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This is unlikely since dusty and metal poor j 1.000L Asiouldheavetohaceunphgsicallyhighedusllo melalratios(D=10D Y. which is rather difficult to produce (Inoue2003). | This is unlikely since dusty and metal poor $ < $ -1.0) DLAs would have to have unphysically high dust-to-metal ratios ${\cal D}\ge 10\cal D_{\rm MW}$ ), which is rather difficult to produce \citep{InoueA_03a}. |
On the other hand. metal-rich DLAs with high wwould have larger (713) (Ménard&Chelouche2008) and therefore would be easier to obscure. but are in fact present in our sample. | On the other hand, metal-rich DLAs with high would have larger $E(B-V)$ \citep{MenardB_08b} and therefore would be easier to obscure, but are in fact present in our sample. |
Finally. we looked at the distribution of the QSO magnitudes in the pplane. and found no evidence for a selective dust-bias. | Finally, we looked at the distribution of the QSO magnitudes in the plane, and found no evidence for a selective dust-bias. |
Our results show the presence of a metallicity gradient in the pplane of intervening absorbers (Fig. 2). | Our results show the presence of a metallicity gradient in the plane of intervening absorbers (Fig. \ref{fig:intro}) ). |
In other words. the metallicity of absorbers is a bimodal function of aand1 | In other words, the metallicity of absorbers is a bimodal function of and. |
1,275, As a direct consequence. a population of DLAs. selected with logNyy,2»20.3. will be heterogeneous. | As a direct consequence, a population of DLAs, selected with $\log \NHI>20.3$, will be heterogeneous. |
At lowHV. the -selected sample is metal poor. whereas at high27. it is found to be more metal rich. | At low, the -selected sample is metal poor, whereas at high, it is found to be more metal rich. |
Therefore. the correlation between the metallicity aand the line-of-sight velocity width Av reported by (2006) and by Murphyetal.(2007) arises from the sselection and can not be interpreted as a signature of the relation akin to normal field galaxies. | Therefore, the correlation between the metallicity and the line-of-sight velocity width $\Delta v$ reported by \citet{LedouxC_06a}
and by \citet{MurphyM_07a} arises from the selection and can not be interpreted as a signature of the mass-metallicity relation akin to normal field galaxies. |
We argue that the bivariate distribution can be explained by two different physical[EX/H]tGNgR originsMUI] of absorbers. which are the ISM of small galaxies and out-flowing material. with distinct physical properties (such as metallicities and dust-to-gas ratios). | We argue that the bivariate distribution )] can be explained by two different physical origins of absorbers, which are the ISM of small galaxies and out-flowing material, with distinct physical properties (such as metallicities and dust-to-gas ratios). |
This is supported by the distribution of the absorbers in the pplane. | This is supported by the distribution of the absorbers in the plane. |
If there are two distinct ΔΗpopulationsjM of absorbers. as shown in Fig. 4.. | If there are two distinct populations of absorbers, as shown in Fig. \ref{fig:model}, |
this naturally explains the two classes of DLAs Clow-cool and high-cool). reported by Wolfeetal.(2008). using [C II] 1587; m cooling rates. | this naturally explains the two classes of DLAs (`low-cool' and `high-cool'), reported by \citet{WolfeA_08a} using [C II] $\mu$ m cooling rates. |
DLAs with large velocity dispersions (as measured by 11,7) are more metal rich than those with low velocity widths and will have different dust-to-gas ratio for a given dust-to-metal ratio. | DLAs with large velocity dispersions (as measured by ) are more metal rich than those with low velocity widths and will have different dust-to-gas ratio for a given dust-to-metal ratio. |
Therefore. the correlation between metallicity aand eor Av) for DLAs (which we showed to be apparent). the two classes of DLAs of Wolfeetal. (2008).. the dust-to-gas results of Ménard&Chelouche (2008).. andthe results ofBouché indicating that 1I--selected absorbers are tracing out-flowing material can all be put into one coherent context. | Therefore, the correlation between metallicity and (or $\Delta v$ ) for DLAs (which we showed to be apparent), the two classes of DLAs of \citet{WolfeA_08a}, , the dust-to-gas results of \citet{MenardB_08b}, , andthe results of\citet{BoucheN_06c} indicating that -selected absorbers are tracing out-flowing material can all be put into one coherent context. |
We thank S.Ellison for providing ffor her sample. | We thank S.Ellison for providing for her sample. |
We acknowledge inlighting scientitic discussions with M.T. Muprhy. C. Pérroux. | We acknowledge inlighting scientific discussions with M.T. Muprhy, C. Pérroux. |
We gratefully acknowledge M.T. Murphy and S. Genel for their thorough reading of the manuscript. | We gratefully acknowledge M.T. Murphy and S. Genel for their thorough reading of the manuscript. |
primordial power spectrum, h is the dimensionless Hubble parameter today, n; is the scalar spectral index and 7 is the optical depth at recombination. | primordial power spectrum, $h$ is the dimensionless Hubble parameter today, $n_s$ is the scalar spectral index and $\tau$ is the optical depth at recombination. |
The exact definitions of the parameters are given by the CosmoMC code. | The exact definitions of the parameters are given by the CosmoMC code. |
In addition to these basic six parameters we have also studied changes in w, Cris (or ovis) and Cham: | In addition to these basic six parameters we have also studied changes in $w$ , $\cvis$ (or $\avis$ ) and $\clam$. |
The most constraining CMB dataset at present is the 3- data release from the WMAP team. | The most constraining CMB dataset at present is the 3-year data release from the WMAP team. |
In our analysis we have used both the temperature (7) and polarization (7) data from this experiment together with the likelihood code provided by the WMAP team!. | In our analysis we have used both the temperature \citep{hinshaw:2006} and polarization \citep{page:2006} data from this experiment together with the likelihood code provided by the WMAP team. |
. Since the effects we are studying here are most prominent on large angular scales in the CMB signal, we do not take additional small-scale CMB experiments into account in this analysis. | Since the effects we are studying here are most prominent on large angular scales in the CMB signal, we do not take additional small-scale CMB experiments into account in this analysis. |
In one case we have also utilized LSS data from the Sloan Digital Sky Survey Luminous Red Galaxy Sample (SDSS-LRG) (?).. | In one case we have also utilized LSS data from the Sloan Digital Sky Survey Luminous Red Galaxy Sample (SDSS-LRG) \citep{tegmark:2006}. |
When using information on SNIa distance-redshift relation, we use data from the Supernova Legacy Survey (SNLS) (?).. | When using information on SNIa distance-redshift relation, we use data from the Supernova Legacy Survey (SNLS) \citep{astier:2006}. |
We havealso used a prior of h=0.72+0.08 from the Hubble Space Telescope Key Project (HST) (?) and a top-hat prior on the age of the universe, 10Gyr<Age<20Gyr, throughout the entire analysis. | We havealso used a prior of $h=0.72 \pm 0.08$ from the Hubble Space Telescope Key Project (HST) \citep{freedman:2001} and a top-hat prior on the age of the universe, $<$ $<$ 20Gyr, throughout the entire analysis. |
To start with we have used the c?;, parameterization, looking at two distinct scenarios. | To start with we have used the $\cvis$ parameterization, looking at two distinct scenarios. |
In one case we have (w> 0), and in the other case (w<—1,c2;,«0]. | In one case we have $\{ w>-1, \cvis>0 \}$ , and in the other case $\{ w<-1, \cvis<0 \}$. |
Here, and for the rest of subsection 4.1,, we have set C?im= 1. | Here, and for the rest of subsection \ref{cons_vis}, we have set $\clam=1$ . |
In Figure 3 we show the and confidence level (CL) contours in the w—c2;, plane for the two main scenarios mentioned above. | In Figure \ref{fig:cvis_w} we show the and confidence level (CL) contours in the $w-\cvis$ plane for the two main scenarios mentioned above. |
We see that in the first case there is no clear degeneracy between c2;, and w, and we find no upper limit on c2;, here. | We see that in the first case there is no clear degeneracy between $\cvis$ and $w$, and we find no upper limit on $\cvis$ here. |
This is exactly what we would expect from an inspection of Figure 1;; when {w>—1,c2;, 0], the effects of varying c2;, are negligible. | This is exactly what we would expect from an inspection of Figure \ref{fig:cls_cvis}; when $\{ w>-1, \cvis>0 \}$ , the effects of varying $\cvis$ are negligible. |
For the latter case, where w«—1 and c2;,«0, we do however find a degeneracy between these parameters, and in this case we also find lower limits on c2;,. | For the latter case, where $w<-1$ and $\cvis<0$, we do however find a degeneracy between these parameters, and in this case we also find lower limits on $\cvis$. |
Using only WMAP data we find c2;,>—19.5 at confidence level (CL) from the 1 dimensional distribution of c2;,. | Using only WMAP data we find $\cvis>-19.5$ at confidence level (CL) from the 1 dimensional distribution of $\cvis$ . |
Since there are observable effects of a non-zero c2;, in this scenario, we also tried to add SDSS-LRG and SNLS data to see if this would improve our constraints on c2;,. | Since there are observable effects of a non-zero $\cvis$ in this scenario, we also tried to add SDSS-LRG and SNLS data to see if this would improve our constraints on $\cvis$. |
In this case the lower limit on c2;, becomes c2;,>—24.9 at CL. | In this case the lower limit on $\cvis$ becomes $\cvis>-24.9$ at CL. |
We can also easily see from the figure that adding SDSS-LRG and SNLS data does not improve the limits on c2;,, only on w. | We can also easily see from the figure that adding SDSS-LRG and SNLS data does not improve the limits on $\cvis$, only on $w$. |
The reason is that the effects of c?,, occur at larger scales than probed by the SDSS-LRG. | The reason is that the effects of $\cvis$ occur at larger scales than probed by the SDSS-LRG. |
Therefore this additional data would only be interesting if it could break degeneracies between c2;, and other parameters that govern the shape of the power spectrum for low /s. We see from Figure 1 that although we do have a degeneracy between c2;, and w, the limits on c2;, would only be improved by some data set that would favor aw«—1. Next, we turn to the o,;, parameterization. | Therefore this additional data would only be interesting if it could break degeneracies between $\cvis$ and other parameters that govern the shape of the power spectrum for low $l$ s. We see from Figure \ref{fig:cls_cvis} that although we do have a degeneracy between $\cvis$ and $w$, the limits on $\cvis$ would only be improved by some data set that would favor a$w<-1$. Next, we turn to the $\avis$ parameterization. |
To constrain this parameter we focus on a model where 0, since we find no upper limits on a positive αυις. | To constrain this parameter we focus on a model where $\avis <0$ , since we find no upper limits on a positive $\avis$. |
In Figure 4 we show the and CL contours for w and avis in this model. | In Figure \ref{fig:alpha_w} we show the and CL contours for $w$ and $\avis$ in this model. |
We see that αυις is bounded from below and that values of αυις slightly below zero are allowed. | We see that $\avis$ is bounded from below and that values of $\avis$ slightly below zero are allowed. |
In this case we find that axis>—0.23 at CL. | In this case we find that $\avis> -0.23$ at CL. |
Since we got a lower limit on c2;, whenhaving w<—1, we would also expect to find an upper limit on αυιςin this case. | Since we got a lower limit on $\cvis$ whenhaving $w<-1$, we would also expect to find an upper limit on $\avis$in this case. |
In Figure ὅwe show the 1 dimensional marginalized likelihood for logayis for a model with w= —1.2. | In Figure \ref{fig:alpha_1D} we show the 1 dimensional marginalized likelihood for $\log \avis$ for a model with $w=-1.2$ . |
We find that logavis«3.2 at CL (avis< 24.5), which corresponds well to the limits we found for c2;, with w< —1. | We find that $\log \avis < 3.2$ at CL $\avis<24.5$ ), which corresponds well to the limits we found for $\cvis$ with $w<-1$ . |
In this section we investigate what constraints can be put | In this section we investigate what constraints can be put |
Weak gravitational flexion is a relatively new addition to the panoply of gravitational lensing effects. but has considerable potential for measuring substructure in the density distribution of matter in the Universe (seee.g.222222). | Weak gravitational flexion is a relatively new addition to the panoply of gravitational lensing effects, but has considerable potential for measuring substructure in the density distribution of matter in the Universe \citep[see e.g.][]{2002ApJ...564...65G, 2005ApJ...619..741G, 2005NewAR..49...83I, 2006MNRAS.365..414B, 2008ApJ...680....1O, 2008A&A...485..363S}. |
Flexion is proportional to third angular derivatives of the projected gravitational potential along the line of sight. | Flexion is proportional to third angular derivatives of the projected gravitational potential along the line of sight. |
As such. it is at the next order of differentiation compared to shear and convergence. Which are the more studied weak lensing measures (see2.foranextensivereview).. | As such, it is at the next order of differentiation compared to shear and convergence, which are the more studied weak lensing measures \citep[see][ for an extensive review]{2001PhR...340..291B}. |
Since. as we shall see. there are wo independent combinations of third derivatives. there are two different flexion effects: the |-flexion. which is a vector distortion eading to objects being skewed: and the 3-flexion. which is a spin hree distortion changing circular objects into trefoils. | Since, as we shall see, there are two independent combinations of third derivatives, there are two different flexion effects: the 1-flexion, which is a vector distortion leading to objects being skewed; and the 3-flexion, which is a spin three distortion changing circular objects into trefoils. |
Up until now. these have been the only known image distortions at this order. | Up until now, these have been the only known image distortions at this order. |
However. in this paper we will show that here is a further neglected image distortion at the flexion level. with wo alternative deseriptions which we eall twist and turn for reasons which will become obvious. | However, in this paper we will show that there is a further neglected image distortion at the flexion level, with two alternative descriptions which we call twist and turn for reasons which will become obvious. |
This distortion is not activated by gravity under the most straightforward approximations: but it will be activated by systematic effects. | This distortion is not activated by gravity under the most straightforward approximations; but it will be activated by systematic effects. |
The latter are of great concern ο weak lensing. so finding a further signature of systematics is yotentially very valuable to upcoming lensing surveys. | The latter are of great concern to weak lensing, so finding a further signature of systematics is potentially very valuable to upcoming lensing surveys. |
In this paper we show how twist or turn arises. and account or why it has not been noticed before. | In this paper we show how twist or turn arises, and account for why it has not been noticed before. |
We show how it affects images in real and shapelet space. and give details of how it can be measured with fairly straightforward estimators. | We show how it affects images in real and shapelet space, and give details of how it can be measured with fairly straightforward estimators. |
We then measure wist for the first time using the Space Telescope A901/902 Galaxy Evolution Survey (STAGES.?).. a large mosaic observed with the Hubble Space Telescope (HST). | We then measure twist for the first time using the Space Telescope A901/902 Galaxy Evolution Survey \citep[STAGES,][]{2007AAS...21113220G}, a large mosaic observed with the Hubble Space Telescope (HST). |
We show that the twist is consistent with zero for STAGES on all scales. both in terms of its mean values and its correlation functions. incrementally adding confidence in the management of systematics for this survey. | We show that the twist is consistent with zero for STAGES on all scales, both in terms of its mean values and its correlation functions, incrementally adding confidence in the management of systematics for this survey. |
The paper is organised as follows. | The paper is organised as follows. |
In Section ??.. we recount he theory of image distortions in weak lensing at the more studied first order. | In Section \ref{sect_lensing_first_order}, we recount the theory of image distortions in weak lensing at the more studied first order. |
We note that there is already a non-gravitational mode at this order: image rotation. | We note that there is already a non-gravitational mode at this order; image rotation. |
We write the distortions in terms of Pauli matrices. which will give us the necessary clues for how to reat higher order distortions later. | We write the distortions in terms of Pauli matrices, which will give us the necessary clues for how to treat higher order distortions later. |
In Section ??.. we extend the account to second order. | In Section \ref{sect_lensing_second_order}, we extend the account to second order. |
We tind that there are combinations of Pauli matrices orthogonal to hose describing the conventional flexion degrees of freedom: these orthogonal combinations give twist and turn distortions. | We find that there are combinations of Pauli matrices orthogonal to those describing the conventional flexion degrees of freedom; these orthogonal combinations give twist and turn distortions. |
We are herefore able to write down for the first time the complete weak image distortion to second order. and show how twist and turn are related to one another observationally. | We are therefore able to write down for the first time the complete weak image distortion to second order, and show how twist and turn are related to one another observationally. |
Section ??— describes the behaviour of twist/turn. | Section \ref{sect_twist_turn} describes the behaviour of twist/turn. |
The rotational properties of the distortion is worked out. and we tind that is is a vector quantity. | The rotational properties of the distortion is worked out, and we find that is is a vector quantity. |
We show the impact of twist and turn on simple images: we find that they do not affect the shape circularly symmetric images. but only images with non-zero ellipticity. | We show the impact of twist and turn on simple images; we find that they do not affect the shape of circularly symmetric images, but only images with non-zero ellipticity. |
We show explicitly the nature of twist and turn in Paljapelet space. proving that they have no impact on circularly symmetric sources. and derive how they move power between PalYapelet coefficients. | We show explicitly the nature of twist and turn in shapelet space, proving that they have no impact on circularly symmetric sources, and derive how they move power between shapelet coefficients. |
In Section ??) we go about finding practical estimators for measuring twist and turn. | In Section \ref{sect_estimators} we go about finding practical estimators for measuring twist and turn. |
We derive simple estimators in shapelet Palσος. | We derive simple estimators in shapelet space. |
Noting that like flexion. twist and turn affect the centroids of objects. we correct the estimators by constructing slightly more complicated expressions which take this shift into account. | Noting that like flexion, twist and turn affect the centroids of objects, we correct the estimators by constructing slightly more complicated expressions which take this shift into account. |
However. we will show that our estimators are not perfect: they | However, we will show that our estimators are not perfect; they |
To compute Aly, we used (Iy,,AV) profiles of nine “template” clusters shown in Fig. 1.. | To compute $\Delta I_V$, we used $(I_{M_V},\,\Delta V)$ profiles of nine “template” clusters shown in Fig. \ref{fig:mag_int}. |
The templates were selected to satisfy two constraints: to be uniformly distributed over the brightest stellar magnitudes of the clusters and to represent a sufficiently long observed main sequence (MS). | The templates were selected to satisfy two constraints: to be uniformly distributed over the brightest stellar magnitudes of the clusters and to represent a sufficiently long observed main sequence (MS). |
In Fig. | In Fig. |
1. we show the profiles as a function of AV;=V;—Vp, (Vj are individual magnitudes of the most probable members of a template and V;,=min{V;}). | \ref{fig:mag_int} we show the profiles as a function of $\Delta V_i=V_i-V_{br}$ $V_i$ are individual magnitudes of the most probable members of a template and $V_{br}=\mathrm{min}\{V_i\}$ ). |
At AV;=0, the integrated magnitude 7j, is identical to the absolute magnitude of the brightest cluster member. | At $\Delta V_i=0$, the integrated magnitude $I_{M_V}$ is identical to the absolute magnitude of the brightest cluster member. |
As one can see, stars that are seven or more magnitudes fainter than the brightest member (AV27) do not have a significant impact on /j,. | As one can see, stars that are seven or more magnitudes fainter than the brightest member $\Delta V\geqslant7$ ) do not have a significant impact on $I_{M_V}$. |
On the other hand, the typical absolute magnitude of cluster stars at AV=7 is brighter than My=6 or m>0.9Μο in our sample. | On the other hand, the typical absolute magnitude of cluster stars at $\Delta V=7$ is brighter than $M_V=6$ or $m>0.9\,M_\odot$ in our sample. |
In this mass range, the mass functions of cluster stars are only weakly dependent on cluster age (?).. | In this mass range, the mass functions of cluster stars are only weakly dependent on cluster age \citep{bamak03}. |
This enables us to safely apply the above templates to the whole cluster sample. | This enables us to safely apply the above templates to the whole cluster sample. |
A correction A/y is computed for each cluster having a short MS as after normalizationγι of the suitable template profile (see Fig. 1). | A correction $\Delta I_V$ is computed for each cluster having a short MS as after normalization of the suitable template profile (see Fig. \ref{fig:mag_int}) ). |
Here Vj, and V;,, are the brightest and faintest magnitudes of the most probable members in the cluster under consideration, V; are template magnitudes, and AV=7 mag. | Here $V_{br}$ and $V_{fnt}$ are the brightest and faintest magnitudes of the most probable members in the cluster under consideration, $V_i$ are template magnitudes, and $\Delta
V=7$ mag. |
The constant d is computed assuming that the cluster and the matching template have equal integrated magnitudes at Ven. | The constant $I_V^{fnt}$ is computed assuming that the cluster and the matching template have equal integrated magnitudes at $V_{fnt}$. |
Since the integrated magnitude is mainly defined by the brightest cluster members, A/y is relatively small: it is always less than 0.85 mag, with an average of 0.13 mag, and for of the clusters Aly«0.3. | Since the integrated magnitude is mainly defined by the brightest cluster members, $\Delta
I_V$ is relatively small: it is always less than 0.85 mag, with an average of 0.13 mag, and for of the clusters $\Delta I_V<0.3$. |
On the other hand, in 33 clusters the MS exceeds a length of 7 magnitudes. | On the other hand, in 33 clusters the MS exceeds a length of 7 magnitudes. |
We truncated their profiles to AV=7, for homogeneity. | We truncated their profiles to $\Delta V=7$, for homogeneity. |
The other membership samples, i.e., samples including stars with a membership probability less than61%,, produce somewhat brighter magnitudes (on average, by about half a magnitude) but they are more strongly contaminated by field stars than is the sample of the most probable cluster members. | The other membership samples, i.e., samples including stars with a membership probability less than, produce somewhat brighter magnitudes (on average, by about half a magnitude) but they are more strongly contaminated by field stars than is the sample of the most probable cluster members. |
Throughout the paper we use the following definitions of cluster luminosity and mass functions. | Throughout the paper we use the following definitions of cluster luminosity and mass functions. |
If the AN is the number of open clusters having absolute integrated magnitude in the range [1µν.Iu,+AIy,] and which are observed in an area AS in the Galactic disc, then the luminosity function ¢ is i.e., the ην.luminosity function is a surface density distribution of open clusters over the integrated magnitude. | If the $\Delta N$ is the number of open clusters having absolute integrated magnitude in the range $[I_{M_V}\,,I_{M_V}+\Delta I_{M_V}]$ and which are observed in an area $\Delta S$ in the Galactic disc, then the luminosity function $\phi$ is i.e., the luminosity function is a surface density distribution of open clusters over the integrated magnitude. |
Similarly, the mass function η is defined as a surface density distribution of open clusters over the logarithm of mass: Since the aboveog distributions include clusters of all ages, it is reasonable to call $(/y,) and η(Μο) the present-day luminosity and mass functions of clusters, or CPDLF and CPDMF, respectively. | Similarly, the mass function $\eta$ is defined as a surface density distribution of open clusters over the logarithm of mass: Since the above distributions include clusters of all ages, it is reasonable to call $\phi(I_{M_V})$ and $\eta(M_c)$ the present-day luminosity and mass functions of clusters, or CPDLF and CPDMF, respectively. |
In the following, we also consider the luminosity and mass distributions of clusters confined by some upper limit of their age t. | In the following, we also consider the luminosity and mass distributions of clusters confined by some upper limit of their age $t$. |
We call them current luminosity/mass functions of clusters or simply cluster luminosity/mass functions with the abbreviations CLF and CMF. | We call them current luminosity/mass functions of clusters or simply cluster luminosity/mass functions with the abbreviations CLF and CMF. |
To distinguish them from present-day distributions we denote them as $;(Iy,) and 7,(M.). | To distinguish them from present-day distributions we denote them as $\phi_t(I_{M_V})$ and $\eta_t(M_c)$. |
Both functions are in fact cumulative with respect to age distributions. | Both functions are in fact cumulative with respect to age distributions. |
The aim of the present paper is the construction of an initial mass function of star clusters, which indeed describes the initial distribution, i.e. the distribution after re-virialisation after residual gas expulsion (?).. | The aim of the present paper is the construction of an initial mass function of star clusters, which indeed describes the initial distribution, i.e. the distribution after re-virialisation after residual gas expulsion \citep{krobo02}. |
Hereafter, we denote the initial luminosity/mass distributions as CILF and CIMF. | Hereafter, we denote the initial luminosity/mass distributions as CILF and CIMF. |
A formal definition of these functions is given in Sect.4.. | A formal definition of these functions is given in \ref{sec:evol}. |
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