the Plank function $(J_\nu (T) = [2h\nu^3/c^2] [\exp{(h\nu/k_B T)} - 1]^{-1}$, where $c$ is the speed of light), $T_{\rm ex}$ is the excitation temperature and equals the kinetic temperature $T_{\rm k}$ under LTE conditions, $T_{\rm bg}$ is the temperature of the cosmic microwave background ($2.73$ K) and $\tau_\nu$ is the optical depth.
Under the assumptions that 1) both $^{12}$CO and $^{13}$CO lines are emitted from the same cloud (same $\Phi$ for $^{12}$CO and $^{13}$CO), and 2) both molecules are thermalized (same $T_{\rm ex}=T_{\rm k}$ for $^{12}$CO and $^{13}$CO), the line ratio of ${T_{^{12}\rm{CO}}}/{T_{^{13}\rm{CO}}}$ can be described as a function of the optical depth of $^{12}$CO as,
\begin{equation}
\frac{T_{^{12}\rm{CO}}}{T_{^{13}\rm{CO}}} \approx \frac{1-\rm{exp}(-\tau_{^{12}\rm{CO}})}{1-\rm{exp}(-\tau_{^{13}\rm{CO}})} \approx \frac{1-\rm{exp}(-\tau_{^{12}\rm{CO}})}{1-\rm{exp}(-\frac{\tau_{^{12}\rm{CO}}}{\it R_{\rm 12/13}})},
\label{eq:12}
\end{equation}
where $R_{12/13}$ is the abundance ratio of $^{12}$C and $^{13}$C.
$R_{12/13}$ can be used as a proxy for the $N_{\rm ^{12}CO}/N_{\rm ^{13}CO}$ ratio as long as the isotope fractionation is negligible\footnote{
To be precise, the $N_{\rm ^{12}CO}/N_{\rm ^{13}CO}$ ratio may be affected by the isotope fractionation in response to the competing processes of the isotope exchange reaction \citep{Watson+1976,SmithAdams1980} and the selective dissociation \citep{BallyLanger1982,vanDishoeck+1988,Kopp+1996}.
}.
The $T_{^{12}\rm{CO}}/T_{^{13}\rm{CO}}$ ratio as a function of $\tau_{\rm ^{12}CO}$ is shown in figure \ref{fig:tau12CO}.
According to the equation (\ref{eq:12}),
a larger $\tau_{\rm ^{12}CO}$ gives us a lower $T_{^{12}\rm{CO}}/T_{^{13}\rm{CO}}$ with a fixed $R_{12/13}$ and a lower $R_{12/13}$ gives us a lower $T_{^{12}\rm{CO}}/T_{^{13}\rm{CO}}$.
\citet{Milam+2005} showed a radial dependence of $R_{12/13}$ of our Galaxy as
\begin{equation}
R_{12/13}(D) = 6.21\ D +18.71,
\label{eq-R1213}
\end{equation}
where $D$ is the galactocentric distance in kpc.
With an assumption that the profile of the emission line is expressed by a Gaussian function, the optical depth of the $^{13}$CO line can be described as
\begin{equation}
\tau_{\rm ^{12}CO} \approx \frac{4 \pi^3 \nu_{\rm ^{12}CO} \mu^2 N_{\rm ^{12}CO}}{3 k_{\rm B} T_{\rm ex} \Delta v} \exp{\left(\frac{-h \nu_{\rm ^{12}CO} J}{2 k_{\rm B} T_{\rm ex}}\right)} \left\{ 1 - \exp{\left(\frac{-h \nu_{\rm ^{12}CO}}{k_{\rm B} T_{\rm ex}}\right)}\right\},
\end{equation}
where $N_{\rm ^{12}CO}$ is the column density of $^{12}$CO and $\Delta v$ is the line width.
If $h \nu \ll k T_{\rm ex}$, the optical depth can be described as
\begin{equation}
\tau_{\rm ^{12}CO} \propto \frac{N_{\rm ^{12}CO}}{\Delta v\ T_{\rm k}^2}.
\label{eq:tau}
\end{equation}
Therefore, $T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ ratio is a function of $N_{\rm ^{12}CO}$, $\Delta v$ and $T_{\rm k}$ as well as $R_{12/13}(D)$.

We can estimate the $\tau_{\rm ^{12}CO}$ from the $T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ ratios of each region, if we assume that the $R_{12/13}$ dependence on the galactocentric distance of NGC~3627 is the same as that of the Galaxy.
In table \ref{tab-7}, the $T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ ratios estimated by linear fitting in figures \ref{fig:SpectraComparison1213} and \ref{fig:SpectraComparison1213Interarm}, radial extents, expected $R_{12/13}$ and $\tau_{\rm ^{12}CO}$ of each region are presented.
The $T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ ratios of each region are overplotted on the $\tau_{\rm ^{12}CO}-T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ plot in figure \ref{fig:tau12CO}.

Figure \ref{fig:tau12CO} and table \ref{tab-7} indicate the variety of $\tau_{\rm ^{12}CO}$ among different regions in NGC~3627.
The bar-end, offset and arm regions seem to have high values of $\tau_{\rm ^{12}CO}$ larger than $\sim3$.
On the other hand, $\tau_{\rm ^{12}CO}$ in the center region, bar region and of the larger FWHM component in the interarm region are expected to be $\sim0.2-0.9$, $\sim0.2-0.7$ and $\sim0.3-1.5$, respectively.
If we adopt the local interstellar medium value of $R_{12/13}\sim68$ \citep{Milam+2005}, the optical depths in these three regions are expected to be $\sim4.0$, $\sim2.9$ and $\sim2.4$.
Therefore, the higher $T_{^{12}\rm{CO}}/T_{^{13}\rm{CO}}$ ratios in the center, bar, and interarm regions are likely due to the lower optical depth of $^{12}$CO than the other regions as far as we assume the Galactic $R_{12/13}(D)$.

\begin{figure}
\includegraphics[width=70mm]{tau_12CO-01.eps}

 \vspace{0cm}

 \caption{Brightness temperature ratio, $\frac{T_{\rm ^{12}CO}}{T_{\rm ^{13}CO}}$ as a function of $\tau_{\rm ^{12}CO}$ in case of $R_{12/13}=68,\ 60,\ 50,\ 40,\ 30,\ 20$.
 The horizontal lines show $\frac{T_{\rm ^{12}CO}}{T_{\rm ^{13}CO}}$ in the center (red), bar (green), bar-end (blue), offset (orange), arm (purple) regions and the ``outskirt'' component of the $^{12}$CO spectrum in the interarm region (yellow).
 }
  \label{fig:tau12CO}
\end{figure}

\begin{table*}
 \caption{The $T_{\rm ^{12}CO}/T_{\rm ^{12}CO}$ ratios, radial extents, expected $R_{12/13}$ and $\tau_{\rm ^{12}CO}$ of each region.}
 \label{tab-7}
 \begin{minipage}{\textwidth}
 \begin{center}
 \begin{tabular}{@{}lcccccc}
  \hline
 & Center & Bar & Bar-end & Offset & Arm & Interarm$^\ast$\\
  \hline
  \hline
$T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$$^{\ast\ast}$& $17.1$ & $22.7$ & $12.2$ & $11.2$ & $12.9$ & $26.4$\\
$D$ (kpc) & $0-1$ & $1-2$ & $2-5$ & $3-6$ & $3-6$ & $2-5$\\
$R_{12/13}$ & $19-25$ & $25-31$ & $31-50$ & $37-56$ & $37-56$ & $31-50$ \\
$\tau_{\rm ^{12}CO}$ & $0.2-0.9$ & $0.2-0.7$ & $2.4-4.2$ & $3.3-5.2$ & $2.8-4.5$ & $0.3-1.5$\\
  \hline
  \end{tabular}
\end{center}
\footnotetext[$\ast$]{``outskirt'' range.}
\footnotetext[$\ast\ast$]{The slopes obtained in figure \ref{fig:SpectraComparison1213} and \ref{fig:SpectraComparison1213Interarm}.}
\end{minipage}
\end{table*}

\subsubsection{The cause of the low $\tau_{\rm ^{12}CO}$ in the bar and center regions}

According to equation (\ref{eq:tau}), the $T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ ratio is a function of $R_{12/13}(D)$, $N_{\rm ^{12}CO}$, $\Delta v$ and $T_{\rm k}$.
The physical states of molecular gas in the bar and center regions are discussed in W11\nocite{Watanabe+2011}.
They concluded that the higher value of $I_{\rm ^{12}CO}/I_{\rm ^{13}CO}$ in the center and bar regions are due to differences in the environments:
the high $T_{\rm k}$, which is due to the starburst or nuclear activity in the center region, and the low $N_{\rm CO}/\Delta v$, which is due to a streaming motion in the bar region.
The moderate value of $\tau_{\rm ^{12}CO}$ in the central region has also been reported in the study of our Galaxy \citep{Oka+1998}.

\subsubsection{The possible origin of the low $\tau_{\rm ^{12}CO}$ gas component in the interarm region}

The previous studies of GMCs in the Milky Way and in the extragalactic objects have proposed an evolution scenario of GMCs in a galactic disk.
\citet{Sawada+2012a} investigated the structure and physical conditions of molecular gas in the Milky Way including the arm and interarm regions using data taken with the 45-m telescope at NRO (spatial resolution of $\sim0.5$ pc).
They concluded that when faint and diffuse molecular gas in the interarm region enters the spiral arm, this gas develops bright and compact structures at the arm and once the gas leaves the arms, it returns to a diffuse state \citep{Sawada+2012b}.
\citet{Koda+2009} utilized CARMA data of M~51 (spatial resolution of $\sim160$ pc) and showed that molecular clouds with mass of $\sim 10^{7-8}$ $M_\odot$ are found only in the arm region while one with $\sim 10^{5-6}$ $M_\odot$ can be found in the interarm as well as arm regions.
They claimed that massive clouds that are accumulated in the arm region are not fully dissociated into atomic gas, but dissolved into small clouds as they pass through the arm due to the shear motion in the interarm region.
Recently, \citet{Colombo+2014} confirmed the results of \citet{Koda+2009} quantitatively with a large number of GMC samples of M~51 (spatial resolution of $\sim50$ pc) by comparing the mass function of GMC in different regions.
However, these extragalactic studies mainly treat individual and discrete clouds and might miss the diffuse and extended objects.

Our result suggests the existence of diffuse non-optically thick $^{12}$CO component ($\tau_{\rm ^{12}CO}\sim0.3-1.5$) in the interarm region.
This is consistent with the conclusion given in Sawada et al. (2012a; 2012b)\nocite{Sawada+2012a,Sawada+2012b} although they did not analyze the optical depth of the ``diffuse'' component.
\citet{Polk+1988} also reported that a significant contribution to the large-scale CO emission from the Galaxy is made by diffuse gas, which is indicated from the extremely high $I_{\rm ^{12}CO}/I_{\rm ^{13}CO}$ ratio of $\sim20-50$ \citep{KnappBowers1988}.
The diffuse component observed in our study might be a result of the dissolution of massive molecular clouds in the interarm region, as suggested by \citet{Koda+2009} and \citet{Colombo+2014}.
Relatively low $^{12}$CO optical depth of the interarm region may be a result of low $N_{\rm ^{12}CO}$$/\Delta v$ due to a shear motion.
Therefore, it is possible that GMCs formed at the arm are dissolved into smaller GMCs and diffuse molecular component in the interarm regions.
This picture is consistent with the prediction from a recent numerical simulation of gas component under spiral potential in a disk galaxy \citep{DobbsPringle2013}.
Some of the GMCs at the arm may be dissociated into atomic gas in the interarm region by star-formation feedback (e.g., \cite{Dobbs+2006}).
However, a detailed understanding {\rm of} the mechanism of dissolution of GMC or dissociation of molecular gas requires molecular and atomic gas observations in high resolution and sensitivity with Atacama Large Millimeter/submillimeter Array (ALMA) and Square Kilometer Array (SKA).

There may be a contribution of the bar structure on the low $\tau_{\rm ^{12}CO}$ value in the interarm region, since the interarm region that we define in this study includes the neighboring areas on the sides of the bar region.
The bar consists of a lot of characteristic orbits of stars and one of the most prominent orbits is called the x1 orbit, which shapes the elongated structure.
Since the gas component has viscosity contrary to stars, its orbit around the bar structure deviates from the sequence of x1 orbits of the stellar components.
\citet{Wada1994} provided an analytical model for the orbits of gas component in the bar-structure, damped orbit model.
In his model, some gas orbits in the bar, especially at the dust lane, gradually deviate from the bar region (for example, see figure 10 of \cite{Sakamoto+1999}).
Hence, some gas components orbiting the bar structure may be categorized in this study as interarm gas components.
Furthermore, the orbits which are crowded at the bar-end region become sparse on the sides of the bar region.
The gap between orbits widens, perhaps reducing ${N_{\rm ^{12}CO}}/\Delta v$ and consequently decreasing $\tau_{\rm ^{12}CO}$ on the sides of the bar.
Unfortunately, no study so far has investigated this effect in detail.
The investigation of this effect is an issue for a future paper.

\subsection{Non-universal CO-to-H$_2$ conversion factor in a galaxy?}
\label{subsec:conversionfactor}

Most previous studies of nearby galaxies have adopted a universal conversion factor for the entire galaxy and investigated the distribution of molecular gas and star-formation efficiency (SFE), which is determined as a ratio of star-formation rate and molecular gas mass (e.g., \cite{Helfer+2003,Kuno+2007,Leroy+2009}).
Some studies claimed that the SFE in the bar region is lower than the other regions and suggested that intense phenomena such as a streaming motion inhibits star formation in the bar (e.g., \cite{ReynaudDowns1998}).
W11\nocite{Watanabe+2011} compared SFE obtained from the $^{12}$CO data and from $^{13}$CO data of NGC~3627 and concluded that SFE in the bar region is comparable to that of the arm region if $^{13}$CO data were used to estimate the molecular gas mass.
A lower conversion factor in the bar region than the other disk regions is also suggested in the $^{12}$CO data of Maffei II combined with an LVG (large velocity gradient) analysis \citep{Sorai+2012}.

In this study, we detect $^{13}$CO emission from the interarm region of NGC~3627 for the first time and find $^{12}$CO component with a broad line width and high $T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ ratio indicating non-optically thickness.
It is difficult to estimate the molecular gas mass in the interarm region only with $^{13}$CO since a part of the molecular gas in the interarm region is expected to be too diffuse to emit $^{13}$CO emission.
To infer the impact of the non-optically thick $^{12}$CO component on the observed $^{12}$CO integrated intensity and the CO-to-H$_2$ conversion factor, we use the stacked $^{12}$CO spectrum to estimate the fraction of the emission from the diffuse component and the molecular gas mass in the interarm region.

We decomposed the $^{12}$CO spectra with two Gaussians for $^{12}$CO optically thick and non-optically thick components.
For the optically-thick component, we adopted the center velocity of $-13.7$ km s$^{-1}$ and the FWHM of $94.4$ km s$^{-1}$ from the Gaussian fitting results of the $^{13}$CO spectra and assumed three cases of $T_{\rm peak}$ of $T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ = 5, 10 and 13.
The $T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ ratios are determined by reference to the typical $I_{\rm ^{12}CO}/I_{\rm ^{13}CO}$ ratio of the Galactic GMCs of $5-7$ \citep{Solomon+1979,Polk+1988} and the values which we found in the bar-end, offset and arm regions of NGC~3627.
As a result, the fractions of the non-optically thick $^{12}$CO emission with respect to the total $^{12}$CO flux, $f_{\rm thin}$ are $82\pm11$ \%, $64\pm12$ \%, and $52\pm13$ \% if we assume $T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ = 5, 10 and 13, respectively.
The fitting results for these three cases are shown in figure \ref{fig:DualGaussians} and summarized in table \ref{tab-8}.

The surface density of the molecular gas $\Sigma_{\rm mol}$ in the interarm region is described with integrated intensities of the optically thick and thin components, $I_{\rm ^{12}CO, thick}$ and $I_{\rm ^{12}CO, thin}$ using equation (\ref{eq:mol12thick}) and (\ref{eq:mol12thin}) as\footnote{
It is reported that $N_{\rm ^{12}CO}/N_{\rm H_2}$ in the diffuse gas is smaller than the one in the GMCs from the CO-absorption observations \citep{Sonnentrucker+2007,Liszt2007,Burgh+2007,Shetty+2008}.
However, the $N_{\rm ^{12}CO}/N_{\rm H_2}$ values reported in those studies have a large dispersion ($\sim 10^{-7}-10^{-5}$).
Therefore we adopt the GMC value of $10^{-4}$ \citep{YoungScoville1991} throughout this paper.
}
\begin{equation}
\Sigma_{\rm mol,interarm}\approx 1.34\ I_{\rm ^{12}CO, thick} + 0.133\ I_{\rm ^{12}CO, thin}\ \ \ M_\odot\ \rm{pc^{-2}}.
\label{eq-11}
\end{equation}
We obtain the surface densities of $7.4\pm2.3$ $M_\odot$ pc$^{-2}$ ($T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ = 5), $12.0\pm2.6$ $M_\odot$ pc$^{-2}$ (10) and $14.8\pm3.0$ $M_\odot$ pc$^{-2}$ (13), which are significantly lower than the one calculated by assuming all $^{12}$CO emission is optically thick by factors of $3.8\pm1.2$, $2.3\pm0.6$ and $1.9\pm0.5$, respectively.
Here we assume $N_{\rm ^{12}CO}/N_{\rm H_2}=10^{-4}$ and $T_{\rm k}=20$ K.
It should be noted that this is an extreme case where the non-optically thick component is optically thin ($\tau_{\rm ^{12}CO}\ll 1$) so these factors set only the upper limits.

A radial gradient of $X_{\rm CO}$ in nearby galaxies has been investigated observationally, but the consensus has not been obtained \citep{Sandstrom+2013,Blanc+2013}.
\citet{Blanc+2013} investigated the dependence of $X_{\rm CO}$ of NGC~628 on the metallicity, gas surface density, and UV radiation field, which all affect the balance between the shielding and dissociation of CO molecule in the photodissociation regions on the edge of molecular clouds.

The conversion factor is expected to vary according to not only the radiative transfer of UV between the star-forming region and the subjected clouds in the galaxy but also the radiative transfer of $^{12}$CO between the clouds and us.
The previous studies have mainly focused on the factors that affect the former radiative transfer and investigated the dependence of $X_{\rm CO}$ on the metallicity, gas surface density, and UV radiation field.
Here we show that the optical depth of $^{12}$CO that influences the latter radiative transfer may be different in the different regions in NGC~3627, resulting in the different conversion factor.
We need careful consideration and treatment when we estimate the molecular gas mass not only in the region with quite different metallicity, ISM density and UV radiation field but also in the region where $^{12}$CO is not expected to be optically thick.
Accurate estimation of the molecular gas mass is also important to evaluate other physical parameters of galaxies such as SFE.

\begin{figure*}
\includegraphics[width=140mm]{DualGaussians.eps}

 \vspace{0cm}

 \caption{Fitting results with two Gaussians of $^{12}$CO spectrum in the interarm region. Blue and green solid lines show the fitting results for non-optically thick and optically thick components, respectively. Red solid line shows the sum of them.}
  \label{fig:DualGaussians}
\end{figure*}

\begin{table*}
\caption{Integrated intensity estimated with a dual-Gaussian fitting$^\ast$ to the stacked $^{12}$CO spectra of the interarm region.}
 \begin{minipage}{\textwidth}
 \begin{center}
 \begin{tabular}{lcccc}
  \hline
$T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ & $T_{\rm peak, ^{12}CO, thick}$ & $I_{\rm ^{12}CO, thick}$ & $I_{\rm ^{12}CO, thin}$ & $f_{\rm thin}$\\
&  (mK) &  (K km s$^{-1}$) &  (K km s$^{-1}$) & (\%)\\
\hline
\hline
5 & $38.2\pm4.5$ & $3.8\pm0.7$ & $17.2\pm1.7$ & $82\pm11$\\
10 & $76.5\pm9.0$ & $7.7\pm1.4$ & $13.3\pm2.0$ & $64\pm12$\\
13 & $99.4\pm11.7$ & $10.0\pm1.8$ & $10.8\pm2.2$ & $52\pm13$\\
\hline
\end{tabular}
\end{center}
\footnotetext[$\ast$]{
Fitting with two Gaussians: one is for the optically thick component and the other for the non-optically thick component.
The free parameters for fitting are $T_{\rm peak}$, line center velocity and FWHM for the non-optically thick component.
The center velocity and FWHM for the optically thick component are fixed to $-13.7$ km s$^{-1}$ and 94.1 km s$^{-1}$, respectively, which are estimated by fitting the $^{13}$CO spectra with a Gaussian.
}
\end{minipage}
\label{tab-8}
\end{table*}%

\section{Summary}\label{Summary}
We obtained the averaged spectra of $^{12}$CO and $^{13}$CO in the center, bar, bar-end, offset, arm and interarm regions of NGC~3627 with the stacking analysis after the velocity-axis alignment (VA) procedure according to the velocity field estimated from the $^{12}$CO mapping data.
The $^{13}$CO spectrum in the interarm region of NGC~3627 where the emission does not have enough S/N in the original data was successfully detected.
Main results of this paper are as follows:

\begin{enumerate}
\item A weak $^{13}$CO emission in the interarm region of NGC~3627 is successfully detected for the first time with the stacking analysis after the VA procedure (figure \ref{fig:StackedSpectra} of section \ref{Results}).

\item The validity of the stacking method with VA is confirmed by comparing the integrated intensity between stacked spectra with and without the VA procedure.
Moreover, the S/N of stacked spectra with VA is improved by a factor of up to 3.2 compared to those without VA (table \ref{tab-2} of section \ref{Results}).

\item The integrated intensity ratios $I_{^{12}\rm{CO}}/I_{^{13}\rm{CO}}$ in the bar and interarm regions are almost two times higher than those in the other regions.
$I_{^{12}\rm{CO}}/I_{^{13}\rm{CO}}$ in the center region is the intermediate value between them.
High values of $I_{^{12}\rm{CO}}/I_{^{13}\rm{CO}}$ in the bar and center regions are attributed to the higher intensity ratios ($T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$) and one in the interarm regions is attributed to the higher FWHM$_{^{12}\rm{CO}}/$FWHM$_{^{13}\rm{CO}}$ ratio than the other regions.
The difference in the line width between $^{12}$CO and $^{13}$CO suggests two gas components, one with a narrow ($\sim$ FWHM$_{\rm ^{13}CO}$) and the other with a broad line width ($\sim$ FWHM$_{\rm ^{12}CO}$) in the interarm region (tables \ref{tab-4} and \ref{tab-5} of section \ref{subsec-Discussion2}).

\item $T_{\rm ^{12}CO}/T_{\rm ^{13}CO}$ in the center and bar regions and of the broad line width components in the interarm region are $17.1$, $22.7$ and $26.4$ indicating that the $^{12}$CO lines are not completely optically thick in those regions if we assume the same $^{12}$C/$^{13}$C radial gradient as that of our Galaxy
(figures \ref{fig:SpectraComparison1213}, \ref{fig:SpectraComparison1213Interarm} and \ref{fig:tau12CO} of sections \ref{subsec:slope} and \ref{subsec:physicalstate}).

\item More than half of the $^{12}$CO emission from the interarm region is likely to be radiated from the diffuse gas component, if the $^{12}$CO spectra is decomposed with two Gaussians, one with FWHM$_{^{13}\rm{CO}}$ and the other with $\sim$ FWHM$_{^{12}\rm{CO}}$ (figure \ref{fig:DualGaussians} of section \ref{subsec:conversionfactor}).

\item The existence of non-optically thick component of $^{12}$CO in the center, bar, and interarm regions indicates a lower CO-to-H$_2$ conversion factor compared to the other regions.
It is necessary to take into account the non-universal conversion factor in a galaxy in case of comparing the molecular gas distribution and SFE in the different regions.
Otherwise, the molecular gas mass and SFE may be respectively overestimated and underestimated by factors of a few in case of the interarm region of NGC~3627 (section \ref{subsec:conversionfactor}).

\end{enumerate}

\bigskip

We would like to thank an anonymous referee for very productive comments.
KMM thanks Shuuro Takano, Tetsuhiro Minamidani, Tomoki Morokuma, Junichi Baba, Daisuke Iono, Jin Koda and all members of NRO for their support and fruitful discussions.

This research has made use of the NASA/ IPAC Infrared Science Archive, which is operated
by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the
National Aeronautics and Space Administration.

redpajama_set_name: RedPajamaArXiv


text:
Velasquez gets ready for big fight with cognac
By Vic Tafur on October 6, 2014 at 8:01 AM
As UFC heavyweight champ Cain Velasquez gets ready for his title bout against Fabricio Werdum in Mexico City next month, he took some time out to have a drink with Bay Area fans.
Velasquez was pouring GM Titanium Cognac, a new spirit by Grand Marnier, but only after he trained and did some light sparring with fans and media members at his home gym, American Kickboxing Academy in San Jose. (The event was Sept. 16 and I couldn't make it because of my football duties; I heard Cain was relieved.)
Students learned the proper technique to knee someone in the face, among other things.
Velasquez, the first Latino to win the world heavyweight title in any major combat sport, was enlisted in 2013 to represent GM Titanium, personifying its audacious and ambitious spirit. Available in California, Washington D.C., Illinois and Florida, GM Titanium features a bold combination of wild tropical orange essence, Asian Calamansi citrus and a unique five-spice blend, rounded out by exceptionally smooth Cognac.
"Touring with GM Titanium will be such an amazing way for me to connect with my fans throughout the West Coast, and I couldn't be more excited to partner with them again," Velasquez said. "As a brand, GM Titanium represents how I approach the ring every time I step in it – proving I'm the best and dominating the competition."
Velasquez's favorite cocktail combines GM Titanium and pineapple juice with a dash of Angostura bitters.
Vic Tafur
Tweets from @SFGate/sf-chronicle-sports

redpajama_set_name: RedPajamaCommonCrawl


text:
PRISM Bombshell: A Rainbow of Worries
UPDATE National Intelligence chief James Clapper hits the leak in strong terms--but, cat out of bag, says he will now release some of details and terms of the NSA phone program, asks public to understand.
Earlier: So, how do you top last night's NSA bombshell? This evening from the estimable Bart Gellman and Laura Poitras at Wash Post, who obtained slides for briefings:
The National Security Agency and the FBI are tapping directly into the central servers of nine leading U.S. Internet companies, extracting audio, video, photographs, e-mails, documents and connection logs that enable analysts to track a person's movements and contacts over time.
The highly classified program, code-named PRISM, has not been disclosed publicly before. Its establishment in 2007 and six years of exponential growth took place beneath the surface of a roiling debate over the boundaries of surveillance and privacy. Even late last year, when critics of the foreign intelligence statute argued for changes, the only members of Congress who know about PRISM were bound by oaths of office to hold their tongues.
And how's this?
Firsthand experience with these systems, and horror at their capabilities, is what drove a career intelligence officer to provide PowerPoint slides about PRISM and supporting materials to The Washington Post in order to expose what he believes to be a gross intrusion on privacy. "They quite literally can watch your ideas form as you type," the officer said.
The Guardian, again partly via Glenn Greenwald, has much the same (even the same slides?) and it's hard to tell who got what first or joint or what. Glenn, now in the crosshairs for two scoops, just tweeted: :I wish English language were broader so I could express my simultaneous contempt & mockery for the investigation threats emanating from DC."
For what it's worth, Apple spokesman says they've never heard of PRISM. Twitter notable by its absence in program (refused to cooperate?).
Wall Street Journal adds: They've got our credit card receipts, too.


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text:
I AM SOMEBODY: Raising Hope and Awareness for Children in Foster Care
What if a public awareness campaign changed the foster care narrative from hopeless to hopeful, and from worthless to worth it?
Written by Melanie Gilbert
I want my children to grow up in a world that respects their past, honors their life journey and believes in their future. All children deserve to be valued in their communities. Our society is learning to embrace children who were previously marginalized. Campaigns like the It Gets Better Project (http://www.itgetsbetter.org/) challenge stigmas and stereotypes of LGBTQ youth, replacing those damaging narratives with stories that speak instead to their sense of self, purpose and belonging. Numerous surveys (https://davethomasfoundation.org/wp-content/uploads/2012/10/DTFA-HarrisPoll) show that the American public still questions the wellbeing for at least one group of children - those who call the foster care system home. The perception is that these children are broken, unlovable and unadoptable. As a mom to awesome siblings from foster care, I felt this damaging dynamic had to be changed - not just for the wellbeing of my children, but for the wellbeing of the 400,000+ children currently in the care system, 100,000+ of whom need a family right now. I designed the "I AM SOMEBODY" public awareness campaign - featuring kids from foster care - to start a conversation that kids in care are worth it and deserve a loving family. Ultimately, I hope the campaign speaks so directly to people that they will either consider growing their family through foster care adoption or be more supportive of foster care issues. "If not us, then who? If not now, then when?"
http://melanieinboston.com/
Right now, "I AM SOMEBODY" is creating impact in the virtual universe of Twitter and Facebook. "I AM SOMEBODY" launched as a social media project during National Adoption Month in November 2014. The response was phenomenal (tracking showed global reach) with the campaign generating millions of impressions and thousands of engagements on Twitter. The cross-sector support for I AM SOMEBODY convinced me that the public was ready for a message of hope and change about foster care.
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"Splish Splash" The message: kids from foster care are like any other kid.
"Friends" The message: kids in foster care are lovable.
"Cannonball!" The message: Kids from foster care make a big splash.
"Balancing Act" The message: kids from foster care have hidden talents.
Video of the "I AM SOMEBODY" campaign.
Family is the place in which a child nurtures their sense of self, purpose and belonging. "I AM SOMEBODY" is a public awareness campaign that changes the foster care narrative from hopeless to hopeful, and from worthless to worth it so that waiting children can find their "forever" family.
"I AM SOMEBODY" is more than a foster care campaign, it's a human rights campaign.
This campaign was inspired by the "I AM A MAN" Memphis sanitation workers strike of 1968. Those men weren't just protesting the lack of their civil rights, they were protesting their lack of human rights. I still find that a powerful message of change.
My work is also inspired by the marriage equality work of the Human Rights Campaign.
Awareness, awareness, awareness.
If people are aware, they are inspired.
When they are inspired, they engage.
When they engage, they are enabled.
When they are enabled, they act.
When they act, children in care find a loving family.
Aware. Inspired. Engaged. Enabled. Action.
There are more than 400,000 children in the U.S. foster care system. Almost 110,000 of these children - enough to fill the University of Michigan's "Big House" football stadium - need a family right now.
Research has shown that growing up without a loving, stable family leads to a range of developmental delays, social-emotional problems and a damaged sense of self worth.
The 2013 Adoption Attitudes Survey by the Dave Thomas Foundation for Adoption found that, "There is a long-standing correlation between a high opinion of the foster care system and the consideration of adoption from foster care. The opposite is true as well."
Changing the negative foster care narrative may change these children's current and future wellbeing. Elevating an affirming foster care awareness campaign may encourage more families to be the future now for a child who has been left behind.
The "I AM SOMEBODY" campaign leverages the power of social media, plus traditional publicity channels, to amplify a positive foster care message.
Relentless public awareness messaging that children in foster care are "somebody" who belong in a loving, stable home.
When we spark a foster care revolution in this country, we can change futures now.
Why We Do It: Advocacy and Direct Action
So, why a public awareness campaign? Why not put much-needed funds into direct child and family support and services?
Advocacy/outreach is a process distinct from direct action-based support, yet each depend upon the other to be successful. If you can't reach your target families (advocacy), you can't support them (action) and bring them the services they require.
The "if we build it, they will come" thinking, though, drives the funding decisions of many direct services providers, but it's an incomplete model of children's wellbeing. Social support agencies, just like for-profit companies, need to brand their "products" which in this case, are the children in their care.
Another obstacle to child welfare embracing a public awareness campaign is the thinking is that families are more likely to engage the system if post-adoption support and services are available. This mindset was on full display in the Ashoka #Children'sWellbeing Twitter chat.
Yet, in Britain, and many other European countries, post adoption services, including competitive pay packages, are provided to foster care adoptive families. Despite these generous supports and a range of choices, these agencies still struggle to find families for waiting children.
Direct and support services are not the only answer. Forward-thinking child welfare leaders, who see their nonprofit as providing a service (where their client is the child first, then the foster-adopt family), recognize that a total rebranding of foster care is required to engage families for waiting children.
In 2013, The Dave Thomas Foundation for Adoption released the results of their Adoption Attitudes Survey which found that "while the perception of foster care adoption has improved, Americans – even those who are considering foster care adoption – still have a negative impression of the process, the costs, and potential behavioral and medical issues with children in foster care."
CEO Rita Soronen said, "The survey is a clear call to action. Armed with this information, we will continue to share real-life stories of successful foster care adoptions and dispel prevailing myths at every opportunity about the children available for adoption from foster care. We will not rest until every child in the United States has a nurturing and permanent home."
The biggest national player for foster care adoption awareness is AdoptUsKids, an information gateway funded by the Children's Bureau of the US Health and Human Services, through their "Myths" and "Perfect Parent" campaigns. They are closely followed by the Dave Thomas Foundation for Adoption, with their "When I First Met My Child" and "I Am Not" campaigns.
To date, none of these efforts have moved the needle on the number of waiting children. I believe that's because these campaigns pitch their message to the perspective of the adoptive parent versus framing it through the eyes of the children from foster care. Additionally, these laudable efforts were insufficiently promoted, failing to break through to the public domain outside of the existing foster care community.
When foster children, according to the DTFA survey, are still perceived as broken, unlovable and adoptable, changing the narrative of the parents' perspective is like putting the horse before the cart. A national campaign like "I AM SOMEBODY" speaks to the child's worth from the child's perspective using foster-adopt children to convey that message.
The national Heart Gallery portrait project is another unsuccessful awareness campaign. Though hugely popular with adoption agencies, and heavily subsidized by local and national partners, this awareness effort yields disappointing results with barely more than a 1% return on engagement. The portrayals of waiting children without a storytelling context - reduces children in foster care to a static, impersonal and desperate status. Plus, it's a dated, mall-driven concept (a valid, if limited, space to intercept people) that isn't leveraging the shareable, dynamic environment of social media.
A New Model: Why "I AM SOMEBODY" (IAS) Works
If we agree that having a family is a basic human right, then we should all be outraged that 400,000 children are growing up in a care system and not in a loving, stable family.
IAS challenges the myths, stereotypes and misinformation that children in foster care are broken, unwanted and unadoptable - by putting them in the "picture".
IAS raises awareness from a place of our love and their self worth - by connecting their wellbeing with empowerment.
IAS portrays children from the foster-adopt space in an authentic way - by involving them in their storytelling idea.
IAS invites the viewer to really "see" the child behind the label - by normalizing childhood without demonizing their foster care reality.
Awareness, awareness, awareness. If people aren't aware, they can't engage. Let's engage them together by raising this much-need awareness of children waiting for a family.
If you chose "other," please share the sector you work within here:
Foster care / child welfare
"I AM SOMEBODY" for foster care is a shareable, relateable awareness campaign. Based on Twitter analytics, a social media rollout for National Adoption Day 2014, reached a global audience and was viewed by millions, a majority of whom were not associated with traditional foster care communities. Two take-aways 1) a positive foster care message resonates 2) awareness increases engagement Through Twitter and Facebook, people who had seen the campaign reached out to me for foster care adoption information. I'm just a private citizen. Imagine the impact if this message was amplified and directed. Children's wellbeing is enhanced by belonging to a family. 400,000 children need families. Let's go find them families - right now.
"I AM SOMEBODY" continues to encourage engagement by challenging the damaging narrative of foster kids as broken, unlovable and unadoptable. Awareness is measurable through social media analytics and metrics. Engagement (asking for foster care adoption info) that translates into action (adopting a child from foster care) is only anecdotally available at this time in the "poised to launch" phase. The majority of public and private child welfare agencies focus on budgeting to direct services such as training and events, and staff and support programs like adoption parties and information resources for families. Perhaps that's why the field is wide open for "I AM SOMEBODY" - no one is doing it because no one wants to invest in socially-responsible consciousness raising for children in foster care.
Great question. To date, foster care agencies at both the public/private level, are reluctant to allocate resources from direct service programs to a marketing campaign. Short of founding a national nonproift (opening access to grants and corporate donations) I believe the public citizen crowd sourcing platforms could be an effective fundraising route. Foster care issues are rising to the national level making broader engagement possible.
The unique value proposition to the "I AM SOMEBODY" campaign is its portrayal of kids from foster care in a first-person narrative way with positive, affirming and powerful imagery and language. This approach not only challenges the negative perceptions of kids from foster care as broken, unlovable and unadoptable, but it also challenges it with their voice. They speak to their wellbeing. Shockingly, except for the out-dated Heart Gallery project, there are no agencies or organizations currently doing a large-scale foster care public relations campaign. The field is wide open.
The most important or promising shift in foster care is that people are starting to talk about it. Positive foster care messages are trending, lately, including Fmr. President Bill Clinton and other speakers at the Democratic Convention. Gold medalist gymnast Simone Biles and Olympic footballer Carlin Isles showed that kids from foster care can be champions. https://www.ispot.tv/ad/Almm/mini-usa-us-olympic-games-defy-labels-feat-serena-williams Imagine a world where families compete to foster care adopt, and the idea of 400,000 children waiting in care will seem cruel and unjust.
Program Design Clarity
Unlike the other Children's Wellbeing entries, "I AM SOMEBODY" is an advocacy/awareness campaign and not a direct services project. Think of the impact of Autism Speaks, Ice-Bucket Challenge and the Red-Nose campaigns to raise awareness of their social issue. My day-to-day work is designed like any other human rights campaign: Changing hearts and minds with a powerful, empathetic and inspiring message.
I promote the hell out of "I AM SOMEBODY", and actively solicit feedback from stakeholders across the foster care spectrum, as well as from outlying communities. This outreach is partly evidenced by my 50 evaluations, 26 comments and 47 likes. As a social media and public relations project, I AM SOMEBODY hasn't yet been "means" tested where feedback would emerge related to market reach resulting in family placement of youth from foster care.
Age of Children Impacted
1.5 -3
Spread Strategies
Twitter was a toe-dipping experiment to see if the public was ready to accept positive imagery of kids from foster care. The resounding answer: yes. It's time to bring in partners, sponsors and visionary backers to fund a nationwide campaign for foster care awareness. I'm also storyboarding "Foster Futures" another awareness campaign that targets the prospective adoptive parent and which complements the "I AM SOMEBODY" child-centered message.
Reflect on how your work helps children to thrive. How are you cultivating children's sense of self, belonging, and purpose through your model?
I think it is imperative to build a sense of belonging through empowerment. As an "I AM SOMEBODY" supporter said, "The stories kids are told about themselves make such a huge impression." We've seen the impact that organizing around "Black Lives Matter" is having on the race and policing conversation in this country. Let's have a conversation about finding families for children in foster care using "I AM SOMEBODY" as the launching off place.
Leadership Story
I started my activism journey as a college campus organizer for "Take Back the Night" marches. From there, I worked for the NOW on the Sexual Violence Against Women Task Force, as well as the annual National March for Women's Lives. These projects schooled me in the art of using public activism to raise awareness and encourage engagement. I bring those lessons, plus my background as a former staff writer for the Detroit News, to my work. My defining life moment, though, was becoming a mom to siblings from foster care. I do this work for my kids, and for all the kids still in foster care.
What awards or honors has the project received? (Optional)
Using "I AM SOMEBODY" campaign as their theme, Cambridge Family and Children Services, a MA-based foster care nonprofit challenged donors at their annual gala to "Be SOMEBODY" raising a record-breaking $350,000 for their foster care adoption programs. This fundraising sum validated the message.
Organization's Twitter Handle
@melanieinboston
Organization's Facebook Page (URL)
https://www.facebook.com/melanieinboston/
50 evaluations so far
5 - Yes, this is great! The project lays out a strong, compelling case for how its model nurtures children's wellbeing. - 76%
3 - I think so. The project seems related to children's wellbeing, but the logic is vague. - 6%
2 - Not sure. The project doesn't have much to do with wellbeing, or it doesn't give enough information. - 4%
5 - I loved this! The project describes a novel model that addresses important cultural or systemic barriers. - 58%
3 - I feel like there's something there, but I want more details about what makes it distinctive. - 8%
5 - Lots of potential. This project is achieving impressive results, and it's growing quickly. It could absolutely inspire changes in the ways we approach caring for kids nationally, across sectors (e.g. childcare, healthcare, education). - 46%
4 - Pretty good potential. This project demonstrates significant positive impact so far, and it could scale regionally or nationally one day and fundamentally change how a system operates (e.g. childcare, healthcare, education). - 34%
2 - Some potential. This project demonstrates some initial positive impact, but it would require major changes before it could scale. - 6%
5 - This idea rocked my world. It's awesome! - 55.1%
4 - This idea seems really exciting. With a little more polishing, it'd be among my favorites. - 26.5%
3 - I think the idea is great, but it needs some work before it moves onto the next round. - 10.2%
2 - I liked it fine but preferred others. - 4.1%
1 - It didn't make my heart beat faster. Needs significant revisions. - 4.1%
DEFINING THE PROBLEM. Make sure to articulate the root causes or main barriers of the social issue your project addresses. (Founding Story, Problem, Solution). - 4.2%
CLARITY OF MODEL. Make sure to mention (a.) the beneficiary, b) the main activities, and c) how those activities drive social impact. Keep it streamlined! - 37.5%
MARKETPLACE. Make sure to research other players in this space and articulate how this project is different. I didn't get a complete sense of how this project compares to others. - 29.2%
IMPACT POTENTIAL. Make sure to use specific numbers to describe what your project has achieved so far! And consider how you might scale the model or its insights, through partnerships, trainings, or franchising. - 62.5%
WRITING STYLE. Try to stay concise and make it vivid. Avoid jargon. - 29.2%
Nothing stands out! I thought it was great. - 100%
Melanie Gilbert
Changemaker for Foster Care Awareness, United States
Fostering.jpg
An example of why direct services and support to foster-adopt families aren't enough to address the waiting children crisis. Despite offering extensive support services to foster-adopt families, agencies in Europe struggle to find families for their clients - the foster children. I believe this is because the negative perceptions of children in foster care is an unchallenged narrative. I AM SOMEBODY is a public awareness campaign that offers a vision that kids from foster care are worth it.
This inspired (1)
The Peace Model Project
Karla Horn
Your ideas and motivation continue to inspire. Bravo on building this amazing project that I know has already made a huge difference in many lives.
Ms. Karla Horn!
You are the best! Thanks to your support, we're raising awareness - and the roof - for kids in foster care.
XO - Melanie and family


text:
Philippine E-Journals
Home⇛Philippine Journal of Counseling Psychology⇛vol. 15 no. 1 (2013)
A Measure of the Experience of Being Bullied: An Initial Validation in Philippine Schools
Jerome A. Ouano | Nerissa G. Redbole-buot | Elmer D. Dela Rosa
Bullying in schools concerns parents, teachers, school administrators, counselors, and psychologists in most Philippine schools. Response to this problem needs to draw from a valid measure. Previous formulations of the experience of bullying indicated various forms, some of which are common across research contexts. The Personal Experience Checklist (PECK) by Hunt, Peters, and Rapee (2012) has four dimensions that were seen to be closer to the cases of bullying in Philippine schools. The present study aimed at validating the PECK among Filipino high school students. In the exploratory phase of the validation process, Exploratory Factor Analysis on the 32-item PECK extracted 3 factors from the responses of 231 high school students, namely: verbal-relational bullying, physical bullying, and cyber bullying. In the cross-validation phase, separate Confirmatory Factor Analyses were performed for the new 3-factor model from 443 public school students (χ2/df=4.01, RMSEA=.08, TLI=.90, CFI=.90) and from 201 private school students (χ2/df=2.36, RMSEA=.06, TLI=.95, CFI=.92). CFA generated a relatively acceptable validity evidence of the measure for the experience of being bullied in both private and public schools. Implications point to the use of the new 3-factor model measure of bullying in the Philippine schools, and future research direction to increase the generalizability of the measure.
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