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    {\small\rm\zihao{6}\songti\thepage\hfill
    \quad\quad ACTA ASTRONOMICA SINICA \hfill
    \hspace{2mm} Vol.44\vspace{2mm}}}} %%%%%%%
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    {\small\rm \zihao{6}\songti suppl.\hfill Z. Yu: A Study of Megamaser Galaxies%%（作者：题目名称）
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\zihao{5}\songti

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    \zihao{6}\songti
    \noindent
    \\%%%[-0.5 true mm]
    Vol.44~ Suppl.
    \hfill\hspace{8mm} %%% if ``October/January'' then \hspace{8/10 mm} July
    \small ACTA ASTRONOMICA SINICA
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      Feb.,~2003 \\[-1.5 true mm] %%January
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\vs\vs\vs \bc {\Large\bf
A Study of Megamaser Galaxies   %%（文题）
%\\[1ex]
%$\!\!^*$
}

\vs\vs{\normalsize\zihao{4}\fangsong Zhiyao Yu}  %%（本文作者）

\vs
( \sho) \\%%（本文作者单位）
 ( \nao)\\
{\footnotesize E-mail: zyyu@center.shao.ac.cn}

\vs\vs \ec

\normalsize
\begin{quotation}

\no{\bf A{\scriptsize\bf BSTRACT }}~~~\small The infrared property
of megamaser galaxies, and its relationship with the observational
characters of the OH megamasers are studied.

\vn
 \no{\bf Key words}~~  galaxy:OH
megamaser---OH luminosity---infrared luminosity
\end{quotation}

\para{\large\bf{1}~~ Introduction}

\vs\vs OH megamasers are the most luminous cosmic maser sources
known. The first extragalactic OH emission was detected in NGC253
(Whiteoak and Gardner 1973) and in M82 (Nguyen-Q-Rieu et al.
1976). The more powerful OH megamasers occur only in very luminous
infrared sources, for example IC4553 (Baan, Wood and Haschick
1982). So far powerful OH maser emission has been discovered from
90 external galaxies (Baan et al. 1998; Darling $\&$ Giovanlli
2000; Darling $\&$ Giovalli 2001; Henkel $\&$ Wilson 1990;
Phillips et al. 1998; Staveley-Smith et al. 1992; Yu 1991). An
important observational character of OH megamaser sources is the
relationship between OH luminosity L(OH) and infrared luminosity
L(IR). We have tabulated L(OH) of only 66 OH megamaser sources
among the 90 OH megamaser sources in Table 1 (Baan et al. 1998;
Darling $\&$ Giovanelli 2000; Darling $\&$ Giovanelli 2001; Henkel
$\&$ Wilson 1990; Phillips et al. 1998; Staveley-Smith et al.
1992; Yu 1991). The Hubble constant was taken as
75\,kms$^{-1}$Mpc$^{-1}$ in our calculations. We assume that
emission was isotropic (Baan 1989), so single dish data from
different measurements are comparable.

\para{\large\bf{2}~~ Relationship between L(OH) and L(IR)}

\vs\vs The scenario of amplification requires a galaxy with a
large molecular column density toward the central radio source.
Such an edge-on situation may be needed in absorption or emission
depending on the excitation state of the molecular gas. Meantime
all galaxies with OH megamaser radiation have strong IR radiation.
A quadratic $L(\rm OH)-L(\rm IR)$ relationship rather than a
linear one, i.e. $L(\rm OH) \sim L(\rm IR)^{2}$, is found for the
observed megamasers by Baan(1989) using the parameters of 18 OH
megamaser galaxies. However, accounting for Malmquist bias
Kandalian(1996) obtained that the relationship between $L(\rm OH)$
and $L(\rm IR)$ was close to linear after reanalyzing the IR and
OH data of 49 OH megamaser galaxies, the relationship is as
follows: $\log L(\rm OH)=1.38\log L(\rm IR) - 14.04$, i.e. $L(\rm
OH) \sim L(\rm IR)^{1.38}$.

Methods for correction of the Malmquist effect have been discussed
by e.g. Kandalian 1996. We make use of the partial correlation
coefficient method. The dependence of $\log L(\rm OH)$ on $\log
L(\rm IR)$ for the 66 samples is as follows: With no-consideration
of the Malmquist effect, the regression line with slope 1.71 is
obtained using 1-D least-squares fits. With consideration of the
Malmquist effect, the slope of line is 1.41$\pm$0.11,  and
correlation coefficient is 0.58$\pm$0.02. The intercept of the
regression line is -14.18$\pm$0.12. $S_{R}(\sigma)$ is 4.77. It
means the confidence level of the correlation coefficient is
greater than $3\sigma$($\ge$99.7 percent).
Finally the regression equation is obtained as follows:

$$\log L({\rm OH})=(1.41\pm0.11)\log L({\rm IR})-14.18\,,$$
i.e.
$$L(\rm OH) \sim L(\rm IR)^{1.41\pm0.11}\,.$$

The index is between Baan(1989) and Kandalian(1996), and closes to
Kandalian(1996). For the complete sample of 66 extragalactic
masers, it become clear that the $L(\rm OH)\sim L(\rm IR)^{1.41}$
distribution is more appropriate in describing the $L(\rm OH)\sim
L(\rm IR)$ relationship.

\bc{\small\bf

 Table 1~~   The values of $D$, $\log L(\rm OH)$ and $\log L(\rm IR)$
 of the 66 OH megamaser sources
}\\[2mm]

\fns \tabcolsep 2mm
\begin{tabular}{llllllll}
\hline\\[-3.6mm]\hline
 IRAS & $D$ & $\log L(\rm OH)$ & $\log L(\rm IR)$ & IRAS
 & $D$ & $\log L(\rm OH)$ & $\log L(\rm IR)$\\
name  & (Mpc) & ($L_{\odot}$) & ($L_{\odot}$) & name & (Mpc) & ($L_{\odot}$) & ($L_{\odot}$)\\
\hline
00057+4021 & 168 & 1.9 & 12.3 & 01418+1651 & 109.9 & 2.7 & 11.4\\
02483+4302 & 208 & 2.5 & 11.5 & 03260-1422 & 172 & 2.0 & 11.2\\
04121+0223 & 514 & 2.3 & 11.6 & 04332+0209 & 48 & 0.5 & 10.1\\
05100-2425 & 133.4 & 2.0 & 11.0 & 05414+5840 & 65.3 & 0.8 & 11.1\\
06487+2208 & 618 & 2.86 & 12.0 & 07163+0817 & 470 & 2.35 & 11.5\\
07572+0533 & 757 & 2.71 & 11.9 & 08201+2801 & 731 & 3.42 & 12.0\\
08279+0956 & 925 & 3.19 & 11.9 & 08449+2332 & 653 & 2.56 & 11.8\\
08474+1813 & 626 & 2.67 & 11.9 & 09039+0503 & 535 & 2.8 & 11.8\\
09320+6134 & 159 & 1.6 & 11.7 & 09531+1430 & 958 & 3.38 & 11.8\\
09539+0857 & 554 & 3.45 & 10.5 & 10039-3338 & 135 & 2.6 & 10.5\\
10173+0828 & 201 & 2.7 & 11.5 & 10339+1548 & 868 & 2.62 & 13.0\\
11010+4107 & 146 & 2.0 & 11.3 & 11028+3130 & 879 & 2.94 & 12.1\\
11257+5850 & 41.3 & 1.3 & 11.0 & 11506-3851 & 41.4 & 1.4 & 11.0\\
11524+1058 & 782 & 2.95 & 11.9 & 12018+1941 & 738 & 2.7 & 12.1\\
12032+1707 & 967 & 4.11 & 11.3 & 12112+0305 & 290 & 3.3 & 12.0\\
12243-0036 & 29.5 & -0.1 & 10.7 & 12540+5708 & 170 & 2.9 & 12.1\\
13097-1531 & 91.1 & 1.0 & 11.2 & 13254+4754 & 245 & 1.9 & 11.2\\
13428+5608 & 152 & 2.7 & 11.9 & 15107+0724 & 51.7 & 1.0 & 11.0\\
15224+1033 & 577 & 3.01 & 11.5 & 15247-0945 & 160 & 2.1 & 11.3\\
15250+3609 & 219 & 2.6 & 11.7 & 15327+2340 & 73 & 2.7 & 11.9\\
15587+1609 & 589 & 3.23 & 11.6 & 16100+2527 & 559 & 2.26 & 11.5\\
16255+2801 & 572 & 2.54 & 11.7 & 16300+1558 & 1080 & 2.81 & 12.5\\
16399-0937 & 107 & 1.6 & 11.2 & 17208-0014 & 171 & 3.0 & 12.2\\
17539+2953 & 456 & 1.74 & 11.6 & 18368+3549 & 489 & 2.83 & 12.0\\
18588+3517 & 447 & 2.5 & 11.7 & 20100-4156 & 516 & 4.0 & 12.3\\
20248+1734 & 508 & 2.51 & 11.7 & 20286+1846 & 571 & 3.38 & 11.8\\
20450+2140 & 542 & 2.21 & 11.6 & 20550+1656 & 145 & 2.2 & 11.6\\
21077+3358 & 763 & 3.23 & 11.9 & 21272+2514 & 643 & 3.63 & 11.9\\
22025+4205 & 58.7 & 0.7 & 10.7 & 22055+3024 & 534 & 2.71 & 11.9\\
22116+0437 & 775 & 2.74 & 11.9 & 22491-1808 & 309 & 2.4 & 11.9\\
23019+3405 & 450 & 2.1 & 11.7 & 23028+0725 & 637 & 3.26 & 11.7\\
23129+2548 & 774 & 3.24 & 12.2 & 23135+2516 & 108 & 0.8 & 11.2\\
23199+0123 & 578 & 2.35 & 11.6 & 23234+0946 & 539 & 2.72 & 11.9\\
 \hline\\[-3.6mm]\hline%\\[-4.5mm]\hline
 \end{tabular}
 \ec


\para{\large\bf{3}~~Infrared Characters of Host IRAS Sources
with OH Megamasers}

\vs\vs What is the infrared-properties of the host IRAS sources
with OH megamasers? What is the relationship between the
infrared-properties and the occurrence of detectable OH megamaser
emission? We have obtained the infrared parameters of the only 62
host IRAS sources from the 66 samples. The infrared parameters are
shown in Table 2.

\bc{\small\bf

 Table 2~~   The infrared parameters of the 62 host sources with OH megamaser
}\\[2mm]

\fns \tabcolsep 3mm
\begin{tabular}{llllllll}
\hline\\[-3.6mm]\hline
 IRAS name & $\frac{S(12)}{S(25)}$ & $\frac{S(25)}{S(60)}$ & $\frac{S(60)}{S(100)}$ & IRAS name
 & $\frac{S(12)}{S(25)}$ & $\frac{S(25)}{S(60)}$ & $\frac{S(60)}{S(100)}$\\
\hline
$00057+4021$ & 0.65 & 0.08 & 0.95 & $01418+1651$ & 0.23 & 0.08 & 0.96\\
$02483+4302$ & 1.0 & 0.056 & 0.60 & $03260-1422$ & 1.0 & 1.07 & 0.68\\
$04121+0223$ & 1.12 & 0.27 & 0.57 & $04332+0209$ & 0.23 & 0.27 & 0.93\\
$05100-2425$ & 0.73 & 0.08 & 0.82 & $05414+5840$ & 0.7 & 0.07 & 0.47\\
$06487+2208$ & 0.48 & 0.25 & 0.88 & $07163+0817$ & 0.96 & 0.29 & 0.65\\
$07572+0533$ & 0.96 & 0.27 & 0.73 & $08201+2801$ & 0.98 & 0.22 & 0.71\\
$08279+0956$ & 1.07 & 0.43 & 0.63 & $08449+2332$ & 0.65 & 0.77 & 0.73\\
$08474+1813$ & 0.63 & 0.29 & 0.08 & $09039+0503$ & 0.68 & 0.25 & 0.65\\
$09320+6134$ & 0.24 & 0.09 & 0.6 & $09531+1430$ & 0.78 & 0.42 & 0.76\\
$09539+0857$ & 0.77 & 0.23 & 1.05 & $10039-3338$ & 0.25 & 0.13 & 1.04\\
$10173+0828$ & 0.47 & 0.09 & 1.05 & $10339+1548$ & 0.76 & 0.33 & 0.67\\
$11010+4107$ & 0.66 & 0.06 & 0.57 & $11028+3130$ & 0.73 & 0.12 & 0.71\\
$11257+5850$ & 0.17 & 0.2 & 0.95 & $11506-3851$ & 0.25 & 0.07 & 0.77\\
$11524+1058$ & 1.31 & 0.4 & 0.63 & $12018+1941$ & 0.92 & 0.17 & 0.88\\
$12032+1707$ & 0.51 & 0.34 & 0.97 & $12112+0305$ & 0.4 & 0.08 & 0.84\\
$12243-0036$ & 0.1 & 0.22 & 1.3 & $12540+5708$ & 0.22 & 0.25 & 0.12\\
$13097-1531$ & 0.35 & 0.08 & 0.51 & $13254+4754$ & 1.0 & 0.14 & 0.66\\
$13428+5608$ & 0.13 & 0.1 & 1.06 & $15107+0724$ & 0.31 & 0.04 & 0.69\\
$15224+1033$ & 0.55 & 0.17 & 1.02 & $15247-0945$ & 0.67 & 0.08 & 0.73\\
$15250+3609$ & 0.19 & 0.18 & 1.28 & $15327+2340$ & 0.06 & 0.08 & 0.88\\
$15587+1609$ & 1.5 & 0.3 & 0.82 & $16100+2527$ & 0.98 & 0.12 & 0.52\\
$16255+2801$ & 2.0 & 0.28 & 0.62 & $16300+1558$ & 0.93 & 0.17 & 0.79\\
$16399-0937$ & 0.33 & 0.13 & 0.67 & $17208-0014$ & 0.15 & 0.05 & 0.95\\
$18368+3549$ & 1.0 & 0.11 & 0.58 & $18588+3517$ & 1.3 & 0.1 & 1.02\\
$20100-4156$ & 0.6 & 0.08 & 1.04 & $20248+1734$ & 1.0 & 0.34 & 0.29\\
$20286+1846$ & 1.0 & 0.27 & 0.41 & $20450+2140$ & 1.0 & 0.34 & 0.14\\
$20550+1656$ & 0.13 & 0.17 & 1.13 & $21077+3358$ & 1.57 & 0.28 & 0.57\\
$21272+2514$ & 0.92 & 0.36 & 0.66 & $22025+4205$ & 0.35 & 0.74 & 0.67\\
$22055+3024$ & 1.23 & 0.13 & 0.8 & $22116+0437$ & 1.08 & 0.37 & 0.9\\
$22491-1808$ & 0.44 & 0.1 & 1.19 & $23129+2548$ & 1.0 & 0.14 & 1.06\\
$23135+2516$ & 0.18 & 0.18 & 0.8 & $23234+0946$ & 0.28 & 0.13 & 0.74\\
 \hline\\[-3.6mm]\hline%\\[-4.5mm]\hline
 \end{tabular}
 \ec


We find two extremes: sources with relatively flat infrared
spectra of [large $S(12\,\mu$m)\linebreak $/S(25\,\mu$m) and small
$S(60\,\mu$m)/$S(100\,\mu$m)], and sources with steep spectra of
[small $S(12\,\mu$m)\linebreak
$/S(25\,\mu$m) and large
$S(60\,\mu$m)/$S(100\,\mu$m)]. Furthermore we discuss in quantity
the mentioned suggestion that there are two sizes of dust particle
present and explain why the IR colour suggests this as follows.
Using the Table 2 the relationships between the $\log L(\rm IR)$
and $S(60)/S(100)$, and between the $\log L(\rm IR)$ and
$S(12)/S(25)$ are obtained, respectively. We find the $\log L(\rm
IR)$ is anticorrelated with $S(60)/S(100)$, and the $\log L(\rm
IR)$ is correlated with $S(12)/S(25)$. With least square fit the
correlation coefficient in the anticorrelation is $-0.73$ with
confidence level of greater than 95 percent,  and the correlation
coefficient in the correlation is 0.54 with confidence level of
greater than 95 percent. Thus, from linear fits ($y=ax+b$) to the
anticorrelation and correlation of the sources investigated in the
OH megamaser we obtain

\begin{eqnarray*}
S(60)/S(100) = - 3.70 [\log L(\rm IR) - 10] + 6.56\,,
\end{eqnarray*}
for the anticorrelation,

\begin{eqnarray*}
S(12)/S(25) = 3.23 [\log L(\rm IR) - 10 ] - 4.52\,,
\end{eqnarray*}
for correlation.

Using the above equations the relationship between $S(60)/S(100)$
and $S(12)/S(25)$ is

\begin{eqnarray*}
S(60)/S(100) = -1.15[S(12)/S(25)] + 1.36\,.
\end{eqnarray*}

We try to find the scale of suitable parameters of the dust
particle using the relationships of $S(12)/S(25)$ and
$S(60)/S(100)$. Assuming the dust particle as an ideal black-body
sphere, $r$ represents its radius, and the out-surface area is
2$\pi r^{2}$ for every dust particle. Also assuming the source as
a sphere with radius $R$, $n_{g}$ is the density of dust particle
in the surface area of the sphere, and $T_{g}$
is the temperature of the dust particle. Thus we obtain

\begin{eqnarray*}
 L(\rm IR) = 4 \pi R^{2} n_{g} 2 \pi r^{2} \sigma T_{g}^{4}\,,
\end{eqnarray*}
where $\sigma$ is the Stephanian-Boltzmann constant. Therefore

 \be
 S(60)/S(100)=-3.70\log(R^{2} n_{g} r^{2} \sigma T_{g}^{4})
 +36.54\,,
 \ee
 \be
 S(12)/S(25)=3.23\log(R^{2} n_{g} r^{2} \sigma T_{g}^{4}) -30.683\,.
 \ee

\no When
$$S(60)/S(100)=S(12)/S(25),\quad \log (R^{2}n_{g}r^{2}\sigma
T_{g}^{4})=9.7\,.$$

\no Meantime $$S(60)/S(100)>0,\quad {\rm from} (1)$$
$$\log(R^{2}n_{g}r^{2}\sigma T_{g}^{4}) < 9.9\,.$$
And
$$S(12)/S(25) >0,\quad {\rm from} (2)$$
$$\log(R^{2} n_{g} r^{2}\sigma T_{g}^{4})>9.5\,.$$

Thus at the situation of smaller dust particle,  $r$ is smaller,
when
$$9.5<\log(R^{2}n_{g}r^{2}\sigma T_{g}^{4})\le 9.7\,,$$
$$ S(12)/S(25)\le S(60)/S(100)\,.$$
At the situation of larger dust particle,  $r$ is larger,
when
$$9.7 \le\log(R^{2}n_{g}r^{2}\sigma T_{g}^{4})<9.9\,,$$
$$ S(60)/S(100)\le S(12)/S(25)\,.$$

\para{\large\bf{4}~~Conclusion}

\vs\vs We have studied the relationship between L(OH) and L(IR) of
the complete sample of 66 OH megamaser sources, which have the
data of L(OH) and L(IR). Accounting for Malmquist bias the
relationship $L(\rm OH)\sim L(\rm IR)^{1.41}$ has been obtained.

The IR-properties of the host IRAS sources with the OH megamasers
have also been studied in this paper. The most striking features
are anticorrelation of $S(60\,\mu{\rm m})/S(100\,\mu{\rm m})$ vs.
$S(12\,\mu{\rm m})/S(25\,\mu{\rm m})$, and anticorrelation of
$\log L(\rm IR)$ vs. $S(60\,\mu{\rm m})/S(100\,\mu{\rm m})$, and
correlation of $\log L(\rm IR)$ vs. $S(12\,\mu{\rm
m})/S(25\,\mu{\rm m})$, respectively. The anticorrelation and the
correlation between the flux density ratios and $\log L(\rm IR)$
can be explained by the coexistence of large and very small dust
particles. The very small dust which are heated transiently by
single photon absorption are believed to be responsible for the
bulk of the 25\,$\mu$m radiation. In case the photon energy
density of the host galaxy is small, this implies small
$S(12\,\mu$m)$/S(25\,\mu$m) and large
$S(60\,\mu$m)/$S(100\,\mu$m). However, when the photon energy
density becomes larger, the infrared spectrum will peak at
wavelengths $\le 100\,\mu$m thus enhancing the emission at
100$\mu$. As a consequence large S(12$\mu$m)/S(25$\mu$m) and small
(60$\mu$m)/S(100$\mu$m) color temperatures are observed. This
effect might be enhanced by the destruction of small dust particle
due to shock waves occurring near the nuclear regions.

I am grateful to Dr. Liu Yi for her useful work.

\bc {\bf References} \ec

\vspace{-4mm} \no \fns

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\no Paturel G., in Star Forrmation in Galaxies, ed C.J. Lonsdale,
Persson (Washington:NASA), 1987, p.597\\
\no Darling J., Giovanelli R., AJ, 2000, 119: 3003\\
\no Darling J., Giovanelli R., AJ, 2001, 121: 1278\\
\no Henkel C., Wilson T.L., A\&A, 1990, 229: 431\\
\no Kandalian R.A., Astrophysics, 1996, 39: 237\\
\no Nguyen-Q-Rieu, Mebold U., Winnberg A., et al.  A\&A, 1976, 52: 467\\
\no Phillips C.J., Norris R.P., Ellingsen S.P., et al. MNRAS, 1998, 294: 265\\
\no Staveley-Smith L., Norris R.P., Chapman J.M., et al. MNRAS, 1992, 258: 725\\
\no Whiteoak J.B., Gardner F.F., Ap.Letters, 1973, 15: 211\\
\no Yu Zhi-yao. Astronomy Progress, 1991, 9: 289\\

%\end{CJK}
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