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Similarly. some of the powerful starbursts may contain sizeable AGN contributions.
Similarly, some of the powerful starbursts may contain sizeable AGN contributions.
These effects will lead to a certain amount of double counting. perhaps over-producing the aint source counts.
These effects will lead to a certain amount of double counting, perhaps over-producing the faint source counts.
estimated to beNie 10?! >7.
estimated to be$N$ $\sim10^{21}$ $^{-2}$.
This photoionization model is roughly consitent with the “lukewarm absorber” (dimensionless ionization parameter U =0.032 and Nu= 1.62x1074 7) inferred[rom the absorption svstem in the UV band (Crenshawetal.2002).
This photoionization model is roughly consitent with the “lukewarm absorber” (dimensionless ionization parameter $U$ $=0.032$ and $N$ $=1.62\times10^{21}$ $^{-2}$ ) inferredfrom the absorption system in the UV band \citep{cre02}.
. Their prediction of Novy=1.5xI0! em7 is also consistent with the observed τον. Which⋅⋅ is equivalent⋅ to Noyy⇁~∙2.5Px10- em57.
Their prediction of $N_{\rm OVII}=1.5\times10^{17}$ $^{-2}$ is also consistent with the observed $\tau_{\rm OVII}$, which is equivalent to $N_{\rm OVII}\sim2.5^{+1.8}_{-1.9}\times10^{17}$ $^{-2}$ .
Hence. we conclude that this feature is due to a warm absorber of £~I and Niue 107. 7.
Hence, we conclude that this feature is due to a warm absorber of $\xi\sim1$ and $N$ $\sim10^{21}$ $^{-2}$.
The low-£ warm absorber discussed in (he previous section could be responsible for the narrow absorption lines of Ovil: however. it is dillicul to produce the other higher ionization lines from ο)vill Neix. NeX. and Mg that we see.
The $\xi$ warm absorber discussed in the previous section could be responsible for the narrow absorption lines of O; however, it is difficult to produce the other higher ionization lines from O, Ne, Ne, and Mg that we see.
This is because. if the line-of-sight material is a single homogeneous gas. there should be some observable lines from Ne and Mg that are not seen.
This is because, if the line-of-sight material is a single homogeneous gas, there should be some observable lines from Ne and Mg that are not seen.
Therefore we infer that a second. absorber with higher ionization is present.
Therefore we infer that a second absorber with higher ionization is present.
The suggested detection of the and lines and thelack of the lines also support the multi-phase/zone view.
The suggested detection of the and lines and thelack of the lines also support the multi-phase/zone view.
An order of magnitude estimation of the column density (:Vigg) and the velocity dispersion (ion) Of the ion for the higher-€ warm absorber can be mace using curve of growth analvsis.
An order of magnitude estimation of the column density $N_{\rm ion}$ ) and the velocity dispersion $\sigma_{\rm ion}$ ) of the ion for the $\xi$ warm absorber can be made using curve of growth analysis.
The detection of a pair of absorption lines from the same jon enables us to constrain σ ancl AN. because the equivalent width LV of an absorption line is a ΠιοΙον of IN. e. and the oscillator strength: (Spitzer 1978: Ixotani et al.
The detection of a pair of absorption lines from the same ion enables us to constrain $\sigma$ and $N$, because the equivalent width $EW$ of an absorption line is a function of $N$, $\sigma$, and the oscillator strength (Spitzer 1978; Kotani et al.
2000).
2000).
It should be noted that the EWs of the Ix2 lines are as large as the Ka lines for ο ancl Ne ions.
It should be noted that the EWs of the $\beta$ lines are as large as the $\alpha$ lines for O and Ne ions.
To explain the high value of the EM,/EWy; atleast the Ίνα lines of these ions must be saturated.
To explain the high value of the $EW_{\rm K\alpha}$ $EW_{\rm K\beta}$, at least the $\alpha$ lines of these ions must be saturated.
This gives the upper and lower limits on σ and NV. respectively.
This gives the upper and lower limits on $\sigma$ and $N$, respectively.
The IX-9 lines are not useful due to poor statistics.
The $\delta$ lines are not useful due to poor statistics.
The inferred column densities are Voyy~LOMem 7. Noa~108em7. ANN.~103cm3c. Λίνοςx10Pcm5-. and Next'~Lolem>7.
The inferred column densities are $N_{\rm O VII}\sim10^{17}~{\rm cm}^{-2}$ , $N_{\rm O VIII} \sim10^{18}~{\rm cm}^{-2}$, $N_{\rm Ne IX}\sim10^{17}~{\rm cm}^{-2}$, $N_{\rm Ne X}\sim10^{17}~{\rm cm}^{-2}$, and $N_{\rm Mg XI}\sim10^{16.5}~{\rm cm}^{-2}$.
The velocity dispersion iso 100 kms +.
The velocity dispersion is$\sigma\sim$ 100 km $^{-1}$ .
Using these column densities and assuming cosmic abundances. we infer that the photoionizd gashas the ionization parameter loοc2 and the column density Vue10?! 7.
Using these column densities and assuming cosmic abundances, we infer that the photoionizd gashas the ionization parameter $\log\xi\sim2$ and the column density $N$ $\sim 10^{21}$ $^{-2}$ .
ratios larger than 2.
ratios larger than 2.
Nevertheless, for all three energy spectra considered it is possible to produce manifestly asymmetric structures, comparable to those observed.
Nevertheless, for all three energy spectra considered it is possible to produce manifestly asymmetric structures, comparable to those observed.
As a strong departures from symmetry in the columnconsequence, densities are not generally evidence for unstable structures.
As a consequence, strong departures from symmetry in the column densities are not generally evidence for unstable structures.
In addition to the excitation mechanism, the evolution of the underlying core properties and the non-linear damping of oscillations can imprint themselves upon the pulsation energy spectrum.
In addition to the excitation mechanism, the evolution of the underlying core properties and the non-linear damping of oscillations can imprint themselves upon the pulsation energy spectrum.
Ultimately, the relative importance depends upon the relationship between the timescale associated with each process.
Ultimately, the relative importance depends upon the relationship between the timescale associated with each process.
Here we present some observationally motivated constraints and discuss the consequences for the stability and appearance of starless cores.
Here we present some observationally motivated constraints and discuss the consequences for the stability and appearance of starless cores.
In particular we motivate a in which the oscillations are inherited from the parent picturemolecular cloud turbulence, and the fundamental modes are at the of shorter wave length during a slow amplifiedcontraction phase expenseresulting in a fundamental-mode dominated spectrum.
In particular we motivate a picture in which the oscillations are inherited from the parent molecular cloud turbulence, and the fundamental modes are amplified at the expense of shorter wave length during a slow contraction phase resulting in a fundamental-mode dominated spectrum.
non-linear of the pulsations then eliminates the Subsequentadditional turbulent decaysupport leading to collapse and star formation in those cores that are super-critical with respect to the static BE model.
Subsequent non-linear decay of the pulsations then eliminates the additional turbulent support leading to collapse and star formation in those cores that are super-critical with respect to the static BE model.
The relevant timescales for the starless cores are the evolution timescale of the core, T, the oscillatingpulsation periods, Pum, lifetimes, Τη, and excitation timescale t,.
The relevant timescales for the oscillating starless cores are the evolution timescale of the core, $T$, the pulsation periods, $P_{nlm}$ , lifetimes, $\tau_{nlm}$, and excitation timescale $t_e$.
Even without knowing the excitation mechanism we can begin to place these into a hierarchy based upon the observation that cores with large-amplitude, long-period pulsations exist.
Even without knowing the excitation mechanism we can begin to place these into a hierarchy based upon the observation that cores with large-amplitude, long-period pulsations exist.
In addition to the observations of Ladaetal.(2003),, Redmanetal.(2006) and Agutietal.(2007) mentioned in the introduction, the observations of Sohnetal.(2007) find that about 2/3 of all their 85 observed cores show clear evidence of either expansion or contraction.
In addition to the observations of \citet{Lada2003}, \citet{Redman2006} and \citet{Aguti2007} mentioned in the introduction, the observations of \citet{Sohn2007} find that about 2/3 of all their 85 observed cores show clear evidence of either expansion or contraction.
Most of the remaining 1/3 show complex spectral line profiles that also indicate internal motions but are difficult to characterize.
Most of the remaining 1/3 show complex spectral line profiles that also indicate internal motions but are difficult to characterize.
The presence of coherent oscillations immediately implies that Phim«T,Trim,te.
The presence of coherent oscillations immediately implies that $P_{nlm}<T,\,\tau_{nlm},\,t_e$.
That is, for coherent oscillations to exist the core must persist in a fixed state sufficiently long for the pulsation to coordinate the large-scale motions throughout the core, and the pulsation amplitudes cannot change significantly this
That is, for coherent oscillations to exist the core must persist in a fixed state sufficiently long for the pulsation to coordinate the large-scale motions throughout the core, and the pulsation amplitudes cannot change significantly during this process.
Violations of either of these would result in duringmotions that process.appear stochastic (microturbulent) instead of coherent.
Violations of either of these would result in motions that appear stochastic (microturbulent) instead of coherent.
That the observed pulsations have Eos.~Ey implies TrimSfe.
That the observed pulsations have $\Eo\sim\Eb$ implies $\tau_{nlm}\lesssim t_e$.
Were the observed modes the result of a excitation, or many individual excitation events, we would prolongedexpect with near unit that a core will have had a sequence of excitations probabilityresulting in givenEo;>>Ey, at which point the core is torn in direct conflict with the observation of numerous cores apart,with substantial internal motions.
Were the observed modes the result of a prolonged excitation, or many individual excitation events, we would expect with near unit probability that a given core will have had a sequence of excitations resulting in $\Eo\gg\Eb$, at which point the core is torn apart, in direct conflict with the observation of numerous cores with substantial internal motions.
In principle, this can be prevented the transfer during each excitation event.
In principle, this can be prevented by limiting the energy transfer during each excitation event.
However,by limitingin that case energythe development of pulsations is itself rare, in direct conflict with large-scaleobservations.
However, in that case the development of large-scale pulsations is itself rare, again in direct conflict with observations.
Thus, as long as the againexcitation mechanism is uncorrelated with the themselves, i.e., there is no oscillation "feedback", a given pulsationsmode must have, on average, originated from only a single excitation event.
Thus, as long as the excitation mechanism is uncorrelated with the pulsations themselves, i.e., there is no oscillation “feedback”, a given mode must have, on average, originated from only a single excitation event.
Finally, we have TSThm.
Finally, we have $T\lesssim\tau_{nlm}$.
As the pulsations damp away, the support arising from the oscillations is lost, forcing the core to evolve towards higher central densities and then ultimately towards collapse.
As the pulsations damp away, the support arising from the oscillations is lost, forcing the core to evolve towards higher central densities and then ultimately towards collapse.
Thus, for cores in which the pulsations are dynamically important the mode lifetimes set an upper limit upon the core evolution time; a core may evolve on shorter timescales but itwill evolve as modes decay.
Thus, for cores in which the pulsations are dynamically important the mode lifetimes set an upper limit upon the core evolution time; a core may evolve on shorter timescales but it evolve as modes decay.
Thus, in summary, the very presence of starless cores with dynamically significant pulsations gives the following hierarchy among the relevant timescales: This simplifies dramatically the determination of the consequences of mode decay and core evolution.
Thus, in summary, the very presence of starless cores with dynamically significant pulsations gives the following hierarchy among the relevant timescales: This simplifies dramatically the determination of the consequences of mode decay and core evolution.
Given that Tf, we are justified in imagining that pulsations on super-criticalSZ cores are relics of the core formation process.
Given that $T\lesssim t_e$, we are justified in imagining that pulsations on super-critical cores are relics of the core formation process.
The natural mechanism for the excitation of the oscillations is then the turbulence within the parent cloud, inherited at the formation of the core.
The natural mechanism for the excitation of the oscillations is then the turbulence within the parent cloud, inherited at the formation of the core.
This does not mean that the energy spectrum of an observed core is always the same as the cloud.
This does not mean that the energy spectrum of an observed core is always the same as the parent cloud.
If cores are formed by a prolonged collapse, the parentevolution of the underlying equilibrium modifies the spectrumof the oscillations.
If cores are formed by a prolonged collapse, the evolution of the underlying equilibrium configuration modifies the energy spectrumof the oscillations.
Since configurationPrim«T, this process is energyslow in the sense described in Section 2.2,, and again we may use the adiabatic invariant to estimate the evolution of the turbulent spectrum.
Since $P_{nlm}<T$, this process is slow in the sense described in Section \ref{sec:RoPtSC}, and again we may use the adiabatic invariant $E_{nlm}/\omega_{nlm}$ to estimate the evolution of the turbulent spectrum.
If this Exnim/Wnimformation occurs at constant temperature and mass, the mode periods are functionsof ¢ alone, with the dependencies implied by Figure 2..
If this formation occurs at constant temperature and mass, the mode periods are functionsof $\zeta$ alone, with the dependencies implied by Figure \ref{fig:omegas}. .
Thus, the evolved energy spectrum is
Thus, the evolved energy spectrum is
independently of the host morphologies (Vitoresctal.1996b3).
independently of the host morphologies \cite{vitores96b}) ).
The large intrinsic dispersion in the correlations with IIubble type is a shortcoming in the use of all the above iudices (Vitoresetal. 199G6a)).
The large intrinsic dispersion in the correlations with Hubble type is a shortcoming in the use of all the above indices \cite{vitores96a}) ).
The surface brightuess corresponding to an outermost isophote such as 4/45 shows no correlation with the above concentration indices or with IDIubble type.
The surface brightness corresponding to an outermost isophote such as $\mu_{24.5}$ shows no correlation with the above concentration indices or with Hubble type.
However. Doietal.1993 used it in combination with a new concentration index e;,(0) to show that galaxies of different morphological types tend to segregate around different sets of values.
However, \cite{doi93} used it in combination with a new concentration index $c_{in}(\alpha)$ to show that galaxies of different morphological types tend to segregate around different sets of values.
In particular. Sevfert type l aud 2 galaxies are found to be well separated ou the οί) VS flops diagrain. Sevfert Ls being segregated in t1ο region e;4,60 )20.6-0.7. fro, 5=21.8-22.1 characterisic of carly type galaxies. while Sevfert 2s lie in the region of later type galaxies with larec scatter.
In particular, Seyfert type 1 and 2 galaxies are found to be well separated on the $c_{in}$ $\alpha$ ) vs $\mu_{24.5}$ diagram, Seyfert 1s being segregated in the region $c_{in}$ $\alpha$ )=0.6-0.7, $\mu_{24.5}$ =21.8-22.4 characteristic of early type galaxies, while Seyfert 2s lie in the region of later type galaxies with large scatter.
We have computed many of the above light concentration indicators: the most useful of them are tabulated in Table 3..
We have computed many of the above light concentration indicators; the most useful of them are tabulated in Table \ref{tab3}.
In order to calculate concentration iices an estimate of the£ofal ealaxian light is uecded.
In order to calculate concentration indices an estimate of the galaxian light is needed.
Iu Chatzichristou1999 we describe in detail how or cllipse fitΠιο procedure works. includiue the calculation of total uaenitudes inteerating from the outermost fitted isoshote to infinity.
In \cite{thesis} we describe in detail how our ellipse fitting procedure works, including the calculation of total magnitudes integrating from the outermost fitted isophote to infinity.
Were we use these magnitudes to calculate the various characteristic radii aud t1C corresponding indices.
Here we use these magnitudes to calculate the various characteristic radii and the corresponding indices.
Iu Table 3 we list the couceutration piruueters C'y;o. [INID. N/T. C31. the characteristic radius +» and the diuneter corresponding to f1C 425* mag P7 isophotalB level (see Paper IT).
In Table \ref{tab3} we list the concentration parameters $C_{I/O}$, $N/D$, $N/T$, $c_{31}$, the characteristic radius $r_{1/2}$ and the diameter corresponding to the $\mu$ =25 mag $^{-2}$ isophotal level (see Paper II).
Note tha this table contains more objects than Tab because itf includes objects for which photometry is available (and thus concentration iudices). but profile decomposition was donc.
Note that this table contains more objects than Table \ref{tab1}, because it includes objects for which photometry is available (and thus concentration indices), but no profile decomposition was done.
We shall now discuss the various structural parameters characterizing the ealaxy bulges and disks for our three samples: their distributions. their correlations with each other aud with additional observed galaxia properties.
We shall now discuss the various structural parameters characterizing the galaxy bulges and disks for our three samples: their distributions, their correlations with each other and with additional observed galaxian properties.
We shall first consider the distributious of morphological index T (as defined in RC3) aud bulec-to-disk ratio. plotted in Figure 2..
We shall first consider the distributions of morphological index T (as defined in RC3) and bulge-to-disk ratio, plotted in Figure \ref{f2}.
Iu general. a morphological classification is not precise and depends upon the type of data and tlic classification iethod usec.
In general, a morphological classification is not precise and depends upon the type of data and the classification method used.
The uucertaiity in icles. T for two independent classificrs can range from 0.89 (RC3) to 2.2 (Lahavetal.1995)) with a1 average of 1.5 (DeJong1996c)).
The uncertainty in index T for two independent classifiers can range from 0.89 (RC3) to 2.2 \cite{lahav95}) ) with an average of 1.5 \cite{jong96c}) ).
Alowing for this uncertainty. which is abot half a bisize In Fieure 2.. we fiud cüffereut treusin the cistributions of T or the three subsamples: Warm Sevfert is ten to reside in carlicr type hosSs COlMpArTCe to Warm Sevtert 2s. alhough both distributions peak at similar values.
Allowing for this uncertainty, which is about half a binsize in Figure \ref{f2}, we find different trends in the distributions of T for the three subsamples: Warm Seyfert 1s tend to reside in earlier type hosts compared to Warm Seyfert 2s, although both distributions peak at similar values.
This teudeucv was noticed in a variety of previous studies. where Sevterts were also found to prefercutially have spiral or barred spiral morphologics or other kinds of disturbances rmgs) Adams1977.Wehinger&Wyck-19001).
This tendency was noticed in a variety of previous studies, where Seyferts were also found to preferentially have spiral or barred spiral morphologies or other kinds of disturbances rings) \cite{adams77,wehinger77,simkin80,dahari84,kenty90}) ).
In these respects. our IR-Wuiu Sevferts do not appear to be different than their optically seleced COIiterparts.
In these respects, our IR-Warm Seyferts do not appear to be different than their optically selected counterparts.
Our Cold sample galaxies show a clear shift towards later tvpe hosts. although an accurate classification for these objects is difficult eiven that most are iuenibers of closelv iuteracting svstellis. tlis often severcly distorted.
Our Cold sample galaxies show a clear shift towards later type hosts, although an accurate classification for these objects is difficult given that most are members of closely interacting systems, thus often severely distorted.
Cousequenutlv. iu what follows we «enote with T210 the svsteius with severe distortions. recent πασος or strong tidal features one-sded armis) whose main body cannot be classified 1iorpliologicallv.
Consequently, in what follows we denote with $\ge$ 10 the systems with severe distortions, recent mergers or strong tidal features one-sided arms) whose main body cannot be classified morphologically.
The iudex C; is. as defue in the previous section. ecualent to the commonly used bulee-to-disk ratio fracBD)) and its distribution for the various samples is shown i1 Figure 2..
The index $C_{I/O}$ is, as defined in the previous section, equivalent to the commonly used bulge-to-disk ratio ) and its distribution for the various samples is shown in Figure \ref{f2}.
The C5 distributions of the Wart Sevtert 2 and Cold samples are similar. while the Seyfert 1s show a tail to higrer values with a sieuificautv larger median (Table 1).
The $C_{I/O}$ distributions of the Warm Seyfert 2 and Cold samples are similar, while the Seyfert 1s show a tail to higher values with a significantly larger median (Table \ref{tab4}) ).
The F-test and Studeut’s t-test however show ιο statistically sienificaut differences in the variaaces or means of the three samples.
The F-test and Student's t-test however show no statistically significant differences in the variances or means of the three samples.
Let us compare our sauiple’s Cρω witi that for normal galaxies: A classification scheme established from a sample of field galaxies from the IST Medium Deep Survey through a classical De Vaucouleurs|exponential decomposition (Sclunidtke 1997)). predicts <110 for »ilee-donminated
Let us compare our sample's $C_{I/O}$ with that for normal galaxies: A classification scheme established from a sample of field galaxies from the HST Medium Deep Survey through a classical De Vaucouleurs+exponential decomposition \cite{schmidtke97}) ), predicts 10 for bulge-dominated
The third concern. namely (he isotropy of MONDian dynamics. is an interesing issue.
The third concern, namely the isotropy of MONDian dynamics, is an interesting issue.
If MONDian behavior arises from a modification of inertia (Alilgrom2005).. then (his scalar quantity will determine an objects response toany applied force. and it will exhibit (he same modified dynamics in all directions.
If MONDian behavior arises from a modification of inertia \citep{Milgrom05}, then this scalar quantity will determine an object's response to applied force, and it will exhibit the same modified dynamics in all directions.
On the other hand one might imagine that NMOND only applies component by component. with a modified response only to those forces that. would eive rise to accelerations below the αμ threshold.
On the other hand one might imagine that MOND only applies component by component, with a modified response only to those forces that would give rise to accelerations below the $a_0$ threshold.
This could produce a difference in the radial and vertical dynamics and could perhaps account for a ratio of oui/Heecsieat hat differs from unity.
This could produce a difference in the radial and vertical dynamics and could perhaps account for a ratio of $\mu_{radial}/\mu_{vertical}$ that differs from unity.
I this circumstance however a terrestrial. Cavendish. experiment conducted αἱ the North or South pole shoukl see differing effective values of G in different regimes of ji.
In this circumstance however a terrestrial Cavendish experiment conducted at the North or South pole should see differing effective values of $G$ in different regimes of $\mu$.
sensible next steps to obtaining observations (hat are optimally suited to the test we propose include 1) assessing the relative merits of planetary nebulae vs. integrated starlieht as probes of vertical velocity dispersion. 2) selecting a favorable list of target galaxies. ancl 3) carrving out a sel of appropriate observations.
Sensible next steps to obtaining observations that are optimally suited to the test we propose include 1) assessing the relative merits of planetary nebulae vs. integrated starlight as probes of vertical velocity dispersion, 2) selecting a favorable list of target galaxies, and 3) carrying out a set of appropriate observations.
lt is sensible to include. as a control. exaniples of high surface brightness disk galaxies which should have their inner regions in the Newtonian disk-dominated regime where ji —1. to verily that CP is constant and equal to unity for these svstems.
It is sensible to include, as a control, examples of high surface brightness disk galaxies which should have their inner regions in the Newtonian disk-dominated regime where $\mu$ =1, to verify that $CP$ is constant and equal to unity for these systems.
IIo: and 21 em observations of the velocity field might also contribute to this techiique.
$\alpha$ and 21 cm observations of the velocity field might also contribute to this technique.
We are grateful to J. Deckenstein. G. Dothun. J. Daleanton. and Ix. Cook for interesting conversations about MOND as an alternative to dark matter.
We are grateful to J. Beckenstein, G. Bothun, J. Dalcanton, and K. Cook for interesting conversations about MOND as an alternative to dark matter.
J. Battat. A. Miceli. D. Sherman and the thoughtful stuclents in Harvards Fall 2005 freshman seminar on the ]lidden Universe provided important encouragement.
J. Battat, A. Miceli, D. Sherman and the thoughtful students in Harvard's Fall 2005 freshman seminar on the Hidden Universe provided important encouragement.
We (hank Harvard University and the Department of Energy. Office of Science for their support.
We thank Harvard University and the Department of Energy Office of Science for their support.
ealaxy interaction.
galaxy interaction.
The fact that the scatter is approximately equal on the (wo sides of the Tremaineοἱal.(2002) [it suggests (hat the explanation is not as simple as objects with anomalously high |O HI] widths.
The fact that the scatter is approximately equal on the two sides of the \citet{tremaineetal02} fit suggests that the explanation is not as simple as objects with anomalously high [O III] widths.
Given that one goal of this study is to lav the groundwork lor an exploration of the AL, vs 2, relationship as a function of redshift. it is worthwhile to investigate the extent to which the fit depends on the luminosity range of the sample.
Given that one goal of this study is to lay the groundwork for an exploration of the $_{\bullet}$ vs $\sigma_\ast$ relationship as a function of redshift, it is worthwhile to investigate the extent to which the fit depends on the luminosity range of the sample.
The LOT low redshift racio-cquiet objects were divided into two sub-samples of equal size. one with Lsyyy)<2.7x1011 eres sHl and one with Lei)>2.7x1011 eres s.!.
The 107 low redshift radio-quiet objects were divided into two sub-samples of equal size, one with ${\rm L}_{5100} < 2.7 \times 10^{44}$ ergs $s^{-1}$ and one with ${\rm L}_{5100} > 2.7 \times 10^{44}$ ergs $s^{-1}$.
Figure 2 shows these (wo sub-samples plotted with different svaibols and the bisector fits to the sub-samples.
Figure 2 shows these two sub-samples plotted with different symbols and the bisector fits to the sub-samples.
The coefficients of (he fits are à = 8.02 and 4] = 2.48£0.72 for the low luminosity objects and a = 8.28 and 9] = 1.8120.52 for the high Iuminosity objects.
The coefficients of the fits are $\alpha$ = 8.02 and $\beta$ = $2.48\pm0.72$ for the low luminosity objects and $\alpha$ = 8.28 and $\beta$ = $1.81\pm0.52$ for the high luminosity objects.
Thus. there is a tendency for the slope to flatten in samples restricted to a smaller range of luminosity. particularly for high Iuminosity.
Thus, there is a tendency for the slope to flatten in samples restricted to a smaller range of luminosity, particularly for high luminosity.
This is nol surprising in that the dependence of M, on luminosity results in a dividing line between low and high Iuminosity samples that is flatter than the relation itsell.
This is not surprising in that the dependence of $_\bullet$ on luminosity results in a dividing line between low and high luminosity samples that is flatter than the relation itself.
This. combined with the large scatter. results in a [latter fit.
This, combined with the large scatter, results in a flatter fit.
For comparison with other samples. it certainly seems advisable to maintain the largest possible range of Iuminosits.
For comparison with other samples, it certainly seems advisable to maintain the largest possible range of luminosity.
Tam grateful to Mike Brotherton and Richard Green for helpful conversations.
I am grateful to Mike Brotherton and Richard Green for helpful conversations.
Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation. the Participating Institutions. the National Aeronautics and Space Administration. the National Science Foundation. the U.S. Department of Energy. the Japanese Monbukagakusho. aud the Max Planck Society.
Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society.
The SDSS Web site is http://www.scdss.org/. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory. California Institute of Technology. under contract with the National Aeronautics and Space Acministration.
The SDSS Web site is http://www.sdss.org/. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.