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They applied a statistical correction which attempted. to make the distribution of inclination angles uniform. setting B/T to for those galaxies left over after the correction.
They applied a statistical correction which attempted to make the distribution of inclination angles uniform, setting B/T to 1 for those galaxies left over after the correction.
As Benson et al.
As Benson et al.
point out. this correction will likely overestimate the prevalence of ellipticals ancl unclerestimate the number of spirals. but the magnitude of the uncertainty is very dillieult to quantify.
point out, this correction will likely overestimate the prevalence of ellipticals and underestimate the number of spirals, but the magnitude of the uncertainty is very difficult to quantify.
We have therefore chosen to show
We have therefore chosen to show
fact. the strong correlation between dust-to-gas ratio and gas-phase metallicity has been noted in several previous studies (e.g. 222).
fact, the strong correlation between dust-to-gas ratio and gas-phase metallicity has been noted in several previous studies (e.g. \citealt{Issa1990,Schmidt1993, Lisenfeld1998}) ).
We note that the relation between A/a/Mg and Τι: in Fig.
We note that the relation between $\mdust/\mgas$ and $\mu\tauv$ in Fig.
8 has too much scatter for the dust optical depth in the diffuse ISM to be used as a reliable proxy for the dust-to-gas ratio in galaxies.
\ref{fig:dust8} has too much scatter for the dust optical depth in the diffuse ISM to be used as a reliable proxy for the dust-to-gas ratio in galaxies.
In this section. we briefly mention model uncertainties and discuss potential biases introduced by inclination effects and the presence of obscured AGNS in the results derived in the previous sections.
In this section, we briefly mention model uncertainties and discuss potential biases introduced by inclination effects and the presence of obscured AGNs in the results derived in the previous sections.
We also compare these results with the predictions of models of chemical and dust evolution to illustrate the implications of our study for the evolution of star-forming galaxies.
We also compare these results with the predictions of models of chemical and dust evolution to illustrate the implications of our study for the evolution of star-forming galaxies.
The ? model used in Section 3> to derive the physical properties of galaxies in the matched ssample relies on a combination of the latest version of the ? population svnthesis code and the simple two-component dust model of ?..
The \citet{daCunha2008} model used in Section \ref{dust:model} to derive the physical properties of galaxies in the matched sample relies on a combination of the latest version of the \citet{Bruzual2003} population synthesis code and the simple two-component dust model of \citet{Charlot2000}.
Recently. ? have investigated the uncertainties inherent to such models. in particular. those arising from poorly understood phases of stellar evolution (blue horizontal branch stars. blue straggler stars. thermally pulsing AGB stars). the IMF and the properties of dust in the interstellar Uncertainties inked to the IMF will affect our analysis in the same way as »ointed out by these authors.
Recently, \citet{Conroy2008} have investigated the uncertainties inherent to such models, in particular, those arising from poorly understood phases of stellar evolution (blue horizontal branch stars, blue straggler stars, thermally pulsing AGB stars), the IMF and the properties of dust in the interstellar Uncertainties linked to the IMF will affect our analysis in the same way as pointed out by these authors.
In our case. the uncertainties linked o stellar evolution are somewhat minimized by the fact that blue-straggler and horizontal-branch stars have a negligible contribution o the emission from star-forming galaxies.
In our case, the uncertainties linked to stellar evolution are somewhat minimized by the fact that blue-straggler and horizontal-branch stars have a negligible contribution to the emission from star-forming galaxies.
Also the version of the ? models used here rely on the improved. empirically calibrated models of ?. to better account for the contribution by thermally oxulsing AGB stars to the near-infrared emission from galaxies ?)..
Also the version of the \citet{Bruzual2003} models used here rely on the improved, empirically calibrated models of \citet{Marigo2007} to better account for the contribution by thermally pulsing AGB stars to the near-infrared emission from galaxies \citep[see][]{Bruzual2007}.
We refer the reader to the original studies of ?. and ο. for discussions of the uncertainties in the dust model (e.g. spatial distribution and optical properties of dust grains: typical lifetime of giant molecular clouds) and their influence on the ultraviolet and infrared emission from galaxies.
We refer the reader to the original studies of \citet{Charlot2000} and \citet{daCunha2008} for discussions of the uncertainties in the dust model (e.g., spatial distribution and optical properties of dust grains; typical lifetime of giant molecular clouds) and their influence on the ultraviolet and infrared emission from galaxies.
The model used in Section 3. to derive the physical properties of galaxies in the matched ssample is limited to angle-averaged spectral properties.
The model used in Section \ref{dust:model} to derive the physical properties of galaxies in the matched sample is limited to angle-averaged spectral properties.
However. the observed fluxes and colours of galaxies are observed to depend on inclination. especially for spiral galaxies (e.g.. 2).
However, the observed fluxes and colours of galaxies are observed to depend on inclination, especially for spiral galaxies (e.g., \citealt{Maller2009}) ).
SDSS galaxies have been morphologically classitied using the concentration index €'. detined as the ratio of the radii enclosing 90 per cent and 50 per cent of the r-band luminosity (e.g. 22)).
SDSS galaxies have been morphologically classified using the concentration index $C$ , defined as the ratio of the radii enclosing 90 per cent and 50 per cent of the $r$ -band luminosity (e.g. \citealt{Shimasaku2001,Strateva2001}) ).
We tind that 64 per cent of the galaxies in our sample have concentration indices typical of late-type galaxies νο, ο<2.6).
We find that 64 per cent of the galaxies in our sample have concentration indices typical of late-type galaxies (i.e., $C<2.6$ ).
Thus. we must check that inclination effects do not introduce any strong bias in the results of Section 4..
Thus, we must check that inclination effects do not introduce any strong bias in the results of Section \ref{dust:rel_sfr_dust}.
We use the ratio b/«a of minor to major axes of the SDSS +- isophote at ? as a proxy for dise inclination.
We use the ratio $b/a$ of minor to major axes of the SDSS $r$ -band isophote at $^{-2}$ as a proxy for disc inclination.
This is justified by the way in which galaxy ultraviolet and optical colours correlate with b/«.
This is justified by the way in which galaxy ultraviolet and optical colours correlate with $b/a$.
For example. we find that colours such as gor and NEVr correlate significantly with b/«. with the smaller b/e (presumably tracing higher dise inclinations) corresponding to the redder ultraviolet/optical colours.
For example, we find that colours such as $g-r$ and $NUV-r$ correlate significantly with $b/a$, with the smaller $b/a$ (presumably tracing higher disc inclinations) corresponding to the redder ultraviolet/optical colours.
In Fig. 9..
In Fig. \ref{fig:dust9},
we plot several properties of the galaxies in the high-S/N subsample (Section 4)) against the axis ratio b/e: apparent r-band magnitude. r stellar mass.AM,z star formation rate averaged over the last 107 vr.cz total infraredluminosity..: dust mass.Maz and fraction of ccontributed by dust in the diffuse ISM.fj.
we plot several properties of the galaxies in the high-S/N subsample (Section \ref{dust:rel_sfr_dust}) ) against the axis ratio $b/a$: apparent $r$ -band magnitude, $r$; stellar mass,; star formation rate averaged over the last $10^8$ yr,; total infrared,; dust mass,; and fraction of contributed by dust in the diffuse ISM,.
.. We first highlight a selection effect: at low b/« (i.e. high inclination). the sample includes almost no galaxy fainter than 16mmuag (Fig.
We first highlight a selection effect: at low $b/a$ (i.e. high inclination), the sample includes almost no galaxy fainter than $r \sim 16$ mag (Fig.
Yaa).
\ref{fig:dust9}a a).
This is because of the combined requirements of infrared detection by aand ultraviolet detection byGALEX: edge-on galaxies in our sample must be optically bright enough that the limited relative dust content required for some ultraviolet photons to escape in the plane of the disc be also sufficient to warrant detection in the infrared.
This is because of the combined requirements of infrared detection by and ultraviolet detection by: edge-on galaxies in our sample must be optically bright enough that the limited relative dust content required for some ultraviolet photons to escape in the plane of the disc be also sufficient to warrant detection in the infrared.
It is Important to note that our restriction to the high-S/N subsample in Fig.
It is important to note that our restriction to the high-S/N subsample in Fig.
Yaa explains the lack of galaxies at the faintestmagnitudes near the y=17.77 selection cut-off even at low inclinations.
\ref{fig:dust9}a a explains the lack of galaxies at the faintestmagnitudes near the $r=17.77$ selection cut-off even at low inclinations.
doubled the uncertainties of these seven measurements and did not use them to compute the bisector span.
doubled the uncertainties of these seven measurements and did not use them to compute the bisector span.
The radial velocities shown in Fig.
The radial velocities shown in Fig.
7 present a clear variation in phase with the ephemeris and with a slight but significant eccentric orbit.
\ref{rvfig} present a clear variation in phase with the ephemeris and with a slight but significant eccentric orbit.
The bisector span. listed i Table 5 and shown in Fig. 8..
The bisector span, listed in Table \ref{table423} and shown in Fig. \ref{biss423},
does not reveal any significant variations at à level more than ten times smaller than the radial velocity variations allowing all scenarios of diluted anc blended eclipsing binaries to be excluded.
does not reveal any significant variations at a level more than ten times smaller than the radial velocity variations allowing all scenarios of diluted and blended eclipsing binaries to be excluded.
We performed the spectroscopic analysis of the parent star using spectra.
We performed the spectroscopic analysis of the parent star using spectra.
Individual spectra are too poor i1 quality to allow a proper spectral analysis.
Individual spectra are too poor in quality to allow a proper spectral analysis.
The six spectra not affected by the scattered moonlight were shiftec to the barycentric rest frame and co-added order per order.
The six spectra not affected by the scattered moonlight were shifted to the barycentric rest frame and co-added order per order.
We finally got à co-added spectrum with an S/N of about 110 per pixel on the continuum at 550 nm.
We finally got a co-added spectrum with an S/N of about 110 per pixel on the continuum at 550 nm.
From the analysis of a set of isolated lines. we derived a of 1642.5kms".
From the analysis of a set of isolated lines, we derived a of $\pm$ 2.5.
The spectroscopic analysis was carried out using the same methodology as for the planets described in detail in Bruntt et al. (2010)).
The spectroscopic analysis was carried out using the same methodology as for the planets described in detail in Bruntt et al. \cite{bruntt2010}) ).
We limited the abundance analysis to the iron tons. because of the high of the star and the quite moderate spectral resolution and S/N of the combined spectrum.
We limited the abundance analysis to the iron ions, because of the high of the star and the quite moderate spectral resolution and S/N of the combined spectrum.
In total 53 Fel and 11 Fell spectral lines were used for the temperature and gdetermination.
In total 53 FeI and 11 FeII spectral lines were used for the temperature and $g$ determination.
FollowingtheBrunttetal 42008)
Following the Bruntt et al. \cite{bruntt2008}) )
methodology. aduprdancea naa nadinethd dabbaeaeeFear flm
methodology, abundances were measured differentially with respect to a solar spectrum.
dec Mgr.qe pRBEETEsolar s] —0.29+ 0.1.
We found a marked underabundance of iron, with [Fe/H]=-0.29 $\pm$ 0.1.
This result was further checked using the CCFs.
This result was further checked using the CCFs.
Following the relations established by Boisse et al. (2010)).
Following the relations established by Boisse et al. \cite{boisse2010}) ),
we derived a of 12.6 + 1 and an [Fe/H] of -0.18 + 0.1 dex.
we derived a of 12.6 $\pm$ 1 and an [Fe/H] of -0.18 $\pm$ 0.1 dex.
The metallicity is 1-7 higher than the spectroscopic determination.
The metallicity is $\sigma$ higher than the spectroscopic determination.
The value estimated from the CCF The rotation velocity of KOI-423 derived from the stellar radius and the rotational period estimated from the light curve is 16.2 € 1.7kms7!. in full agreement with the spectroscopic determination. mdicatirisi that ἐν be close to 90 deg.
The value estimated from the CCF The rotation velocity of KOI-423 derived from the stellar radius and the rotational period estimated from the light curve is 16.2 $\pm$ 1.7, in full agreement with the spectroscopic determination, indicating that $i_{\star}$ be close to 90 deg.
The temperature derived from the - equilibrium is = 6260 + 140 K. This is 2 c higher than the value of 5992 K quoted for the star in the Kepler Input Catalog.
The temperature derived from the - equilibrium is = 6260 $\pm$ 140 K. This is 2 $\sigma$ higher than the value of 5992 K quoted for the star in the Kepler Input Catalog.
From infrared magnitudes J and K given in the 2MASS catalog. a reddening of E(J-K)20.091 (from Cardelli et al. 1989)).
From infrared magnitudes J and K given in the 2MASS catalog, a reddening of E(J-K)=0.091 (from Cardelli et al. \cite{cardelli1989}) ),
and Eq.
and Eq.
3 in Casagrande et al. (2010))
3 in Casagrande et al. \cite{casagrande2010}) )
assuming [Fe/H] = -0.3 dex. we derived an effective temperature = 6380 + 150 K. This estimate agrees with our spectroscopic determination,
assuming [Fe/H] = -0.3 dex, we derived an effective temperature = 6380 $\pm$ 150 K. This estimate agrees with our spectroscopic determination.
As already mentioned for KOI-428 (Santerne et al. 2011a)).
As already mentioned for KOI-428 (Santerne et al. \cite{santerne2011a}) ),
the infrared determination of the effective temperature from Casagrande et al. (2010)).
the infrared determination of the effective temperature from Casagrande et al. \cite{casagrande2010}) ),
based on stars of luminosity class IV and V. seems to be more reliable than the one used for the Input Catalog.
based on stars of luminosity class IV and V, seems to be more reliable than the one used for the Input Catalog.
The surface gravity was estimated using pressure-sensitive lines: the Mgilb lines. the D doublet. and the at 6122 andA.
The surface gravity was estimated using pressure-sensitive lines: the 1b lines, the D doublet, and the at 6122 and.
As already noted by Bruntt et al. (2010)).
As already noted by Bruntt et al. \cite{bruntt2010}) ),
the results obtained on the triplet vary from one line to another due to the difficulty in the normalization of these broad lines.
the results obtained on the triplet vary from one line to another due to the difficulty in the normalization of these broad lines.
Fitting each of the observed lines with synthetic spectra calculated using MARCS models. we found = 3.90 + 0.25.
Fitting each of the observed lines with synthetic spectra calculated using MARCS models, we found = 3.90 $\pm$ 0.25.
The D lines gave = 4.0 + 0.2 and the lines = 4.1 + 0.2.
The D lines gave = 4.0 $\pm$ 0.2 and the lines = 4.1 $\pm$ 0.2.
The latter are in good agreement with the value of = 4.2 obtained with VWA System parameters were derived by performing the transit modeling and the Keplerian fit of the radial velocity measurements simultaneously.
The latter are in good agreement with the value of = 4.2 obtained with VWA System parameters were derived by performing the transit modeling and the Keplerian fit of the radial velocity measurements simultaneously.
Transit fitting was carried out following the formalism of Gimenez (2006. 2009)) after removing stellar variability in the out-of-transit light curve to correctly normalize the transits.
Transit fitting was carried out following the formalism of Gimenez \cite{Gimenez06, Gimenez09}) ) after removing stellar variability in the out-of-transit light curve to correctly normalize the transits.
For this purpose. we fitted a third-degree polynomial to the9h intervals of the light
For this purpose, we fitted a third-degree polynomial to the9h intervals of the light
Al that airmass. the atmospheric cillerential refraction at the (wo ends of the recorded wavelength range reaches ~1.0 arcsec FFilippenko 1952).
At that airmass, the atmospheric differential refraction at the two ends of the recorded wavelength range reaches $\sim$ 1.0 arcsec Filippenko 1982).
Our Echelle spectra cover the spectral range AA 4600-9400 iin 25 orders.
Our Echelle spectra cover the spectral range $\lambda\lambda$ $-$ 9400 in 25 orders.
The 15 bluest orders (AA 4600-6890 Aj) are characterized by a continuous spectral overlap. while inter-order gaps are present for the redder orders.
The 15 bluest orders $\lambda\lambda$ $-$ 6890 ) are characterized by a continuous spectral overlap, while inter-order gaps are present for the redder orders.
The following spectral windows are not covered. by our spectra: 6890-6396. 1104-7118. 17334-1356. 1518-1610. 1840-7882. 8120-8173. 8421-8488. 8745-8828. and 9095-9196.
The following spectral windows are not covered by our spectra: 6890-6896, 7104-7118, 7334-7356, 7578-7610, 7840-7882, 8120-8173, 8421-8488, 8745-8828, and 9095-9196.
A... The instrumental PSF (measured from the EWIIM of unblended telluric absorption lines of Os and Π.Ο} remained pretty constant during the observing period. corresponding to a resolving power /2 = 200000.
The instrumental PSF (measured from the FWHM of unblended telluric absorption lines of $_2$ and $_2$ O) remained pretty constant during the observing period, corresponding to a resolving power $R$ = 000.
The PSF. deduced by comparing the FWIIM of the unblended lines in the Thorium wavelength calibration spectra. was found (o be generally uniform over various Echelle orders.
The PSF, deduced by comparing the FWHM of the unblended lines in the Thorium wavelength calibration spectra, was found to be generally uniform over various Echelle orders.
The height of the slit on the skv was 10 arcsec.
The height of the slit on the sky was 10 arcsec.
The program star was always placed close to one end of the slit.
The program star was always placed close to one end of the slit.
The spectrum extracted from the other half of the slit heieht was not illuminated by the star.
The spectrum extracted from the other half of the slit height was not illuminated by the star.
So it was used (to derive an accurate median sky spectrum which was subtracted from the stellar tracing.
So it was used to derive an accurate median sky spectrum which was subtracted from the stellar tracing.
Most of (the program stars were quite bright objects which required short exposure times. so the backeround sky contribution was very weak.
Most of the program stars were quite bright objects which required short exposure times, so the background sky contribution was very weak.
All the data reduction aud calibration was carried out in IRAF.
All the data reduction and calibration was carried out in IRAF.
Spectral tracing was performed by weighting the extraction according to the variance of the recorded spectrum.
Spectral tracing was performed by weighting the extraction according to the variance of the recorded spectrum.
The wavelength calibration was quite accurate. with a (vpical rms of 0.3 km/s for all program stars.
The wavelength calibration was quite accurate, with a typical rms of 0.3 km/s for all program stars.
Scattered light was carefully modeled aud subtracted Irom the bi-dimensional frames.
Scattered light was carefully modeled and subtracted from the bi-dimensional frames.
All spectra were inspected [or possible residuals of the strongest night-skv. emission lines (principally [OI] 5577. 6300. 6364 A)).
All spectra were inspected for possible residuals of the strongest night-sky emission lines (principally [OI] 5577, 6300, 6364 ).
This confirmed the accuracy of sky subtraction.
This confirmed the accuracy of sky subtraction.
after the explosion.
after the explosion.
Phere is no evidence observed that tvpe la supernovae vield dust.
There is no evidence observed that type Ia supernovae yield dust.
Our consideration suggests that a substantial fraction of dust is generated from the material lost in the burning phase of evolved stars.
Our consideration suggests that a substantial fraction of dust is generated from the material lost in the burning phase of evolved stars.
The inventory gives useful cireumstantial constraint on the production and evolution of dust. although it does not cdirectlv suggest anvthing concerning the mechanisms.
The inventory gives useful circumstantial constraint on the production and evolution of dust, although it does not directly suggest anything concerning the mechanisms.
] would like to thank Bruce Draine and Peter Goldreich for encouraging me to publish this work and for stimulating discussion. and. useful. comments improving the earlier version of this manuscript.
I would like to thank Bruce Draine and Peter Goldreich for encouraging me to publish this work and for stimulating discussion and useful comments improving the earlier version of this manuscript.
E also thank Jim. Peebles for a long-term collaboration on the cosmic energy. inventory. which motivated me to seek the "missing dust. problem.
I also thank Jim Peebles for a long-term collaboration on the cosmic energy inventory, which motivated me to seek the missing dust problem'.
E thank Briec Ménnard. for discussion. for his work to find dust in the vicinity of galaxies. anc useful. comments on the present manuscript.
I thank Brice Ménnard for discussion, for his work to find dust in the vicinity of galaxies, and useful comments on the present manuscript.
E acknowledge the support of the Ambrose Monell Foundation (2010) and the Friends of the Institute (2011) in Princeton ancl Grant in Xd of the Ministry. of Ecdueation in Tokyo.
I acknowledge the support of the Ambrose Monell Foundation (2010) and the Friends of the Institute (2011) in Princeton and Grant in Aid of the Ministry of Education in Tokyo.
Given the above Lagrangian density (19)). the momentum of cach constituent is obtained [rom Eq. (2)).
Given the above Lagrangian density \ref{eq.lambda}) ), the momentum of each constituent is obtained from Eq. \ref{eq.4momentum}) ).
The nucleon momentum is given hy where ες is the chemical potential defined by Since the Lagrangian density depends only on the lepton densities n;=n't, (6—e.qi for electrons. muons respectively). the momenta of the leptons are time-like and are given by If the particles are all co-movinge with the 4-velocity s". the nucleon +momenta take the familiar expression where (5?=taiul! asing the identities (13)) and (141).
The nucleon momentum is given by where $\mu_{_{\rm X}}$ is the chemical potential defined by Since the Lagrangian density depends only on the lepton densities $n_\ell=n_\ell^\mu t_\mu$ $\ell=e,\mu$ for electrons, muons respectively), the momenta of the leptons are time-like and are given by If the particles are all co-moving with the 4-velocity $u^\mu$, the nucleon 4-momenta take the familiar expression where $v^2=\eta_{\mu\nu} u^\nu u^\mu$, using the identities \ref{eq.gal.inv}) ) and \ref{eq.gal.inv2}) ).
Phe usual 3-momentum covector. denoted by iLES. is defined by the Aristotelian spatial components of the 4-momoentum. COVOCLOE Wi. where iy is the space projection tensor defined by using the Kronecker unit tensor 07.
The usual 3-momentum covector, denoted by $\Pi^{_{\rm X}}_{\, \mu}$, is defined by the Aristotelian spatial components of the 4-momentum covector $\pi^{_{\rm X}}_{\, \mu}$, where $\eta^\mu_\nu$ is the space projection tensor defined by using the Kronecker unit tensor $\delta^\mu_\nu$.
Lt follows immediately from Eq. (8))
It follows immediately from Eq. \ref{eq.norm_ether}) )
that οLES,=0.
that $e^\mu \Pi^{_{\rm X}}_{\, \mu}=0$.
Lt is readily seen that the lepton 3-momentum vanishes I,=0. while the nucleon 3-momentum is determined solely bv the mobility matrix A77" From the nucleon ancl lepton momenta Eqs. (22))
It is readily seen that the lepton 3-momentum vanishes $\Pi^{\ell}_{\, \mu}=0$, while the nucleon 3-momentum is determined solely by the mobility matrix ${\cal K}^{qq^\prime}$ From the nucleon and lepton momenta Eqs. \ref{eq.nucleon_momentum}) )
and (24)) respectively. we can obtain the generalized pressure V of the Uuids according to I5q. (6)).
and \ref{eq.lepton_momentum}) ) respectively, we can obtain the generalized pressure $\Psi$ of the fluids according to Eq. \ref{eq.general_pressure}) ).
Phe kinetic part of the Lagrangian density Ain=Cian does not contribute to the pressure V which can thus be written as where Xi=0XMa
The kinetic part of the Lagrangian density $\Lambda_{\rm kin} = U_{\rm kin}$ does not contribute to the pressure $\Psi$ which can thus be written as where $\Lambda_{\rm int}= \Lambda-\Lambda_{\rm kin}$.
Due to entrainment effects. this internal Lagrangian density Aga of the E[uüids is not simply. equal to the opposite of the internal energy. density. (including gravitational contribution) Ci|Cy but is given by The gravitational potential energy density does not contribute to the pressure.
Due to entrainment effects, this internal Lagrangian density $\Lambda_{\rm int}$ of the fluids is not simply equal to the opposite of the internal energy density (including gravitational contribution) $U_{\rm int}+U_{\rm pot}$ but is given by The gravitational potential energy density does not contribute to the pressure.