a r X i v :a s t r o -p h /0403714v 1 31 M a r 2004
Draft version February 2,2008
Preprint typeset using L A T E X style emulateapj v.11/12/01
CALIBRATING THE GALAXY HALO –BLACK HOLE RELATION BASED ON THE
CLUSTERING OF QUASARS
J.Stuart B.Wyithe 1and Abraham Loeb 2
swyithe@https://www.doczj.com/doc/568241936.html,.au;aloeb@https://www.doczj.com/doc/568241936.html,
Draft version February 2,2008
ABSTRACT
The observed number counts of quasars may be explained either by long-lived activity within rare massive hosts,or by short-lived activity within smaller,more common hosts.It has been argued that quasar lifetimes may therefore be inferred from their clustering length,which determines the typical mass of the quasar host.Here we point out that the relationship between the mass of the black-hole and the circular velocity of its host dark-matter halo is more fundamental to the determination of the clustering length.In particular,the clustering length observed in the 2dF quasar redshift survey is consistent with the galactic halo –black-hole relation observed in local galaxies,provided that quasars shine at ～10–100%of their Eddington luminosity.The slow evolution of the clustering length with redshift inferred in the 2dF quasar survey favors a black-hole mass whose redshift-independent scaling is with halo circular velocity,rather than halo mass.These results are independent from observations of the number counts of bright quasars which may be used to determine the quasar lifetime and its dependence on redshift.We show that if quasar activity results from galaxy mergers,then the number counts of quasars imply an episodic quasar lifetime that is set by the dynamical time of the host galaxy rather than by the Salpeter time.Our results imply that as the redshift increases,the central black-holes comprise a larger fraction of their host galaxy mass and the quasar lifetime gets shorter.
Subject headings:cosmology:theory –cosmology:observations –quasars:general
1.introduction
The Sloan Digital Sky Survey (York et al.2000)and the 2dF quasar redshift survey (Croom et al.2001a)have measured redshifts for large samples of quasars,and de-termined their luminosity function over a wide range of redshifts (Boyle et al.2000;Fan et al.2001a,b;Fan et al.2003).The 2dF survey has also been used to constrain the clustering properties of quasars (Croom et al.2001b).It has been suggested that quasars have clustering statis-tics similar to optically selected galaxies in the local uni-verse,with a clustering length R 0～8Mpc.The large sample size of the 2dF quasars also provided clues about the variation of clustering length with redshift (Croom et al.2001b)and apparent magnitude (Croom et al.2002).Quasars appear more clustered at high redshift,although with a relatively mild trend.There is also evidence that more luminous quasars may be more highly clustered.As pointed out by Martini &Weinberg (2001)and Haiman &Hui (2001),the quasar correlation length de-termines the typical mass of the dark matter halo in which the quasar resides.One may therefore derive the quasar duty-cycle by comparing the number density of quasars with the density of host dark matter halos.The quasar lifetime then follows from the product of the duty-cycle and the lifetime of the dark-matter halo in between major mergers,although there is a degeneracy between the lifetime and the quasar occupation fraction or beam-ing.Preliminary results suggested quasar lifetimes of t q ～106?107years,consistent with the values determined by other methods (see Martini 2003for a review),includ-ing the transverse proximity e?ect (Jakobsen et al.2003)and counting arguments relative to the local population
of remnant supermassive black holes (SMBHs;see Yu &Tremaine 2002).Kau?mann &Haehnelt (2002)used a de-tailed semi-analytic model (Kau?mann &Haehnelt 2000)to predict the correlation length of quasars and its evolu-tion with redshift.They found that their model reproduces the correct correlation length as well as its redshift evolu-tion for present-day quasar lifetimes of t q ～107years.In this work we argue that the correlation length of quasars is fundamentally determined by the relation be-tween the masses of SMBHs and their host galactic halo rather than by the quasar lifetime.We ?nd that the am-plitude of the correlation length depends on the product of the SMBH–halo relation and the typical fraction of the Eddington luminosity at which quasars shine.Moreover,we show that the evolution of the correlation length is sensitive to how the SMBH –halo relation evolves with redshift,and therefore to the physics of SMBH formation and quasar evolution.
The paper is organized as follows.In §2and §3we dis-cuss the calculation of the correlation function of quasars with a particular apparent magnitude B ,and the di?er-ent scenarios for the evolution of the SMBH –galaxy halo relation.In §4we compare ?ducial model correlation functions to the results of the 2dF quasar redshift survey (Croom et al.2001b,c).We ?nd that the shallow evolution of the correlation length implies that SMBH mass has a redshift-independent scaling with the circular velocity of the host dark matter halo rather than with its mass.The ranges of the normalizations in the SMBH –galaxy halo relation and of the fraction of Eddington allowed by ob-servations of the observed quasar correlation function are explored in §5.In §6we examine the quasar lifetime
1University of Melbourne,Parkville,Victoria,Australia
2
Harvard-Smithsonian Center for Astrophysics,60Garden St.,Cambridge,MA 02138
1
2
by requiring that observational constraints from both the correlation and luminosity functions be satis?ed simulta-neously.Finally,in §8we summarize our results and dis-cuss a very simple,physically motivated model that satis-?es all constraints with no free parameters.Throughout the paper we adopt the set of cosmological parameters de-termined by the Wilkinson Microwave Anisotropy Probe (WMAP,Spergel et al.2003),namely mass density pa-rameters of ?m =0.27in matter,?b =0.044in baryons,?Λ=0.73in a cosmological constant,and a Hubble con-stant of H 0=71km s ?1Mpc ?1.
2.the correlation function of quasars
The mass correlation function between halos of mass M 1and M 2,separated by a co-moving distance R is (see Scannapieco &Barkana 2003and references therein)
ξm (M 1,M 2,R )=
1
kR
W (kR 1)W (kR 2),
(1)
where
R 1,2=
3M 1,2
δc ,0
ν′2+bν′2(1?c )
?ν′2c /
√
ν′2c
+b (1?c )(1?c/2)
,(3)where δc ,0(≈1.69)is the critical overdensity threshold for spherical collapse,δc (z )=δc ,0/D (z ),D (z )is the growth factor at redshift z ,σis the variance on a mass-scale M ,ν≡δ2c (z )/σ2(M ),ν′≡
√L B ,⊙
=5.73×10
12
η
M bh
3 relation between M bh and the stellar velocity dis-
persion does not evolve with redshift.This is ex-
pected if the mass of the black-hole is determined
by the depth of the gravitational potential well in
which it resides,as would be the case if growth is
regulated by feedback from quasar out?ows(e.g.
Silk&Rees1998;Wyithe&Loeb2003).Express-
ing the halo circular velocity,v c,in terms of the
halo mass,M,and redshift,z,the redshift depen-
dent relation between the SMBH and halo masses
may be written as
M bh(M halo,z)=const×v5c
=?M halo M halo3[ζ(z)]52,(7)
where?is a constant,ζ(z)is close to unity and
de?ned asζ≡[(?m/?z m)(?c/18π2)],?z m≡[1+
(?Λ/?m)(1+z)?3]?1,?c=18π2+82d?39d2,and
d=?z m?1(see equations22–25in Barkana&Loeb
2001for more details).
?Case B:we consider the scenario in which the
SMBH mass maintains the same dependence on its
host halo mass at all redshifts,namely
M bh(M halo,z)=const×M5/3
halo
=?M halo M halo3[ζ(0)]5L B,⊙ +5log10 D L
4
Fig. 1.—Predicted correlation function at various redshifts,in comparison to the2dF data(Croom et al.2001b).The dark lines show the correlation function predictions for quasars of various apparent B-band magnitudes(B).The2dF limit is B～20.85.The lower right panel shows data from entire2dF sample in comparison to the theoretical prediction at the mean quasar redshift of z =1.5.The B=20.85 prediction at this redshift is also shown by thick gray lines in the other panels to guide the eye.This case assumes M bh∝v5c,normalized to local observations,andη=1(case AI).
function of redshift was computed from a sample having B 20.85,drawn from the2dF quasar redshift survey (Croom et al.2001b,c).The gray error bars show the val-ues for R0in di?erent redshift bins,while the correlation length measured for the whole sample(plotted at z=1.5 and B=20.3in the left and right hand panels respec-tively)is shown by the dark error bar.We?nd the predic-tions for R0to be consistent with observations.In partic-ular,both the value of the clustering length and its slow evolution with redshift and apparent magnitude are consis-tent with current data.There is little variation of the clus-tering length with apparent magnitude over the range con-sidered,although there is a tendency for brighter quasars to be more highly clustered,as was noted by Croom et al.(2002).
Note that the K-correction assumed in equation(9)is only valid out to z～3where Lyαabsorption enters into the B-band.As a result the extrapolations of redshift de-pendence to z 3shown in Figures2and3do not include Lyαabsorption in the calculation of the quasar luminos-ity.However,these extrapolations are included to illus-trate the evolution of the clustering length at yet higher redshifts(as measured in bands redward of the redshifted Lyαline).
The lower panels of Figure2show the corresponding de-pendence of the clustering length on redshift and apparent magnitude for quasars that shine at Eddington fractionsηlower than unity.Only the cases of B=20.3,correspond-
5
Fig.2.—The correlation length,R0[de?ned throughξq(R0)=1]plotted as a function of redshift(left hand panel)and apparent magnitude (right hand panel).The data is from the2dF quasar redshift survey(Croom et al.2001b,c),with the gray error bars showing the correlation length from di?erent sub-samples,and the dark error bar at z=1.5(left hand panels)and B=20.3(right hand panels)showing the correlation length for the full sample.The theoretical model assumes M bh∝v5c.In the upper panelsη=1(case AI),and the curves are shown for di?erent apparent magnitudes(left),and di?erent redshifts(right).In the lower panels we show curves corresponding to di?erent choices forηand?,(cases AII and AIII)assuming B=20.3and z=1.5respectively.
ing approximately to the median quasar B-magnitude(left
hand panel)and z=1.5(right hand panel)are shown,and
the curve corresponding toη=1(case AI)is reproduced
from the upper panels for comparison(solid lines).As-
suming the local normalization?=?SIS and thatηranges
between0.01and1with a constant dP obs/d(logη)(case
AII),the typical quasar of apparent magnitude B must
be powered by a more massive SMBH and hence reside
in a more massive galaxy than in theη=1case.This
results in a larger clustering length for quasars of a given
apparent magnitude B.The resulting evolution,indicated
by the dashed lines,appears to be incompatible with the
data.The increase in R0may be compensated for by an
increase in the normalization of the M BH?M halo rela-
tion.The dot-dashed curves show the result of increasing
this normalization relative to local observations by a fac-
tor of10(?=10?SIS).This factor equals the inverse of the
median of the distribution dP/d(logη)=const.The re-
sulting curve(corresponding to case AIII)is very similar
to our?ducial case(η=1).
These results demonstrate that while a spread in the
values ofηfor di?erent quasars results in the correlation
function being measured over a wider range of halo masses,
the correlation length is primarily sensitive to the charac-
teristic halo mass,as speci?ed by the characteristic value
ofη.Furthermore,the results demonstrate the important
point that the correlation length measures the product of
the normalization in the M bh–M halo relation and the me-
dian fraction of the Eddington luminosity at which quasars
shine,ηmed.With respect to the correlation function,this
quantity?ηmed(which is the same in cases AI and AIII)
is more fundamental to the correlation function than the
quasar lifetime since it predicts the correlation length in-
dependent from consideration of quasar number counts.
It is important to note that since the normalization of the
local M BH?M halo relation is estimated(?=?SIS,Fer-
rarese2002),the value of the quasar correlation length
at low redshift implies that quasars spend most of their
bright phase shining near their Eddington luminosity.
4.2.The correlation function for models with
M bh∝M5/3halo
We next examine whether the correlation function ob-
served by the2dF survey may be used to constrain the
evolution of the M bh–M halo relation.In the previous sub-
section,we have considered the case of a SMBH mass that
scales with the?fth power of circular velocity independent
of redshift(equation7,case A).The alternative case B
example postulates that the SMBH mass has a redshift
independent scaling with the halo mass rather than halo
circular velocity(equation8).The upper panels of Fig-
ure3plot the correlation length in this case withη=1and
?=?SIS(case BI).Both the evolution of the correlation
length with redshift for di?erent apparent magnitudes(left
6
Fig. 3.—The correlation length,R0as a function of redshift(left hand panel)and apparent B-band magnitude(right hand panel).The data is from the2dF QRS(Croom eta al.2001b,c),with the gray error bars showing the correlation length from di?erent sub-samples,and the dark error bars at z=1.5(left hand panels)and B=20.3(right hand panels)showing the correlation length for the full sample.The model assumes M bh∝M5/3halo.In the upper panelsη=1(case BI),and the curves are shown for di?erent apparent magnitudes(left),and di?erent redshifts(right).In the lower panels we show curves corresponding to di?erent choices forηand?(cases BII and BIII),assuming B=20.3and z=1.5respectively.
hand panel),and the variation of correlation length with a
given apparent magnitude at various redshifts(right hand
panel)are shown.The case B M bh?M halo relation results
in a correlation length that varies signi?cantly more with
redshift than the data requires.The lower panels show
examples with values ofηthat di?er from unity.Only the
cases of B=20.3(left hand panel)and z=1.5(right hand
panel)are shown,and the result assumingη=1(case BI)
is reproduced from the upper panels for comparison(solid
lines).If?=?SIS,andηranges between0.01and1,with
dP obs/dη∝const(case BII),then the typical quasar of
apparent magnitude B must have a larger clustering length
(dashed lines).This may be compensated for by increasing
the normalization of the M BH–M halo relation by a factor
of10(?=10?SIS,case BIII)as considered before(dot-
dashed lines).
The rapid evolution with redshift that results from a
case B M BH–M halo relation could be diminished if the lu-
minosities of quasars were a higher fraction of their Ed-
dington limit at higher redshift.However we have seen
that the locally observed normalization of the M bh–M halo
relation requires most present-day quasars to be shining
near their Eddington luminosity.Quasars at high redshift
would therefore have to be super-Eddington,shining at
～η～(1+z)5/2(η～30at z～3)in order to repro-
duce the observed slow evolution of the clustering length.
This requirement onηmay be somewhat relaxed in models
having?>?SIS,as is discussed in the next section.
5.constrainingηand?using the quasar
correlation function
The M bh–M halo relation for local galaxies requires a
choice for the relationship between the circular velocity
at the radius probed by observations of galaxies,and the
circular velocity at the virial radius.This relationship de-
pends on the dark-matter mass pro?le and is still uncertain
due to the gravitational interaction between the baryons
(which cool and often dominate gravity near the center
of galaxies)and the dark matter.Ferrarese(2002)pre-
sented M bh–M halo relations for three di?erent cases,which
may be summarized in the present notation by?=?SIS,
?=?NFW=3.7?SIS,and?=?S02=25?SIS.The second
case corresponds to the universal pro?le of Navarro,Frenk
&White(1996,NFW),and the third to the normalization
derived based on the weak lensing study of Seljak(2002).
The results in the preceding sections have been pre-
sented for?ducial models with(?,η)=(?SIS,1),(?SIS,0.1)
and(10?SIS,0.1).It was demonstrated that the correlation
function is primarily dependent on the product between?
and the median value ofη,namely?ηmed.This raises the
possibility that?ηmed could be constrained using correla-
tion function data.We have computed the evolution of the
7
Fig. 4.—The probability P (χ2)of case A and case B models as a function of f ?ηmed .The dark lines correspond to ?ts to the redshift dependent correlation length R 0(z )measured by the 2dF quasar redshift survey (Croom et al.2001b).The gray lines show results for a hypothetical larger future sample whose errors on R 0are reduced by a factor of
√2(light lines).Future surveys will better
constrain the gradient dR 0/dz ,and help discriminate fur-ther between di?erent models of the M bh –M halo relation.Our discussion so far has been independent of the quasar luminosity function.In the next section we discuss how the luminosity function may be used to determine the redshift evolution of the quasar lifetime.
6.the luminosity function and quasar lifetime
In the previous sections we have demonstrated that the evolution of the M bh –M halo relation with redshift may be constrained directly from the quasar correlation function.We have shown that the critical parameter determining the SMBH mass is the halo circular velocity rather than
the halo mass.We reiterate that this result does not rely on the luminosity function of quasars.On the other hand,the number counts of quasars are proportional to the quasar lifetime.Therefore,the quasar lifetime and its evolution with redshift may be determined by com-paring the observed quasar number counts to the SMBH mass function.The latter may be obtained from the Press-Schechter (1976)mass-function of dark-matter halos (with the improvement of Sheth &Tormen 1999)combined with the M bh –M halo relation.
Theoretical models of the quasar luminosity function often associate quasar activity with major mergers (e.g.Kau?mann &Haehnelt 2000;Wyithe &Loeb 2003).A simple model that attributes quasar activity to ma-jor mergers,assumes a M bh –M halo relation that is de-scribed by equation (7),and sets the quasar lifetime equal to the dynamical time of a galactic disk,accurately re-produces the entire optical and X-ray luminosity func-tions of quasars at redshifts between 2and 6(Wyithe &Loeb 2003).At lower redshifts (z 2),this prescription correctly predicts the luminosity function at luminosities below the characteristic break (Boyle et al.2000).In dif-ference to Wyithe &Loeb (2003)we have assumed the quasar activity to take place in the larger SMBH before coalescence of the SMBH binary formed during the merger (Volonteri et al.2002).Figure 5shows the comparison of this model with observations.Speci?cally,we show the ?ducial case AI (which corresponds to the model pre-sented in Wyithe &Loeb 2003)using equation (7)with ?=?SIS and η=1(solid curves).We have shown that case AI describes the observed quasar correlation function (see ?gures 1-2).However as discussed in §5,case-B mod-els for the M bh –M halo relation also provide acceptable ?ts to R 0(z )so long as ? 10?SIS and η～1.Therefore a corresponding luminosity function model was also gener-ated for this case assuming a constant lifetime of t q =107years.We have plotted this model in ?gure 5(dot-dashed lines).
8
Fig.5.—Comparison of the model and observed quasar luminosity functions at various redshifts.The data points at z 4are summarized in Pei(1995),while the light lines show the double power-law?t to the2dF quasar luminosity function(Boyle et al.2000).At z～4.3and z～6.0the data is from Fan et al.(2001a;2001b;2003).The gray regions show the1-σrange of logarithmic slope([?2.25,?2.75]at z～4.3 and[?1.6,?3.1]at z～6),and the vertical bars show the uncertainty in the normalization.The open circles show data points converted from the X-ray luminosity function(Barger et al.2003)of low luminosity quasars using the median quasar spectral energy distribution(Elvis et al.1994).The model luminosity functions shown correspond to cases AI(solid curves)and a model assuming case B evolution with?=?S02,η=1and a constant lifetime of t q=107years(dot-dashed curves).The dashed pairs of vertical lines show the range corresponding to apparent B-magnitudes between18.25and20.85.
We?nd that our?ducial model(case AI;solid lines) with a quasar lifetime that equals the dynamical time of a galactic disk,reproduces the observed luminosity function over a wide range of redshifts and luminosities(see Wyithe &Loeb2003).Our second model(case B,? 10?SIS,η=1,t q=107;dot-dashed lines)also reproduces the ob-served luminosity function at z 4.5.However at z～6 this model underestimates the observed number counts by two orders of magnitude.Case B evolution for the M bh–M halo relation is therefore challenged by the existence of the highest redshift quasars,which would imply a quasar lifetime that exceeds the age of the universe at z～6. Moreover,given the Salpeter(1964)time of～4×107 years,the SMBHs powering these quasars would grow to 25times their initial mass during their lifetime.Provided that quasar activity is trigged by major mergers,the re-quirement that the M bh–M halo relation reproduce the ob-served evolution in quasar clustering,together with the observed evolution in the number counts of quasars there-fore implies case A evolution,and a quasar lifetime that is set by the dynamical time of the host galaxy.We reinforce the important qualitative result that since the evolution of quasar correlations require SMBHs to take a larger fraction of the halo mass at high redshift(case A,see equation7), the observed evolution in the number counts requires a quasar lifetime that is shorter at higher redshifts,scaling approximately as the dynamical time of a dark matter halo [∝(1+z)?3/2].
We point out that the model luminosity functions fail to reproduce the rapid drop in the density of luminous quasars seen at low redshift.This drop is thought to be due to the consumption of cold gas in galaxies by star formation(e.g.Kau?mann&Haehnelt2000)and the in-hibition of accretion onto massive halos at late times(e.g. Scannapieco&Oh2004).However,most of the quasars in the2dF quasar redshift survey have B-magnitudes that lie below the characteristic break in the luminosity func-tion at low redshift(Boyle et al.2000;Croom et al.2001). This can be seen in Figure5where the vertical dashed lines show the luminosities bracketing the apparent mag-nitude range18.25 9 functions of quasars. 7.do bright low-redshift quasars shine near their eddington luminosity? In§4we demonstrated that the2dF quasar sample has a correlation length that is consistent with the local M bh?M halo relation,and that quasars shine near their Eddington luminosity.In addition it was shown that this consistency extends to both bright and faint subsamples of quasars.The brightest2dF quasars(18.1≤B≤19.9)pre-sented by Croom et al.(2002)are mostly brighter than the characteristic break luminosity in the di?erential quasar number counts(e.g.Boyle et al.2000).These bright quasars have a lower abundance than expected from merg-ing halos at z 2(see?gure5).Either the lifetime(or occupation fraction)of bright quasars is lower than ex-pected at z 2or else these quasars shine well below their Eddington limit.Figure2indicates that the slow dependence of R0with B reported by Croom et al.(2002) is consistent with the expected trend if all quasars shine near their Eddington luminosity.This consistency sug-gests that bright quasars are under represented at z 2 because of a reduced quasar lifetime(or a reduced occu-pation fraction)rather than a reduced value ofηduring their brightest phase. 8.discussion In this paper we have demonstrated that the relation-ship between the mass of a SMBH and its host dark-matter halo is the fundamental quantity that determines the clus-tering of quasars.In particular the M bh–M halo relation and its evolution with redshift,may be determined directly from the evolution in the correlation length of quasars,in-dependent of consideration of the quasar luminosity func-tion or assumptions about the quasar lifetime.Beginning with the locally observed M bh–M halo relation,we have shown that the observed correlation length of quasars in the2dF quasar redshift survey is consistent with SMBHs that shine at～10–100%of their Eddington luminosity during their bright quasar episode.Moreover,the evo-lution of the clustering length with redshift is consistent with a SMBH mass whose redshift-independent scaling is with the circular velocity of the host dark matter halo (see equation7).In contrast,it appears that a relation for the SMBH mass whose redshift-independent scaling is with the mass of the host dark matter halo(equation8) would have resulted in too much evolution of the clustering length with redshift. The portion of the2dF quasar survey from which the data used in this study were drawn,contains～104 quasars.Upon completion,the Sloan Digital Sky Sur-vey will have spectra for ten times this number of quasars, spread over a larger redshift range(York et al.2000).This will allow more accurate determination of the correlation length and its evolution,and hence provide more accu-rate constraints the SMBH population.The selection of quasars for the spectroscopic survey of SDSS at z<3is restricted to i?<19.Thus,most of the low redshift SDSS quasars will fall at luminosities that are brighter than the characteristic break in the luminosity function(e.g.Boyle et al.2000).These bright quasars have a lower abundance than expected from the number of halos merging at z 2.The reason for this low abundance may be either that the lifetime(or occupation fraction)of bright quasars is lower than expected at z 2,or alternatively that the fraction of the Eddington limit at which the quasars shine is small. The2dF quasar sample straddles the luminosity function break.We have shown that the similarity in the cluster-ing statistics of sub-samples of quasars having di?erent ranges in luminosity suggest that the lifetime(or occupa-tion fraction)of bright quasars is lower than expected at z 2,but that these quasars also shine near their Edding-ton luminosity.Measurements of the correlation length as a function of quasar luminosity in SDSS can help further distinguish between these two possibilities. As we have shown in a previous paper(Wyithe& Loeb2003),feedback–regulated growth of SMBHs during active quasar phases implies M bh∝v5c,consistent with the inferred relation for galactic halos in the local universe (Ferrarese2002).Assumingη=1as suggested by obser-vations of both low and high-redshift quasars(Floyd2003; Willott,McLure&Jarvis2003),we have shown that only ～7%of the Eddington luminosity output needs to be deposited into the surrounding gas in order to unbind it from the host galaxy over the dynamical time of the sur-rounding galactic disk.The power-law index of5in the M bh–v c relation,is larger than the values of4–4.5inferred from the local relation between M bh and the stellar ve-locity dispersionσ?(Merritt&Ferrarese2001;Tremaine et al.2002);the di?erence originating from the observa-tion that the v c–σ?relation is shallower than linear for stellar bulges embedded in cold dark matter halos(Fer-rarese2002).Feedback–regulated growth also implies that the M bh–v c relation should be independent of redshift,as implied by the slow evolution in the clustering length of quasars. A very simple model can therefore be constructed to de-scribe the correlation length of quasars and its evolution in the2dF survey,as well as the number counts of quasars out to very high redshift(z～6).The model includes four simple assumptions,but no free parameters:(i)the locally observed M bh–M halo relation extends to high red-shifts through equation(7)with the SMBH mass scaling as halo circular velocity to the5-th power;(ii)SMBHs shine near their Eddington luminosity with a universal spectrum (Elvis et al.1994)during luminous quasar episodes;(iii) quasar episodes are associated with major galaxy mergers; and(iv)the quasar lifetime is set by the dynamical time of the host galaxy. The assumption of a SMBH mass that scales with halo circular velocity independently of redshift is supported by the observations of Shields et al.(2003)that there is no evolution in the M bh–σ?relation out to z～3.The as-sumption that quasars shine near their Eddington limit is supported by observations of high and low redshift quasars (Floyd2003;Willott,McLure&Jarvis2003).Overall,the sample of available data on the clustering properties and the number counts of quasars is most readily explained by a quasar lifetime that is set by the dynamical time of the host galaxy rather than by the Salpeter(1964)e-folding time for the growth of its mass. This work was supported in part by NASA grant NAG 5-13292,and by NSF grants AST-0071019,AST-0204514 10 (for A.L.).JSBW wishes to thank Princeton University Observatory for their hospitality during the course of this work. 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Write out the following countries’ main language. II. Translate the following expressions. 1. tour guide 2. shop assistant 3. apply for 4. oral English 5. keep up 6. 记日记 7. 听起来不错 8. 拜访朋友 9. 把某人介绍给某人 10. 害怕 III. Complete the following sentences with the proper form of the given phrases. used to keep it up apply for it seemed that agree with be over give it a try try to 1. Do you ________________________me? 2. I think _______________________________ and I will find it a lot of fun. 3. When class _____________________, we talked about where to go for dinner. 4. __________________they couldn’t understand each. 5. I ____________________ a job in a big company. 6. He found it very difficult to _____________ every day. 7. My English ________ be poor but now I am good at it. 8. In English class, everyone _____________speak in English. IV. Choose the best answers. ( ) 1. In the USA, most people speak _________. A. America B. English C. England D. American ( ) 2. _______ has the largest number of speakers. A. China B. Chinese C. French D. English ( ) 3. Is English _______ for the job? A. must B. need C. a must D. a need ( ) 4. English keeps _________ all the time. A. change B. changing C. to change D. changed ( ) 5. He spent a lot of time ________ English these days. A. study B. to study C. is studying D. studying ( ) 6. In some Western countries, people try ______a black cat. A. to avoid B. avoid C. avoiding D. avoided Part II Oral practice I. Match the questions with the answers. 1. What is he? A. He is a tour guide. 2. Where is he from? B. He speaks English. 2014 Final Exam Study Guide for American Literature Class Plan of Final Exam 1.Best Choice Question 10% 2.True or False Question 10% 3.Definition 10% 4.Give Brief Answers to Questions 30% 5.Critical Comments 40% American Literature Review Poe’s Poetic Ideas; Major Ideas in Emerson’s “Nature”; Whitman’s Style; Formal Features of Dickinson’s Poetry; Analysis of “Miniver Cheevy” by Edwin Arlington Robinson; Comment on “Stopping by Woods on a Snowy Evening” by Robert Frost; Naturalistic reading of Sister Carrie by Theodore Dreiser; The Theme and Techniques in Eliot’s “The Waste Land”; Theme and Technique in The Great Gatsby by Fitzgerald; Comment on Hemingway’s style and theme in A Farewell to Arms; Analysis of “Dry September” by William Faulkner; Literary terms: Transcendentalism American Naturalism The Lost Generation The Jazz Age Free Verse The Iceberg Analogy Chapter III WEE QUESTION OF FORTUNE--FOUR-FIFTY A WEEK Once across the river and into the wholesale district, she glanced about her for some likely door at which to apply. As she contemplated the wide windows and imposing signs, she became conscious of being gazed upon and understood for what she was--a wage-seeker. She had never done this thing before, and lacked courage. To avoid a certain indefinable shame she felt at being caught spying about for a position, she quickened her steps and assumed an air of indifference supposedly common to one upon an errand. In this way she passed many manufacturing and wholesale houses without once glancing in. At last, after several blocks of walking, she felt that this would not do, and began to look about again, though without relaxing her pace. A little way on she saw a great door which, for some reason, attracted her attention. It was ornamented by a small brass sign, and seemed to be the entrance to a vast hive of six or seven floors. "Perhaps," she thought, "They may want some one," and crossed over to enter. When she came within a score of feet of the desired goal, she saw through the window a young man in a grey checked suit. That he had anything to do with the concern, she could not tell, but because he happened to be looking in her direction her weakening heart misgave her and she hurried by, too overcome with shame to enter. Over the way stood a great six- story structure, labelled Storm and King, which she viewed with rising hope. It was a wholesale dry goods concern and employed women. She could see them moving about now and then upon the upper floors. This place she decided to enter, no matter what. She crossed over and walked directly toward the entrance. As she did so, two men came out and paused in the door. A telegraph messenger in blue dashed past her and up the few steps that led to the entrance and disappeared. Several pedestrians out of the hurrying throng which filled the sidewalks passed about her as she paused, hesitating. She looked helplessly around, and then, seeing herself observed, retreated. It was too difficult a task. She could not go past them. So severe a defeat told sadly upon her nerves. Her feet carried her mechanically forward, every foot of her progress being a satisfactory portion of a flight which she gladly made. Block after block passed by. Upon streetlamps at the various corners she read names such as Madison, Monroe, La Salle, Clark, Dearborn, State, and still she went, her feet beginning to tire upon the broad stone flagging. She was pleased in part that the streets were bright and clean. The morning sun, shining down with steadily increasing warmth, made the shady side of the streets pleasantly cool. She looked at the blue sky overhead with more realisation of its charm than had ever come to her before. Her cowardice began to trouble her in a way. She turned back, resolving to hunt up Storm and King and enter. On the way, she encountered a great wholesale shoe company, through the broad plate windows of which she saw an enclosed executive 目的。笔者曾进行了这方面的一个实验；对乐理、视唱程度相当的Ａ、Ｂ两个班，在讲小调式时，Ａ班此时视唱只唱小调式作品，边唱边分析；Ｂ班只在乐理课上选一些典型作品作简单分析，而视唱课对小调作品概不介绍，结果发现Ａ班大部分同学对小调式的特点掌握清晰、分析作品透彻，而Ｂ班多数同学对小调式作品的分析仍感糊涂。 （二）乐理和视唱由同一老师任教，选用乐理与视唱进度相当、联系密切的教材。 两门课由同一老师任教，这样就使老师对两门课的进度有更好的把握，从而做到在教学内容上的衔接，使乐理教学与视唱教学融为一体。现在有些院校已开始了这方面的尝试，如河南的黄河科技学院，商丘师院等。据笔者了解，由同一个老师任教班级学生的乐理视唱学习效果明显好于非同一教师任教的班级。 教材的选择对教学影响极大，原来的视唱教材极少有乐理内容，而乐理教材中的谱例也不多。目前新的教材已改变了这种状况，现在视唱教材中有了很好的理论知识讲授，如许敬行、孙虹编著，高教出版社出版的《视唱练习》。乐理教材有了更多的谱例，如贾方爵编著、 西南师大出版社出版的《基本乐理》。选用此种联系密切的教材， 教师在教学的过程中更易做到理论联系实际，学生在自学时也更易理解。 （三）加强乐理、视唱教学与其他科目的横向联系 音乐中的许多课程，如欣赏、民族民间音乐、合唱、音乐史等的学习对学生综合专业素质的提高有很大帮助，对它们的学习与对乐理和视唱的学习又能达到互相促进的目的。在乐理学教学中，学生最易迷惑的就是调式调性的判断，而进行调式判断时首先要靠听觉分辨作品的五声性和西方性。但如何能够分辨其是五声性作品还是西方调式体系作品，靠的是学生对音乐的基本鉴赏力。这就要求学生平时在欣赏课上要认真去听、去辨别，而欣赏老师也应该对不同体裁的音乐作品进行详细的讲解，并引导学生去辨别。经过这样长期的训练，学生对于不同地域、不同风格的音乐作品都有了了解和掌握，辨别调式的问题自然迎刃而解。同样，民族民间课程的学习对于学生了解和掌握各民族的音乐风格、特点起重要作用。经过同学们对民歌、戏曲等曲型片断的实际训练，在视唱这些有特点的作品时，其音乐风格的把握就会更好一些，因律制原因产生的音准问题也会大大减少，学生对民族风格的视唱会唱得更有味，把握得更准确。在这方面，如果乐理和视唱课需要，可会同其他科目的教师对教学进度、教学内容作一些适当的调整，使之与乐理、视唱教学相适应。如有必要，也可请这方面的专家，就某一问题进行一次讲座，以加深同学们对某些问题的理解。教师亦可有目的地向学生介绍一些此方面的书籍，让学生去阅读；介绍一些音响资料，让学生有目的地听，从而拓宽学生的知识面，进而更好地学习和掌握乐理和视唱。 总之，视唱与乐理相结合并密切联系相关科目的教学方法，不仅可以使学生增加对音乐理论的感性认识，加强视唱时的理论指导，更增加了视唱课的趣味性，使乐理不再枯燥，视唱课不再单调。 当然，加强乐理、视唱与其他科目教学的联系并不是说这些课程什么地方都可以互融。有些乐理知识如音律很难让学生唱出来。但这并不能否认加强视唱、乐理与其他学科教学联系的必要性。 作者简介：刘建坤，商丘师范学院音乐系教师。 一、美国自然主义的产生 内战之后，美国处于一段相对和平的时期，资本主义经济蓬勃发展。然而，在经济发展的背后，人们却普遍产生了一种悲观情绪，传统的理想主义被抛弃，宇宙的在规律性和机械性中蕴涵的漠然性使其变成了人类的敌人，至少已经不是人类慈祥的朋友。斯蒂芬?克莱恩（Ｓｔｅｐｈｅｎ Ｃｒａｎｅ（１８７１－１９００））的一首小诗Ｇｏｄ ｉｓ ｃｏｌｄ［１］ 便生动地反映了这种状况： 一个人对宇宙说：／“阁下，我存在的！”／“不过，”传来宇宙的回答，／“你的存在虽是事实，却／并没有使我产生义务感。” 对这一思潮起决定性作用的是达尔文的进化论（Ｔｈｅｏｒｙ ｏｆ Ｅｖｏｌｕｔｉｏｎ）。达尔文认为：影响生物进化的因素有三种，即：自然选择、性的选择及个体有生之期获得特性的遗传。进化论的诞生，是对传统神学及理想主义神学的全盘否定，它取消了上帝设计师和创造者的地位，进而强调人类产生过程的机械性，以及人类进化过程的因果循环性。受其影响，悲观、忧郁的新自然哲学应运而生。新自然哲学指出，自然是一座对人类遭遇无动于衷的庞大机器，人类在自然中必然要为生存而相互竞争，而且，部分人的毁灭是人类进步中不可避免的现象。 悲观的新自然哲学在文学中的反映就是产生悲观宿命的自然主义文学。英国哲学家赫伯特?斯宾塞（ＨｅｒｂｅｒｔＳｐｅｎｃｅｒ）的“社会达尔文主义” （Ｓｏｃｉａｌ Ｄａｒｗｉｎｉｓｍ）以及美国内战后的社会状况，对自然主义在美国的产生和发展起了极大的作用。当时的主要作家往往把人置于庞大的自然和社会背景中，从而显示其渺小、脆弱以及无可奈何。 ＂生存＂是人类活动的最高目标，道德规范对于实际生活已经毫无意义。 在美国自然主义文学中，最为突出的代表是西奥多?德莱塞。 二、德莱塞在美国文学史上的地位 西奥多?德莱塞 ［Ｔｈｅｏｄｏｒｅ Ｄｒｅｉｓｅｒ （１８７１－１９４５）］是美国现代小说的先驱和代表作家，被认为是同海明威、福《嘉莉妹妹》是美国自然主义文学大师西奥多?德莱塞的处女作和成名作。自然主义在书中 主要表现为作者对失败者的深刻同情。 《嘉莉妹妹》中 自然主义赏析 文／姚晓鸣 编辑：冯彬彬 69 美与时代 ２００３．１１下 Have a Positive Attitude in Life After reading this story, I really shocked by what the man had done. He is a murderer who cruelly killed a black cat loved by his wife, then brutishly murdered his wife instead of his second cat, and hid her carcass in the wall. I was confused with the behavior of the man who did all that damn things. I think this man is abnormal, and it is terrible to live with such a person who has something wrong with his mind. I just wonder how can once a righteous and kind man turned out to be so merciless and why the author wanted to show the ugly aspect of human being. After doing some reading about the author, I found the main character in the story is almost the duplicate of author himself; he expressed his own feelings and thoughts through writing. The author lost his parents when he was very young, and he lacked of warm and parental care and sense of security during childhood. What’s more, there’s nobody for him to confess his sufferings and unhappiness, what he could do is to immerse him in alcohol to escape from the anguish. So the reasons were clear for the conversion of the man’s personality. Firstly, is the outside environment: He was always haunting in the bar and was alcoholic, which shows that his life is aimless and disordered. As a result, he was under control of alcohol. Though the surroundings are vital to one’s character development, but it’s not all. In the story, every time when the man did evil things, he blamed them on the alcohol and others. In my perspective, it was just his excuse to avoid the responsibility. As a human, you can’t give way to the madness; instead, you can have strong will to overcome it. Secondly, plenty of negative emotions such as jealousy, violence, irritation make the man envies to the black cat that was loved by his wife and he is violent and angry to the cat in that the cat was so close to the man that the man felt troublesome. When you have such complicated psychology, the most effective and useful way is to talk with your friends or relatives, but not bury deeply in heart, which will later result in vicious cycle. In a word, both inside and outside reasons lead the man to the depth of sin. He seemed accustomed to perform this crime that he had not felt shameful. So after killing the first cat, he acquired some kinds of satisfaction, which later made him tend to abuse things that he didn’t like and eventually killed his wife. So I draw a conclusion from this story: you should find ways to release your dissatisfactions encountered in lif e; don’t find any excuse s to get you away from punishing or it will lead you to crime abyss. Though environment is influential to one’s mood, you should keep a positive and opportunistic attitude toward life. Only in this way, you can drive all the devils away and lead a cozy and comfortable life. The Black Cat Edgar Allan Poe 1FOR the most wild, yet most homely narrative which I am about to pen, I neither expect nor solicit belief. Mad indeed would I be to expect it, in a case where my very senses reject their own evidence. Yet, mad am I not -- and very surely do I not dream. But to-morrow I die, and to-day I would unburthen my soul. My immediate purpose is to place before the world, plainly, succinctly, and without comment, a series of mere household events. In their consequences, these events have terrified -- have tortured -- have destroyed me. Yet I will not attempt to expound them. To me, they have presented little but Horror -- to many they will seem less terrible than barroques. Hereafter, perhaps, some intellect may be found which will reduce my phantasm to the common-place -- some intellect more calm, more logical, and far less excitable than my own, which will perceive, in the circumstances I detail with awe, nothing more than an ordinary succession of very natural causes and effects. 2From my infancy I was noted for the docility and humanity of my disposition. My tenderness of heart was even so conspicuous as to make me the jest of my companions. I was especially fond of animals, and was indulged by my parents with a great variety of pets. With these I spent most of my time, and never was so happy as when feeding and caressing them. This peculiarity of character grew with my growth, and, in my manhood, I derived from it one of my principal sources of pleasure. To those who have cherished an affection for a faithful and sagacious dog, I need hardly be at the trouble of explaining the nature or the intensity of the gratification thus derivable. There is something in the unselfish and self- 黑猫 埃德加·爱伦·坡homely adj.平凡的；朴素的 unburthen vt. 使……安生succinctly adv.简洁地 expound vt.解释；阐述baroque n.巴洛克作品，这里指「奇谈」phantasm n.幻象；幻觉 succession n.继承顺序，自然演替 docility n.温驯 humanity n.仁爱；人道disposition n.性情；性格；气质 conspicuous adj.显眼的jest n.笑话；笑柄 caress vt.爱抚；抚摸sagacious adj.聪明的；精 明的 gratification n.满足；满意derivable adj.可引出的；可诱导的 - 1 - s i s t e r c a r r i e赏析自动保 存的 The latest revision on November 22, 2020 《Sister Carrie》 The author of the book is Theodore Dreiser, a famous realistic writer in Amaican literature history .Realism follows the rule of nature “survival of fittest”.《Sister Carrie》 is a representative of realism which describes a poor countryside girl′s life c hange after her arrival to ,cruel reality makes Carrie feel lonely and she cohabited with Drouet,a young playboy ,Drouet offered her a easier life .Later,she married with Hrustwood ,who had didn′t have a better life in New York. after they spent the money Hurstwood stole from his ex-wife .At the end of the book, Hrustwood died in a shabby little hotel,and Carrie became a famous star and be in high social classes. Lost the job in shoe-making factory is just the turning point in Carrie′s life ,the turning point of her final success and survie she had to rely on someone .On the surface, writer is describing Carrie′s miserable suffering telling readers that is always very hard for woman .However ,to explore the deep meaning .Carrie is just a representative of the people from working-class who are oppressed by the capitalist .Dreiser shows sympathy to them and reveals the social ′s success is driven by dream and wants to change her destiny she is eager to climb into the high social matter how pimping you are ,dream is important and essential to future success because dream or ambution has the power to drive you forward. 《Sister Carrie》 The author of the book is Theodore Dreiser, a famous realistic writer in Amaican literature history .Realism follows the rule of nature “survival of fittest”.《Sister Carrie》is a representative of realism which describes a poor countryside girl′s life change after her arrival to Chicago.However ,cruel reality makes Carrie feel lonely and unhappy.Then she cohabited with Drouet,a young playboy ,Drouet offered her a easier life .Later,she married with Hrustwood ,who had married.They didn′t have a better life in New York. after they spent the money Hurstwood stole from his ex-wife .At the end of the book, Hrustwood died in a shabby little hotel,and Carrie became a famous star and be in high social classes. Lost the job in shoe-making factory is just the turning point in Carrie′s life ,the turning point of her final success and tragedy.To survie she had to rely on someone .On the surface, writer is describing Carrie′s miserable suffering telling readers that is always very hard for woman .However ,to explore the deep meaning .Carrie is just a representative of the people from working-class who are oppressed by the capitalist .Dreiser shows sympathy to them and reveals the social contradictions.Carrie′s success is driven by dream and money.She wants to change her destiny she is eager to climb into the high social class.No matter how pimping you are ,dream is important and essential to future success because dream or ambution has the power to drive you forward. It is right to pursue for material life , but not everything,In fact it is never wrong to pursue for high standard and high class life. The Black Cat ----Edgar Allan Poe Array FOR the most wild, yet most homely narrative which I am about to pen, I neither expect nor solicit belief. Mad indeed would I be to expect it, in a case where my very senses reject their own evidence. Yet, mad am I not -- and very surely do I not dream. But to-morrow I die, and to-day I would unbur d en my soul. My immediate purpose is to place before the world, plainly, succinctly, and without comment, a series of mere household events. In their consequences, these events have terrified -- have tortured -- have destroyed me. Yet I will not attempt to expound them. To me, they have presented little but Horror -- to many they will seem less terrible than baroques. Hereafter, perhaps, some intellect may be found which will reduce my phantasm to the common-place -- some intellect more calm, more logical, and far less excitable than my own, which will perceive, in the circumstances I detail with awe, nothing more than an ordinary succession of very natural causes and effects. From my infancy I was noted for the docility and humanity of my disposition. My tenderness of heart was even so conspicuous as to make me the jest of my companions. I was especially fond of animals, and was indulged by my parents with a great variety of pets. With these I spent most of my time, and never was so happy as when feeding and caress ing them. This peculiarity of character grew with my growth, and, in my manhood, I derived from it one of my principal sources of pleasure. To those who have cherished an affection for a faithful and sagacious dog, I need hardly be at the trouble of explaining the nature or the intensity of the gratification thus derivable. There is something in the unselfish and self-sacrificing love of a brute, which goes directly to the heart of him who has had frequent occasion to test the paltry friendship and gossamer fidelity of mere Man. I married early, and was happy to find in my wife a disposition not uncongenial with my own. Observing my partiality for domestic pets, she lost no opportunity of procuring those of the most agreeable kind. We had birds, gold-fish, a fine dog, rabbits, a small monkey, and a cat.英美文学专业开题报告
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中英-the black cat
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