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The dynamical timescale is where we have used eq. (39))
The dynamical timescale is where we have used eq. \ref{rho_value}) )
below to evaluate p, in terms of the non-dimensional deusitv p,.
below to evaluate $\rho_c$ in terms of the non-dimensional density $\bar \rho_c$.
Given the critical values for p, aud R/M that we find in Section 3.. the evolutionary timescale is longer than the dynamical timescale for A<6.7&LOMAS...
Given the critical values for $\bar \rho_c$ and $R/M$ that we find in Section \ref{Sec3}, the evolutionary timescale is longer than the dynamical timescale for $M \lesssim 6.7 \times 10^{13} M_{\odot}$.
This mass is larger than the value derived iu Shapiro Teukols«kv (1983). where a simular estimate has heen made for nonrotating SMSs stabilized by eas pressure.
This mass is larger than the value derived in Shapiro Teukolsky (1983), where a similar estimate has been made for nonrotating SMSs stabilized by gas pressure.
Also nuportaut is the viscous timescale. which is very uucertain.
Also important is the viscous timescale, which is very uncertain.
Not surprisingly. the mucroscopic viscosity due either to collisions between Ίος or to radiation vields timescales which are larger than the evolutionary timescale by inany orders of niaguitude (see Iippeulali Weigert 1990).
Not surprisingly, the microscopic viscosity due either to collisions between ions or to radiation yields timescales which are larger than the evolutionary timescale by many orders of magnitude (see Kippenhahn Weigert 1990).
The effect of turbulent viscosity cau be estimated by asstunine that the velocity of the turbulent motionce; is an appreciable fraction of the velocity of sound. where we take the dimieusiouless viscosity paraueter à to lie in the rauge (seeShakura Suuvaev 19723: also Zeldovich vvikkov 1971: Balbus Dawley 1991).
The effect of turbulent viscosity can be estimated by assuming that the velocity of the turbulent motion$v_t$ is an appreciable fraction of the velocity of sound, where we take the dimensionless viscosity parameter $\alpha$ to lie in the range (seeShakura Sunyaev 1973; also Zel'dovich kov 1971; Balbus Hawley 1991).
Ássuuiug the
Assuming the
reffig:cmd)) bluer than FUV—r= 6.0!.. Donasetal.(2007) show that nearby RC3 ellipticals (without lenticulars), where the UV excess is known to come from classical UV upturn (old populations), are redder than this limit.
) bluer than ${\rm FUV}-r = 6.0$ \citet{donas} show that nearby RC3 ellipticals (without lenticulars), where the UV excess is known to come from classical UV upturn (old populations), are redder than this limit.
In contrast, we are interested in QETGs with UV excess, so we select galaxies with FUV—r«5.3.
In contrast, we are interested in QETGs with UV excess, so we select galaxies with ${\rm FUV}-r < 5.3$.
There are 60 such galaxies from which we exclude blends, obvious optical disturbances, late-type contaminants, and E+A post-starbursts (based on Hó4 index), to arrive at a final ssample of 30.
There are 60 such galaxies from which we exclude blends, obvious optical disturbances, late-type contaminants, and E+A post-starbursts (based on $\delta_A$ index), to arrive at a final sample of 30.
The UV-optical (FUV —r) color range of our sample can be seen from Figure 2..
The UV-optical ${\rm FUV}-r$ ) color range of our sample can be seen from Figure \ref{fig:cmd}.
The sample is presented with symbols, while greyscale represents all ggalaxies at z«0.12 (the
The sample is presented with symbols, while greyscale represents all galaxies at $z<0.12$ (the underlying population).
By selection, the sample is bluer than the underlyingFUV—r red population).sequence, with two galaxies ( FUV—r z:3) lying squarely in the FUV—r bluesequence.
By selection, the sample is bluer than the ${\rm FUV}-r$ red sequence, with two galaxies ( ${\rm FUV}-r \approx 3$ ) lying squarely in the ${\rm FUV}-r$ blue.
”.. While no optical color cut has been explicitly applied, our strong UV excess sample has distinctlyred optical color reffig:conc)), placing them firmly in the optical red sequence.
While no optical color cut has been explicitly applied, our strong UV excess sample has distinctly optical color \\ref{fig:conc}) ), placing them firmly in the optical red sequence.
Similar confinement to the red sequence is seen in u—r colors (not shown).
Similar confinement to the red sequence is seen in $u-r$ colors (not shown).
Schawinskietal.(2009) and (Kannappanetal.2009) study blue early-type galaxies in SDSS selected by atypically blue u—r.
\citet{sch09} and \citep{kannappan} study blue early-type galaxies in SDSS selected by atypically blue $u-r$.
However, our sample galaxies areredder than their u—r cuts.
However, our sample galaxies are than their $u-r$ cuts.
With FWHM of 5", mmakes it difficult to pinpoint the origin of the FUV light at z»0.1.
With FWHM of $5''$, makes it difficult to pinpoint the origin of the FUV light at $z\sim0.1$.
In contrast, ACS/SBC on the pplaces of point source energy in 074 (Fordetal.2003).
In contrast, ACS/SBC on the places of point source energy in $0\farcs4$ \citep{acsford}.
. Targets were observed with one orbit through the long-pass filter FI2S5LP (Aer=1459
Targets were observed with one orbit through the long-pass filter F125LP $\lambda_{\rm eff}=1459$ ).
Processing was performed MULTIDRIZZLE with A)). parameters, and usingsmoothed using ADAPTSMOOTH SBC-optimized(Zibetti2009).
Processing was performed using MULTIDRIZZLE with SBC-optimized parameters, and smoothed using ADAPTSMOOTH \citep{adapt}.
. Twenty-nine targets were successfully imaged, and each produced a detection, either of a compact central source or of extended structures (or both).
Twenty-nine targets were successfully imaged, and each produced a detection, either of a compact central source or of extended structures (or both).
To our surprise, 22 galaxies (76%)) revealed an extended UV morphology and an additional three had UV patches within several arcsec of the nucleus.
To our surprise, 22 galaxies ) revealed an extended UV morphology and an additional three had UV patches within several arcsec of the nucleus.
In all cases the extended UV emission is structured, and thus results from (unlike a diffuse component one might expect from an old population).
In all cases the extended UV emission is structured, and thus results from (unlike a diffuse component one might expect from an old population).
The UV extent is typically larger than the optical size, though mostly contained within a radius containing Petrosian flux.
The UV extent is typically larger than the optical size, though mostly contained within a radius containing Petrosian flux.
We divide extended structures into strong (15) and weak (7) based on visual appearance and provisional flux measurements.
We divide extended structures into strong (15) and weak (7) based on visual appearance and provisional flux measurements.
These are labeled in figures by circles and diamonds respectively.
These are labeled in figures by circles and diamonds respectively.
In all galaxies save four a compact central source is present as well, which we divide into strong (14; plus sign) and weak point sources (11; dots).
In all galaxies save four a compact central source is present as well, which we divide into strong (14; plus sign) and weak point sources (11; dots).
Several strong extended UV morphologies are illustrated in Figure 3..
Several strong extended UV morphologies are illustrated in Figure \ref{fig:images}.
Galaxy (a) has a weak central source, while others exhibit a strong central source.
Galaxy (a) has a weak central source, while others exhibit a strong central source.
Insets show g-band SDSS images with ACS fields indicated.
Insets show $g$ -band SDSS images with ACS fields indicated.
As required by sample selection, optical images appear like ETGs, though, after the fact, hints of structure are visible in (a), (d) and a couple of other galaxies.
As required by sample selection, optical images appear like ETGs, though, after the fact, hints of structure are visible in (a), (d) and a couple of other galaxies.
The galaxy in panel (a) of Figure 3 shows multiple star forming features, including an inner ring and what look like flocculent spiral arms.
The galaxy in panel (a) of Figure \ref{fig:images} shows multiple star forming features, including an inner ring and what look like flocculent spiral arms.
Two other galaxies in the sample show flocculent features.
Two other galaxies in the sample show flocculent features.
Panel (b) shows a galaxy with a wide SF ring.
Panel (b) shows a galaxy with a wide SF ring.
Such morphology is most common in our sample (eight other cases).
Such morphology is most common in our sample (eight other cases).
Next is one of four galaxies showing thin concentric rings.
Next is one of four galaxies showing thin concentric rings.
The last (panel d) is the most striking in terms of surface brightness, with two bright spiral arms emanating from what appears to be a co-rotation connected a fainter outer Lindblad resonance ring ring,(Schwarz1984).
The last (panel d) is the most striking in terms of surface brightness, with two bright spiral arms emanating from what appears to be a co-rotation ring, connected by a fainter outer Lindblad resonance ring \citep{schwarz}.
. byThe optical image shows a hint of red spiral arms.
The optical image shows a hint of red spiral arms.
Two other galaxies in the sample appear to have spiral arms, albeit less prominent.
Two other galaxies in the sample appear to have spiral arms, albeit less prominent.
We first return to the plot showing concentration ooptical color
We first return to the plot showing concentration optical color
3.2.10 ~2—2.5 of clusters. M87 has been considered to be a classic example of a "cooling flow" system. where the gas cooling time is relatively short compared to the age of the system (e.g. Stewart et al.
$3.2\times10^9$ $\sim2-2.5$ of clusters, M87 has been considered to be a classic example of a “cooling flow” system, where the gas cooling time is relatively short compared to the age of the system (e.g., Stewart et al.
1984. Nulsen Bóhhringer 1995. Bóhhringer et al.
1984, Nulsen Böhhringer 1995, Böhhringer et al.
2001).
2001).
However. observations with XMM-Newton have shown that cooling flows. like that around. M87. deposit cooled gas at much lower rates than expected in the standard cooling flow model (Fabian 1994; Peterson et al.
However, observations with XMM-Newton have shown that cooling flows, like that around M87, deposit cooled gas at much lower rates than expected in the standard cooling flow model (Fabian 1994; Peterson et al.
2003 and references therein).
2003 and references therein).
This requires considerable energy input to compensate for radiative losses.
This requires considerable energy input to compensate for radiative losses.
M87. with its proximity. its active nucleus. jet. and extensive system of radio lobes. provides an ideal system for studying the energy input from the AGN to the hot. cooling gas.
M87, with its proximity, its active nucleus, jet, and extensive system of radio lobes, provides an ideal system for studying the energy input from the AGN to the hot, cooling gas.
Using radio studies. Owen. Eilek Kassim (2000: see also Binney 1999) pioneered the view that the mechanical power produced by the supermassive black hole at the center of M87 was more than sufficient to compensate for the energy radiated in X-rays.
Using radio studies, Owen, Eilek Kassim (2000; see also Binney 1999) pioneered the view that the mechanical power produced by the supermassive black hole at the center of M87 was more than sufficient to compensate for the energy radiated in X-rays.
Tabor Binney (1993) and Binney Tabor (1995) developed models without mass deposition and included energy injection from the central AGN.
Tabor Binney (1993) and Binney Tabor (1995) developed models without mass deposition and included energy injection from the central AGN.
Heinz. Reynolds Begelman (1998: see also Reynolds. Heinz Begelman 2001) modelled shock heating of the IGM by an expanding radio source.
Heinz, Reynolds Begelman (1998; see also Reynolds, Heinz Begelman 2001) modelled shock heating of the IGM by an expanding radio source.
Churazov et al. (
Churazov et al. (
2001: see also Kaiser Binney 2003. Bruggen 2003. De Young 2003. Kaiser 2003) argued that the morphology of the X-ray and radio observations could be explained by radio emitting. plasma bubbles buoyantly rising through the hot X-ray emitting gas.
2001; see also Kaiser Binney 2003, Bruggen 2003, De Young 2003, Kaiser 2003) argued that the morphology of the X-ray and radio observations could be explained by radio emitting plasma bubbles buoyantly rising through the hot X-ray emitting gas.
These buoyant bubbles could uplift the coolest gas and provide energy input as bubble enthalpy is converted to kinetic energy. then thermalized into the gas in the bubble wake.
These buoyant bubbles could uplift the coolest gas and provide energy input as bubble enthalpy is converted to kinetic energy, then thermalized into the gas in the bubble wake.
The results outlined above relied primarily on pre-Chandra
The results outlined above relied primarily on pre-Chandra
lm
.1in
the other 19 square degrees were in the L5 region of Neptune.
the other 19 square degrees were in the L5 region of Neptune.
Subaru was used to covered 21 square degrees while Magellan was used [or the other 28 square degrees of the survey.
Subaru was used to covered 21 square degrees while Magellan was used for the other 28 square degrees of the survey.
The first hish inclination Neptune Trojan. 2005 N54sy. Was discovered al Magellan (Sheppard Trujillo 2006) while the first L5 Neptune Trojan (2008 LCx: Sheppard Trujillo 2010) was found al Subaru.
The first high inclination Neptune Trojan, 2005 $_{53}$, was discovered at Magellan (Sheppard Trujillo 2006) while the first L5 Neptune Trojan (2008 $_{18}$: Sheppard Trujillo 2010) was found at Subaru.
In all. five L4 Neptune Trojans were detected al Magellan ranging from 22.5 to 23.7 magnitudes (about TO to 40 km in radius) while one L5 Neptune Trojan was detected al Subaru with an magnitude of 23.2 in the R-bancl.
In all, five L4 Neptune Trojans were detected at Magellan ranging from 22.5 to 23.7 magnitudes (about 70 to 40 km in radius) while one L5 Neptune Trojan was detected at Subaru with an magnitude of 23.2 in the R-band.
The data were analyzed with a computer algorithm (tuned to detect objects which appeared in all three images from one night with an apparent motion consistent with being bevond the orbit of Jupiter (speeds less than 20 arcseconds per hour).
The data were analyzed with a computer algorithm tuned to detect objects which appeared in all three images from one night with an apparent motion consistent with being beyond the orbit of Jupiter (speeds less than 20 arcseconds per hour).
Objects were flagged as possible Neptune Trojans if thev moved between 3.5 and 4.5 areseconds per hour.
Objects were flagged as possible Neptune Trojans if they moved between 3.5 and 4.5 arcseconds per hour.
These objects were recovered up to lwo mouths later to determine if they had Neptune Trojan like orbits.
These objects were recovered up to two months later to determine if they had Neptune Trojan like orbits.
The survey was designed similar (o our ultra-deep survevs for satellites around the planets (Sheppard et al.
The survey was designed similar to our ultra-deep surveys for satellites around the planets (Sheppard et al.
2005: Sheppard Trujillo 2009).
2005; Sheppard Trujillo 2009).
We determined the limiting magnitude of the survey by placing artificial objects in the fields matched to the point spread function of the images and with motions of 4 arcsecouds per hour.
We determined the limiting magnitude of the survey by placing artificial objects in the fields matched to the point spread function of the images and with motions of 4 arcseconds per hour.
The brightnesses of the objects were binned by 0.1 mae and spanned the range [rom 25 to 27 magnitudes.
The brightnesses of the objects were binned by 0.1 mag and spanned the range from 25 to 27 magnitudes.
Results are shown in Figure 1..
Results are shown in Figure \ref{fig:effTrojans}.
The 50% detection efficiency. [or most of the fields is taken as our limiting magnitude. found to be m,=25.7.
The $50\%$ detection efficiency for most of the fields is taken as our limiting magnitude, found to be $m_{R}=25.7$.
Badii G7) of the Neptune Trojans were determined assuming an albedo of pp=0.05 and using the equation. r=(225x1019RAM/pso(0))/?10207«—2? where is the heliocentric distance in AU. A is the geocentrie distance in AU. m... is the apparent red magnitude of the sun (—27.1). pg is (he red geometric albedo. y 1s the apparent red magnitude of the Trojan and ó(0)=1 is the phase Function at opposition.
Radii $r$ ) of the Neptune Trojans were determined assuming an albedo of $\rho_{R}=0.05$ and using the equation, $r = (2.25\times 10^{16} R^{2} \Delta ^{2} / p_{R}\phi (0))^{1/2} 10^{0.2(m_{\odot} - m_{R})}$ where $R$ is the heliocentric distance in AU, $\Delta$ is the geocentric distance in AU, $m_{\odot}$ is the apparent red magnitude of the sun $-27.1$ ), $p_{R}$ is the red geometric albedo, $m_{R}$ is the apparent red magnitude of the Trojan and $\phi (0) = 1$ is the phase function at opposition.
Using an albedo of 0.05 (Fernandez οἱ al.
Using an albedo of 0.05 (Fernandez et al.
2003: Fernaucdez et al.
2003; Fernandez et al.
2009) we find that 25.7 magnitudes corresponds to à Neptune Trojan with a radius of about 16 km.
2009) we find that 25.7 magnitudes corresponds to a Neptune Trojan with a radius of about 16 km.
The Cumulative Luminosity Function (CLE) describes the skv-plane number density of objects brighter than a given magnitude.
The Cumulative Luminosity Function (CLF) describes the sky-plane number density of objects brighter than a given magnitude.
The CLF can be described by where X(ng) is the number of objects brighter than mg. m, is the magnitude zero point. and a describes the slope of the huninosity function.
The CLF can be described by where $\Sigma (m_{R})$ is the number of objects brighter than $m_{R}$, $m_{o}$ is the magnitude zero point, and $\alpha$ describes the slope of the luminosity function.
The CLE found for Neptune Trojans is shown in Figure 2..
The CLF found for Neptune Trojans is shown in Figure \ref{fig:cumTrojans}.
The CLF of the brightest Neptune Trojans Gry,<23.5 magnitude) follows a steep power law of à~0.8 similar to the brightest Kuiper Belt objects. Jupiter Trojans and main belt asteroids (Jewitt et al.
The CLF of the brightest Neptune Trojans $m_{R}<23.5$ magnitude) follows a steep power law of $\alpha \sim 0.8$ similar to the brightest Kuiper Belt objects, Jupiter Trojans and main belt asteroids (Jewitt et al.
2000: Jeclicke et al.
2000; Jedicke et al.
2002: Bottke et al.
2002; Bottke et al.
2005: Fraser Wavelaars 2008: Fuentes Holman 2008).
2005; Fraser Kavelaars 2008; Fuentes Holman 2008).
The Neptune Trojans discovered in our
The Neptune Trojans discovered in our
ssumples.
samples.
After this work was being completed. louche(2008) showed that aabsorbers on the ssequence shown in Fig. 2
After this work was being completed, \citet{MenardB_08b} showed that absorbers on the sequence shown in Fig. \ref{fig:intro}( (
a) have indeed a constant dust-to-gas ratio Interestingly. they concluded that the dust-to-gas ratio was not consistent with that of dwarf galaxies (SMC). therefore rejecting the alternative hypothesis often invoked for absorbers. namely that the sight-lines go through dwarfs near more normal galaxies.
a) have indeed a constant dust-to-gas ratio Interestingly, they concluded that the dust-to-gas ratio was not consistent with that of dwarf galaxies (SMC), therefore rejecting the alternative hypothesis often invoked for absorbers, namely that the sight-lines go through dwarfs near more normal galaxies.
We note that the dust-to-gas ratio for the data points in the upper left of Fig. 2t
We note that the dust-to-gas ratio for the data points in the upper left of Fig. \ref{fig:intro}( (
) (i.e. not on ssequence) must be Aysmaller pum(Ménard&Chelouche2008)... as concluded by Wolfeetal.(2008). for DLAs with low velocity widths.
a) (i.e. not on sequence) must be smaller \citep{MenardB_08b}, as concluded by \citet{WolfeA_08a} for DLAs with low velocity widths.
Both Prochaskaetal.(2008) and. Ledouxetal.(2006) used a sample of DLAs at higher redshifts (with 1.7<zin; 4.3) than the Rao et al.
Both \citet{ProchaskaJ_08a} and \citet{LedouxC_06a} used a sample of DLAs at higher redshifts (with $1.7<z_{\rm abs}<4.3$ ) than the Rao et al.
sample of low-z absorbers dominating our study.
sample of $z$ absorbers dominating our study.
However. Fig. 2
However, Fig. \ref{fig:intro}( (
b) does not change qualitatively for absorbers with zu1.6 in our sample.
b) does not change qualitatively for absorbers with $z_{\rm abs}>1.6$ in our sample.
The overall metallicity is lower. reflecting the redshift evolution of metallicity in DLAs and DLAs (Prochaskaetal.2003:Péroux2007: 2007)..
The overall metallicity is lower, reflecting the redshift evolution of metallicity in DLAs and sub-DLAs \citep{ProchaskaJ_03b,PerouxC_07a,KulkarniV_07a}.
Another difference between our analysis and (2006) and Prochaskaetal.(2008).. is that we used aas a proxy for velocity width Av (Ellison2006) whereas they used the measured velocity width from high-resolution spectra of the low-ionsaandΠΠ.
Another difference between our analysis and \citet{LedouxC_06a} and \citet{ProchaskaJ_08a}, is that we used as a proxy for velocity width $\Delta v$ \citep{EllisonS_06a} whereas they used the measured velocity width from high-resolution spectra of the low-ionsand.
, However. for the dozen of absorbers with both aand Ae(Sill or Zn I). we find that the Ar¢ ΙΟ) correlates with Ae(SiIL or ZnII) at ccontidence level.
However, for the dozen of absorbers with both and $\Delta v(\SiII$ or $\ZnII)$ , we find that the $\Delta v$ ) correlates with $\Delta v(\SiII$ or $\ZnII)$ at confidence level.
Thus. the selection effect shown in Fig.
Thus, the selection effect shown in Fig.
3. exists against citepfasin][]MurphyMu reenedegeinstzNe(Silt or Zntl) Ledouxetal.2006:Prochaska 2008).
\ref{fig:gradient} exists against \\citep[as in][]{MurphyM_07a} and against $\Delta v(\SiII$ or $\ZnII)$ \citep[as in][]{LedouxC_06a,ProchaskaJ_08a}.
One might invoke dust obscuration to account for the results shown in Fig. 3..
One might invoke dust obscuration to account for the results shown in Fig. \ref{fig:gradient}. .
However. such a dust-bias would have to selectively remove metal rich DLAs with low1
However, such a dust-bias would have to selectively remove metal rich DLAs with low.
1,7ος, The results of Yorketal.(2006) and Ménardetal.(2008). showed that dust obscuration in 1--selected samples with the lowest iis low. Le. Et13)x0.02 below pem2A. 77which implies a very low fraction of missed absorbers below num2À irrespective ofΔΗΙ.
The results of \citet{YorkD_06a} and \citet{MenardB_08a} showed that dust obscuration in -selected samples with the lowest is low, i.e. $E(B-V)<0.02$ below $\EW<2$, which implies a very low fraction of missed absorbers below $\EW<2$ irrespective of.
. Similarly. such a dust-bias would have to selectively remove metal poor DLAs with high".
Similarly, such a dust-bias would have to selectively remove metal poor DLAs with high.