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If ambipolar diffusion is included in our model. (hen (he ambipolar diffusion process is more important in the central part of a core where the degree of ionization is lower than that of the outer part of the core. | If ambipolar diffusion is included in our model, then the ambipolar diffusion process is more important in the central part of a core where the degree of ionization is lower than that of the outer part of the core. |
Since our svnthesized line profiles are more sensitive to the conditions at the outer laver (see section 3). our main results are not likely to be significantly alfected by: ambipolar diffusion. | Since our synthesized line profiles are more sensitive to the conditions at the outer layer (see section 3), our main results are not likely to be significantly affected by ambipolar diffusion. |
We also take the isothermal approximation which enables us not to solve (he energy equation with cooling and heating processes. | We also take the isothermal approximation which enables us not to solve the energy equation with cooling and heating processes. |
To take into account the cooling aud heating processes of gas realistically entails a heavy calculation because molecular cooling lines are usually optically thick. | To take into account the cooling and heating processes of gas realistically entails a heavy calculation because molecular cooling lines are usually optically thick. |
When line profiles are. however. svulhesizecl we calculate (wo cases wilh a constant temperature and temperature variations of gas and dust inside (he core (see section 3). | When line profiles are, however, synthesized, we calculate two cases with a constant temperature and temperature variations of gas and dust inside the core (see section 3). |
M We present the latter case only because the line features from both cases are not much different [rom each other. | We present the latter case only because the line features from both cases are not much different from each other. |
In order to calculate the chemical evolution in the core picked-up from the dynamical simulation as described in the previous subsection. we adopt the evolutionary chemical model developed by Lee et al. ( | In order to calculate the chemical evolution in the core picked-up from the dynamical simulation as described in the previous subsection, we adopt the evolutionary chemical model developed by Lee et al. ( |
2004). in particular. the model before collapse begins. | 2004), in particular, the model before collapse begins. |
In (he prestellar phase where this paper focuses on. the model calculates the chemical evolution al each grid point as density grows with Gime. | In the prestellar phase where this paper focuses on, the model calculates the chemical evolution at each grid point as density grows with time. |
The chemical network in the model has been updated to include more recent results on (he binding energy of No (Obbere et al. | The chemical network in the model has been updated to include more recent results on the binding energy of $_2$ (Öbberg et al. |
2005) and | 2005) and |
Long and frequent ground-based monitoring at optical and near-infrared (NIR) wavelengths of Gamma-Ray Burst (GRB) counterparts Is necessary to constrain the emission models and disentangle the contribution of the GRB host galaxy and of a possible underlying supernova (SN) explosion simultaneous with or shortly preceding the GRB (e.g.. McFadyen Woosley 1999; Vietri Stella 1998). | Long and frequent ground-based monitoring at optical and near-infrared (NIR) wavelengths of Gamma-Ray Burst (GRB) counterparts is necessary to constrain the emission models and disentangle the contribution of the GRB host galaxy and of a possible underlying supernova (SN) explosion simultaneous with or shortly preceding the GRB (e.g., McFadyen Woosley 1999; Vietri Stella 1998). |
The connection of GRBs with Se was first suggested by the close angular and temporal proximity of GRB980425 and SN1998bw (Galama et al. | The connection of GRBs with SNe was first suggested by the close angular and temporal proximity of GRB980425 and SN1998bw (Galama et al. |
1998) and. based on that event. this association was systematically explored (e.g.. Castro-Tirado Gorosabel 1999: Bloom et al. | 1998) and, based on that event, this association was systematically explored (e.g., Castro-Tirado Gorosabel 1999; Bloom et al. |
1999: Galama et al. | 1999: Galama et al. |
2000: Reichart 2001: Garnavich et al. | 2000; Reichart 2001; Garnavich et al. |
2003: Greiner at al. | 2003; Greiner at al. |
2003: Price et al. | 2003; Price et al. |
2003a; Masetti et al. | 2003a; Masetti et al. |
2003). | 2003). |
The recent direct spectroscopic detections of SNe 20021t (Della Valle et al. | The recent direct spectroscopic detections of SNe 2002lt (Della Valle et al. |
2003). 2003dh (Stanek et al. | 2003), 2003dh (Stanek et al. |
2003: Hjorth et al. | 2003; Hjorth et al. |
2003) and 2003Iw (Malesani et al. | 2003) and 2003lw (Malesani et al. |
2004) associated with GRBs 021211. 030329 and 031203. respectively. firmly established that at least a fraction of GRBs is connected with core-collapse SNe. | 2004) associated with GRBs 021211, 030329 and 031203, respectively, firmly established that at least a fraction of GRBs is connected with core-collapse SNe. |
However. given the high redshifts (22 1) of most GRBs. SNe associated with them are difficult to. study spectroscopically. and only good observational coverage of the optical light curve can reveal the presence of an underlying S (see Zeh et al. | However, given the high redshifts $z \ga 1$ ) of most GRBs, SNe associated with them are difficult to study spectroscopically, and only good observational coverage of the optical light curve can reveal the presence of an underlying SN (see Zeh et al. |
2004: Dar De Rujjula 2003). | 2004; Dar De Rújjula 2003). |
In addition. due to the possible dust obscuration near the source. NIR data may play an even more important role than optical data (e.g.. Palazzi et al. | In addition, due to the possible dust obscuration near the source, NIR data may play an even more important role than optical data (e.g., Palazzi et al. |
1998; Gorosabel et al. | 1998; Gorosabel et al. |
1998; Pian et al. | 1998; Pian et al. |
1998: Vreeswi]k et al. | 1998; Vreeswijk et al. |
1999; Castro-Tirado et al. | 1999; Castro-Tirado et al. |
1999; Masetti et al. | 1999; Masetti et al. |
2000: Klose et al. | 2000; Klose et al. |
2000: Rhoads Fruchter 2001: Sokolov 2001: Le | 2000; Rhoads Fruchter 2001; Sokolov 2001; Le |
evolves with redshift, with higher mean luminosity at higher redshifts. | evolves with redshift, with higher mean luminosity at higher redshifts. |
The scatter in the luminosity distribution of central AGN increases toward lower redshift, indicating that the luminosities for a given halo mass are more uniform at high redshift than at low redshift. | The scatter in the luminosity distribution of central AGN increases toward lower redshift, indicating that the luminosities for a given halo mass are more uniform at high redshift than at low redshift. |
As a result of this, at low redshifts AGN samples based on luminosity will have a wider range of host halo masses and hence clustering will depend weakly on luminosity. | As a result of this, at low redshifts AGN samples based on luminosity will have a wider range of host halo masses and hence clustering will depend weakly on luminosity. |
However at high redshifts luminosity dependent clustering will be more prominent. | However at high redshifts luminosity dependent clustering will be more prominent. |
Similar redshift evolution of luminosity dependent clustering has been observed with SDSS quasars (??).. | Similar redshift evolution of luminosity dependent clustering has been observed with SDSS quasars \citep{shenetal09, shenetal07}. |
We note that the clustering properties of AGN will be largely related to their host halo mass. | We note that the clustering properties of AGN will be largely related to their host halo mass. |
However we find that accretion rates and hence luminosity depends strongly on local properties particularly at low redshifts (e.g., feedback discussed in 83.1) which erases some of the dependences of bolometric luminosity on halo mass and hence the luminosity dependent clustering at low redshifts. | However we find that accretion rates and hence luminosity depends strongly on local properties particularly at low redshifts (e.g., feedback discussed in 3.1) which erases some of the dependences of bolometric luminosity on halo mass and hence the luminosity dependent clustering at low redshifts. |
This will not be the case in black hole mass selected sample since black hole mass is more tightly correlated with halo mass regardless of redshifts (?).. | This will not be the case in black hole mass selected sample since black hole mass is more tightly correlated with halo mass regardless of redshifts \citep{c&d08}. |
The shape of the satellite luminosity function cannot be identified definitively due to lack of statistics. | The shape of the satellite luminosity function cannot be identified definitively due to lack of statistics. |
We note that the lower end of the satellite luminosity function is affected by the resolution of the simulation and the seed black hole mass, which is manifested in the cut-off of the luminosity function. | We note that the lower end of the satellite luminosity function is affected by the resolution of the simulation and the seed black hole mass, which is manifested in the cut-off of the luminosity function. |
The satellite distribution also shows some variation with halo mass. | The satellite distribution also shows some variation with halo mass. |
For a given halo mass the peak of the satellite distribution tends to be at a lower luminosity than the central AGN. | For a given halo mass the peak of the satellite distribution tends to be at a lower luminosity than the central AGN. |
'To examine the effect of the central AGN on the number distribution of satellites within a halo, we compare the conditional luminosity functions of satellite AGN for halos differing in central AGN luminosities. | To examine the effect of the central AGN on the number distribution of satellites within a halo, we compare the conditional luminosity functions of satellite AGN for halos differing in central AGN luminosities. |
This is defined as the conditional distribution of satellite AGN luminosities for a fixed Mnhaio and μοι. | This is defined as the conditional distribution of satellite AGN luminosities for a fixed $M_{\rm halo}$ and $L_{{\rm Bol}}^{{\rm cen}}$. |
We used a large halo mass bin to increase the statistics of our sample. | We used a large halo mass bin to increase the statistics of our sample. |
We note that there is a correlation between central AGN luminosity and halo mass. | We note that there is a correlation between central AGN luminosity and halo mass. |
To eliminate the effect of mass-dependent central AGN luminosity, we divide halos according to the central AGN luminosity as follows. | To eliminate the effect of mass-dependent central AGN luminosity, we divide halos according to the central AGN luminosity as follows. |
For each redshift, at each halo mass, we tag halos as ‘high Lcen' (‘low Lcen’) if their central AGN luminosities are above (below) the mean central AGN luminosity at that mass (Fig.5). | For each redshift, at each halo mass, we tag halos as `high Lcen' (`low Lcen') if their central AGN luminosities are above (below) the mean central AGN luminosity at that mass (Fig.5). |
Then the conditional luminosity functions of satellite AGN are computed for the | Then the conditional luminosity functions of satellite AGN are computed for the |
These are the positions of the galaxy and the source plus the constant Zzj. the cllipticity e and the exponent v for the bulge as well as the bar mass normalisation 5e. the axis b and the exponent A for the bar. | These are the positions of the galaxy and the source plus the constant $E_0$, the ellipticity $e$ and the exponent $\nu$ for the bulge as well as the bar mass normalisation $\kappa_{\rm c}$, the semi-minor axis $b$ and the exponent $\lambda$ for the bar. |
Εις number can be reduced by two if the observed ellipticity of the bulge and. only fixed values for A are used. | This number can be reduced by two if the observed ellipticity of the bulge and only fixed values for $\lambda$ are used. |
For the length of the semi-major axis of the bar we used the observed: value. of (taken from the figures in Yee 1988 or Irwin 1989). | For the length of the semi-major axis of the bar we used the observed value of (taken from the figures in Yee 1988 or Irwin 1989). |
Phe lens elfect is insensitive to the precise value of @ because e is much larger than the radius of the ring of images (zz 1 arcsec). | The lens effect is insensitive to the precise value of $a$ because $a$ is much larger than the radius of the ring of images $\approx$ 1 arcsec). |
The length of the semi-minor axis must. however. remain a free parameter of the model since it is comparable to this radius. but not known well enougharcsec.. sce section 3)). | The length of the semi-minor axis must, however, remain a free parameter of the model since it is comparable to this radius, but not known well enough, see section \ref
{PropertiesOfTheBar}) ). |
There are. ten observational constraints the svsteni imposes upon theoretical models. | There are ten observational constraints the system imposes upon theoretical models. |
These are the coordinates of the four observed. quasar images and the galaxy centre. | These are the coordinates of the four observed quasar images and the galaxy centre. |
The positions for the images and galaxy centre were aken from Crane (1991). | The positions for the images and galaxy centre were taken from Crane \shortcite
{Crane1991}. |
. These positions have been determined from observations and have quoted measurement. errors of 07005. | These positions have been determined from observations and have quoted measurement errors of $0\farcs 005$. |
In. general. he ratios of the fluxes of the clifferent images of a eravitational lens also provide goocl constraints for a model. | In general, the ratios of the fluxes of the different images of a gravitational lens also provide good constraints for a model. |
Unfortunately. in the case of Q2237|0305 the lighteurves rom Corrigan (1991) or Ostensen (1996) clearly show that all optical image fluxes are subject to lux variations due to microlensing of the quasar light from the stars in the lensing galaxy. | Unfortunately, in the case of Q2237+0305 the lightcurves from Corrigan \shortcite {Corrigan1991} or stensen \shortcite {Ostensen1996} clearly show that all optical image fluxes are subject to flux variations due to microlensing of the quasar light from the stars in the lensing galaxy. |
In addition. the light from the quasar is non-uniformiy dust reddened. during the passage through the galaxy. | In addition, the light from the quasar is non-uniformly dust reddened during the passage through the galaxy. |
The Duxes were. therefore. neglecd in the modelling procedure. | The fluxes were, therefore, neglected in the modelling procedure. |
We will. however. compare the model. predictions with the recently. measured. radio. [ux densities by Falco (1996). | We will, however, compare the model predictions with the recently measured radio flux densities by Falco \shortcite
{Falco1996}. |
Let 04. 8, be the positions on the sky the model predicts for quasar iniages and the galaxy centre and. Oi, Oy. the observed positions with their positional uncertaintles 0. m. | Let $\vec{\btheta}_{k}$ , $\vec{\btheta}_{g}$ be the positions on the sky the model predicts for quasar images and the galaxy centre and $\vec{\btheta}_{ko}$, $\vec{\btheta}_{go}$ the observed positions with their positional uncertainties $\sigma_{k}$, $\sigma_{g}$. |
‘To find the best fit model. the expression (Wambseanss&Paczviiski1994) was minimised through variation of the model parameters using a multidimensional minimisation routine (direction set. or downhill. simplex methods according to Press 1992). | To find the best fit model, the expression \cite {Wambsganss1994} was minimised through variation of the model parameters using a multidimensional minimisation routine (direction set or downhill simplex methods according to Press 1992). |
In order to find an estimator for the separations 6, between modelled and observed images for the first term on the right hand. side of Equation (5)). we used the method by Ixochanek (1991): the separations between an optimally weighted source position ancl the positions in the source plane where the observed image positions are mapped to by a given lens model are propagated back into the lens plane. | In order to find an estimator for the separations $\vec{\btheta}_{k}-
\vec {\btheta}_{ko}$ between modelled and observed images for the first term on the right hand side of Equation \ref {ChisquareWP}) ), we used the method by Kochanek \shortcite {Kochanek1991}; the separations between an optimally weighted source position and the positions in the source plane where the observed image positions are mapped to by a given lens model are propagated back into the lens plane. |
For a nearly circularly svmmoetric lens with a source almost in the origin. it [follows [from Newton's theorem in two climensions (Foltzefa£.1992:Schramm1994). that the mass inside the circle. of images is approximately given. by. the separation 48 of the images at opposite ends of the cross via (see for example Naravan Bartelmann 1996). | For a nearly circularly symmetric lens with a source almost in the origin, it follows from Newton's theorem in two dimensions \cite
{Foltz1992,Schramm1994} that the mass inside the circle of images is approximately given by the separation $\Delta \theta$ of the images at opposite ends of the cross via (see for example Narayan Bartelmann 1996). |
The galaxy 2237|0305 is situated relatively close to us at an angular size distanceCpe. so that {λοςzx1. | The galaxy 2237+0305 is situated relatively close to us at an angular size distance, so that $D_{\rm
ds}/D_{\rm s}\approx 1$. |
The separations of the quasar images are aresec. so that we get. ALz1.5LOMbetMee. | The separations of the quasar images are arcsec, so that we get $M\approx1.5\times10^{10}\,{\rm h}_{75}^{-1}{\cal M}_{\sun}$. |
Dhis value was also found in previous models for this svstem (Rix 1992: 0.010310hA4... Wambseanss Paezviisski 1904: 148+0.001ohA4 2). | This value was also found in previous models for this system (Rix 1992: $1.44\pm 0.03\times 10^{10} {\rm h}_{75}^{-1} {\cal
M}_{\sun}$ , Wambsganss Paczyńsski 1994: $1.48\pm 0.01\times
10^{10} {\rm h}_{75}^{-1} {\cal M}_{\sun}$ ). |
The other value theoretical mocels for 61 | The other value theoretical models for 2237+0305 agreed on was the resulting shear direction of $\approx 67\degr$ . |
1n our barred. lens model. the bulge acts as the main lensing mass and the bar às a perturbation: for a given ellipticitv e or exponent ο. the bulge parameter fy and hence the bulge mass do not change very much for different A-bar models. | In our barred lens model, the bulge acts as the main lensing mass and the bar as a perturbation; for a given ellipticity $e$ or exponent $\nu$, the bulge parameter $E_0$ and hence the bulge mass do not change very much for different $\lambda$ -bar models. |
In fact. experiments with different bar masses as in figure 2. showed that for similar masses of bulge and bar inside the quasar images the cruciform image symmetry gets skewed. | In fact, experiments with different bar masses as in figure \ref {StrongBar} showed that for similar masses of bulge and bar inside the quasar images the cruciform image symmetry gets skewed. |
Aloclels with a strong bar thus cannot reproduce a svmnmetric image geometry as in 223710305. | Models with a strong bar thus cannot reproduce a symmetric image geometry as in Q2237+0305. |
In order to explore the elfect of A on the mocels. we used fixed. values À—0.5. 1 and 2. | In order to explore the effect of $\lambda$ on the models, we used fixed values $\lambda=0.5$, $1$ and $2$. |
Besides [£jand A. the parameter space of e. $6. od and b had to be examined. | Besides $E_0$and $\lambda$, the parameter space of $e$, $\nu$, $\kappa_{\rm c}$ and $b$ had to be examined. |
We first scanned the parameter space of e and v while leaving &s« and b as free parameters. | We first scanned the parameter space of $e$ and $\nu$ while leaving $\kappa_{\rm c}$ and $b$ as free parameters. |
In figure 3. à contour plot of the confidence regions tha contain68.34... ancl of normally distributed models around. the minimum of 47 (Pressefa£1992). in the parameter space of v and e is shown. | In figure \ref {enuDegeneracy} a contour plot of the confidence regions that contain, and of normally distributed models around the minimum of $\chi^2$ \cite
{Press1992} in the parameter space of $\nu$ and $e$ is shown. |
Only the plo for A=2 is presented: the cases with A=0.5 and A= are very similar. | Only the plot for $\lambda=2$ is presented; the cases with $\lambda=0.5$ and $\lambda=1$ are very similar. |
The parameter space was scanned with a stepsize of 0.02 for v and 0.01 for e. | The parameter space was scanned with a stepsize of $0.02$ for $\nu$ and $0.01$ for $e$. |
For every point the best parameters were determined through minimisation a a x7-value was computed. | For every point the best parameters were determined through minimisation and a $\chi^2$ -value was computed. |
The best fit models lie in a long valley that extends up tovz1.25. | The best fit models lie in a long valley that extends up to $\nu\approx 1.25$. |
Ehe unclear structure at the lower end of the valley for v0.5 and e<0.1 is due to numerical cllects. | The unclear structure at the lower end of the valley for $\nu\leq 0.5$ and $e\leq 0.1$ is due to numerical effects. |
Detailed investigation shows that the valley continues towards smaller £7. becoming shallower. | Detailed investigation shows that the valley continues towards smaller $\nu$, becoming shallower. |
The models in this region. with low e and £. are similar to circular disks with constant surface mass density ancl are not examined here because they do not represent. realistic galaxymoclels. | The models in this region, with low $e$ and $\nu$, are similar to circular disks with constant surface mass density and are not examined here because they do not represent realistic galaxymodels. |
The external-shear models by Wambsganss cezviisski (L994) vieldleck no constraints on their circular mass distributions for the whole range of parameters from tov 2. | The external-shear models by Wambsganss czyńsski \shortcite
{Wambsganss1994} yielded no constraints on their circular mass distributions for the whole range of parameters from to . |
. The smaller allowed range for v in figure shows that the ellipticity does not allow the same kind of freeclom as the shear. | The smaller allowed range for $\nu$ in figure \ref
{enuDegeneracy} shows that the ellipticity does not allow the same kind of freedom as the shear. |
For high cllipticities of the powerLaw bulges. the quasar image geometry. cannot be reproduced anymore. | For high ellipticities of the power–law bulges, the quasar image geometry cannot be reproduced anymore. |
solar cycle 23 although by nature it is a weak rule with significant scatter. | solar cycle 23 although by nature it is a weak rule with significant scatter. |
Pevtsov et al. ( | Pevtsov et al. ( |
2008) further compared data from four different instruments and concluded that "the notion that the hemispheric helicity rule changes sign in some phases of solar cycle is not supported at a high level of significance”. | 2008) further compared data from four different instruments and concluded that “the notion that the hemispheric helicity rule changes sign in some phases of solar cycle is not supported at a high level of significance". |
Apart from these arguments, Zhang (2006) did a statistical study using 17,200 vector magnetograms obtained by SMFT. | Apart from these arguments, Zhang (2006) did a statistical study using 17,200 vector magnetograms obtained by SMFT. |
She separated her data into two parts, the weak fields (100 G «|B.| 500 G) and the strong fields (|B.]21000 G). | She separated her data into two parts, the weak fields (100 G $< |B_z| <$ 500 G) and the strong fields $|B_z| > $ 1000 G). |
She calculated the @ and A, of weak and strong fields separately and found that the weak magnetic fields follow the usual hemispheric helicity sign rule but strong fields not. | She calculated the $\alpha$ and $h_{c}$ of weak and strong fields separately and found that the weak magnetic fields follow the usual hemispheric helicity sign rule but strong fields not. |
She interpreted this as the reason why Bao et al. ( | She interpreted this as the reason why Bao et al. ( |
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