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However, the full PSF outside of this core has much structure due to the diffraction from the secondary mirror and its support structure amd it is recommended to use equivalent beam areas of 501, 944 and 1924 arcsec? respectively to calculate surface brightness when observing extended sources (SPIRE Observer’s Manual 2010)).
However, the full PSF outside of this core has much structure due to the diffraction from the secondary mirror and its support structure and it is recommended to use equivalent beam areas of 501, 944 and 1924 $^2$ respectively to calculate surface brightness when observing extended sources (SPIRE Observer's Manual \cite{spire10}) ).
These values are quoted as the mean for all detectors in an array, there is some minor variation across the arrays as demonstrated in Fig.
These values are quoted as the mean for all detectors in an array, there is some minor variation across the arrays as demonstrated in Fig.
4 which shows the centroid positions and the relative beam sizes from a point source scanned across the PSW array.
\ref{phot_beams} which shows the centroid positions and the relative beam sizes from a point source scanned across the PSW array.
The variation in beam size has been found to vary by no more than for the majority of detectors across any of the three arrays.
The variation in beam size has been found to vary by no more than for the majority of detectors across any of the three arrays.
In the example shown here the maximum and minimum beam sizes of the nominally operational detectors are 17.3 and 19.5 arcsec.
In the example shown here the maximum and minimum beam sizes of the nominally operational detectors are 17.3 and 19.5 arcsec.
The apparently large beamsizes in two of the detectors are caused by their very slow time response and these detectors are excluded from the map making.
The apparently large beamsizes in two of the detectors are caused by their very slow time response and these detectors are excluded from the map making.
Measurement of the beam width versus wavelength within the bands is not possible in flight but characterisation was performed during ground test campaigns (Ferlet et al. 2008)).
Measurement of the beam width versus wavelength within the bands is not possible in flight but characterisation was performed during ground test campaigns (Ferlet et al. \cite{ferlet08}) ).
The measured positions of the detectors in each array are folded into the map reconstruction algorithms together with the knowledge of the spacecraft pointing.
The measured positions of the detectors in each array are folded into the map reconstruction algorithms together with the knowledge of the spacecraft pointing.
Comparison between fields with sources seen at other wavelengths (mostly from and radio catalogues) shows that, with the present knowledge and algorithms, the typical astrometric accuracy of SPIRE maps processed with the current version of the processing pipeline is around 4 arcsec.
Comparison between fields with sources seen at other wavelengths (mostly from and radio catalogues) shows that, with the present knowledge and algorithms, the typical astrometric accuracy of SPIRE maps processed with the current version of the processing pipeline is around 4 arcsec.
The cause of part of the inaccuracy has already been identified and subsequent versions of the pipeline have an astrometric accuracy of 2 arcsec or better.
The cause of part of the inaccuracy has already been identified and subsequent versions of the pipeline have an astrometric accuracy of 2 arcsec or better.
This should be compared to the telescope relative pointing error of 0.2 arcsec 1-sigma over 1 minute and the spatial relative pointing error of 1.5 arcec (Pilbratt et al. 2010)).
This should be compared to the telescope relative pointing error of 0.2 arcsec 1-sigma over 1 minute and the spatial relative pointing error of 1.5 arcec (Pilbratt et al. \cite{pilbratt10}) ).
The shape and extent of the beam in the spectrometer has been subject to much study (Ferlet et al. 2008))
The shape and extent of the beam in the spectrometer has been subject to much study (Ferlet et al. \cite{ferlet08}) )
both on the ground and in flight.
both on the ground and in flight.
The beam size versus frequency has been measured directly by taking medium resolution spectra on a point source of Neptune placed at different locations with respect to the central detectors by stepping the satellite position.
The beam size versus frequency has been measured directly by taking medium resolution spectra on a point source of Neptune placed at different locations with respect to the central detectors by stepping the satellite position.
The results are shown in Fig. 5..
The results are shown in Fig. \ref{spectrometer_beam}.
The highly structured nature of the variation in beam size with frequency is expected from the multi-moded feedhorns used for the spectrometer arrays.
The highly structured nature of the variation in beam size with frequency is expected from the multi-moded feedhorns used for the spectrometer arrays.
The beams are only Gaussian at the low frequency end of each band and methods for conversion between calibration valid for point and extended sources require further investigation.
The beams are only Gaussian at the low frequency end of each band and methods for conversion between calibration valid for point and extended sources require further investigation.
The central wavelengths for the three photometer bands are derived from pre-flight measurements of the passbands of the detectors and the instrument optical filter chain (Spencer 2009,, SPIRE Observers Manual 2010)).
The central wavelengths for the three photometer bands are derived from pre-flight measurements of the passbands of the detectors and the instrument optical filter chain (Spencer \cite{spencer09}, , SPIRE Observers Manual \cite{spire10}) ).
As described in Griffin et al. (2010))
As described in Griffin et al. \cite{griffin10}) )
these are integrated over the waveband assuming a flat spectrum to give band centres at 250, 352 and 504 wm. The edges of the bands as defined at of the average in band transmission are 211-290 um (PSW), 297-405 um (PMW), and 409-611
these are integrated over the waveband assuming a flat spectrum to give band centres at 250, 352 and 504 m. The edges of the bands as defined at of the average in band transmission are 211-290 m (PSW), 297-405 m (PMW), and 409-611
as a [function of magnitude.
as a function of magnitude.
Particular care was taken to ensure a good Lit close to the survey's limit. for which there is minimal morphological information and ¢»0. even for galaxies.
Particular care was taken to ensure a good fit close to the survey's limit, for which there is minimal morphological information and $\stat \rightarrow 0$, even for galaxies.
‘These desiderata are met by a log-normal distribution: where Rather than specifving the functions pm) and e(m) of the standard parameterisation of the log-normal distribution (Eq. 14)).
These desiderata are met by a log-normal distribution: where Rather than specifying the functions $\mu(m)$ and $\sigma(m)$ of the standard parameterisation of the log-normal distribution (Eq. \ref{equation:lognormstdpara}) ),
we have modelled the mean y(n) and standard deviation. σ/(m) ofH the log-normal. by the empirical functions below. where mayas is the upper detection limit in the reference
we have modelled the mean $\mu'(m)$ and standard deviation $\sigma'(m)$ of the log-normal by the empirical functions below, where $m_{\rmn{max}}$ is the upper detection limit in the reference
a threshold error o 70.04.
a threshold error of 0.04.
Note how the bins are larger. but the level of noise is signifieantly less.
Note how the bins are larger, but the level of noise is significantly less.
A real feature has been lost from the image. however.
A real feature has been lost from the image, however.
A point source present in the upper left radio lobe has disappeared.
A point source present in the upper left radio lobe has disappeared.
Ts counts were merged into rest of the emission from that region.
Its counts were merged into rest of the emission from that region.
In Fig.
In Fig.
5 is shown the error map for the adatively binned map above.
\ref{fig:per_adbin4_err} is shown the error map for the adaptively binned map above.
In it are easily visible the changes in bin size as the count rate decreases towards the outside.
In it are easily visible the changes in bin size as the count rate decreases towards the outside.
As the count rate decreases. the error of the bins increases until it reaches the tireshold. and then the bin-size doubles.
As the count rate decreases, the error of the bins increases until it reaches the threshold, and then the bin-size doubles.
For comparison. Fig.
For comparison, Fig.
6. shows an adaptively smoothed (AS) image of the cluster calculated from the data in Fig. 2..
\ref{fig:per_asmooth} shows an adaptively smoothed (AS) image of the cluster calculated from the data in Fig. \ref{fig:per_raw}.
Tt was smoothed with a minimum significance o "d-c using the algorithm of Ebeling et al.
It was smoothed with a minimum significance of $\sigma$ using the algorithm of Ebeling et al.
The contours are at the same levels as the raw image.
The contours are at the same levels as the raw image.
The AS image contains sharp posiive features. such as the edges of the radio lobes.
The AS image contains sharp positive features, such as the edges of the radio lobes.
It does not perform as well in the determination of the number of counts in he negative features. such as the radio lobes themselves. where the numberof counts per pixel is half that of the raw οata.
It does not perform as well in the determination of the number of counts in the negative features, such as the radio lobes themselves, where the number of counts per pixel is half that of the raw data.
However. the algorithm is designed to find positive features. so using it to look a holes is a misapplication.
However, the algorithm is designed to find positive features, so using it to look at holes is a misapplication.
Also apparent are some edge effects. wjere does not find enough counts to dlace a high significance on the generated features.
Also apparent are some edge effects, where does not find enough counts to place a high significance on the generated features.
Tye edge effects are avoidable by smoothing a larger area of sky than required. and cropping he image thereafter.
The edge effects are avoidable by smoothing a larger area of sky than required, and cropping the image thereafter.
One disadvantage of this is that running time increases quickly with image size.
One disadvantage of this is that running time increases quickly with image size.
In Fig.
In Fig.
7 we show another adatively binned image of the Perseus cluster.
\ref{fig:per_acisi_ab} we show another adaptively binned image of the Perseus cluster.
This. however. was created from data from an observaion using the ACIS-I detector onChandra. with an exposure o| KKks.
This, however, was created from data from an observation using the ACIS-I detector on, with an exposure of ks.
We present it because the number of counts per pixel is lower than the ACIS-S image. and so it is a good demonstration of the algorithm used on data with more noise.
We present it because the number of counts per pixel is lower than the ACIS-S image, and so it is a good demonstration of the algorithm used on data with more noise.
Adaptive binning of the ACIS-I image brings out an interesting feature of the cluster: it clearly demonstrates that the southern rim of the northern radio lobe (hole) lies south of the nucleus.
Adaptive binning of the ACIS-I image brings out an interesting feature of the cluster; it clearly demonstrates that the southern rim of the northern radio lobe (hole) lies south of the nucleus.
There is a linear diagonal structure present to the south of the nucleus. running from the north-west to the south-east.
There is a linear diagonal structure present to the south of the nucleus, running from the north-west to the south-east.
Tis structure is also present in the raw data. but is not clearon the AC image. despite the longer exposure. as the ACIS-S raw image contains a dark strip due to the node-line of the detector. where the effective exposure is short.
This structure is also present in the raw data, but is not clear on the ACIS-S image, despite the longer exposure, as the ACIS-S raw image contains a dark strip due to the node-line of the detector, where the effective exposure is short.
The dark bin to the south-east of the nucleus shows a "stranded bin’. an occasional problem with the algorithm. which we discuss later.
The dark bin to the south-east of the nucleus shows a `stranded bin', an occasional problem with the algorithm, which we discuss later.
Both Re and V. band data were submitted by [our different observers. three of whom observed (his star in both fillers on at least one night.
Both $R_{C}$ and $V$ band data were submitted by four different observers, three of whom observed this star in both filters on at least one night.
We attempted to create color curves using data Irom these three observers by. phasing individual observers’ nightly measures of (V—R) with the ephemeris given above.
We attempted to create color curves using data from these three observers by phasing individual observers' nightly measures of $(V-R)$ with the ephemeris given above.
The resulüing phased color curve is shown in Figure 3..
The resulting phased color curve is shown in Figure \ref{fig_color}.
The phase curve is flat within (he errors on individual points. but the average value of (V—R) is around +0.4. which is somewhat bluer than is tvpical for Milkv. Wavy long period Cepheids (Bercdiikov&Turner1995).
The phase curve is flat within the errors on individual points, but the average value of $(V-R)$ is around +0.4, which is somewhat bluer than is typical for Milky Way long period Cepheids \citep{BT1995}.
. ILowever. we caution that while observers are using well-calibrated comparison stars for photometry. the data for these observers was not fully calibrated. ancl (transformed to a standard system.
However, we caution that while observers are using well-calibrated comparison stars for photometry, the data for these observers was not fully calibrated and transformed to a standard system.
The fact that there are zero-point Atc differences between observers suggests Chat there will be V-band differences as well.
The fact that there are zero-point $R_{C}$ -band differences between observers suggests that there will be $V$ -band differences as well.
Unfortunately there are no calibrated reference observations in V. band as there are in. Ae which means that our caleulated average of (V.—R)=0.4 is not reliable.
Unfortunately there are no calibrated reference observations in $V$ band as there are in $R_{C}$, which means that our calculated average of $(V-R) = 0.4$ is not reliable.
IIowever. we can sav that the variation in color over the evele is smaller (han we can measure given the photometric errors.
However, we can say that the variation in color over the cycle is smaller than we can measure given the photometric errors.
Both IHIubble(1929). and Baacde&Swope(1965) published all of their photometry in an easily extractable format. and we kevpunched the observations from these (wo papers into electronic. machine-readble tables.
Both \citet{Hubble1929} and \citet{BS1965} published all of their photometry in an easily extractable format, and we keypunched the observations from these two papers into electronic, machine-readble tables.
These observations have since been added (to theDatabase aad are lreely available via the AAVSO website.
These observations have since been added to the and are freely available via the AAVSO website.
As part of (his project. we wanted to compare how the old data compare to the new by performing {he same analvses on (the archival data as we did on our own photometry.
As part of this project, we wanted to compare how the old data compare to the new by performing the same analyses on the archival data as we did on our own photometry.
In (his section. we present analvses of the IIubble(1929). aud. Daade&Swope(1965) data using the same procedure as in Section 3.
In this section, we present analyses of the \citet{Hubble1929} and \citet{BS1965} data using the same procedure as in Section 3.
llubble's observations were described in IInbble(1929).. and will be briefly reviewed here.
Hubble's observations were described in \citet{Hubble1929}, and will be briefly reviewed here.
The measurements were made from plates taken with the Mount Wilson 60- and. telescopes bv ten different. observers between JD 2418562.7 (1909 September 13) and 2425149.6 (1921 September 26).
The measurements were made from plates taken with the Mount Wilson 60- and 100-inch telescopes by ten different observers between JD 2418562.7 (1909 September 13) and 2425149.6 (1927 September 26).
We digitized 130 positive observations of M31-V1 by IIubble: we included. all observations regardless of Hubble's qualitw flag (good. "Dr. or "poor) but we did not digitize observations where the star was below (he faintest comparison. or
We digitized 130 positive observations of M31-V1 by Hubble; we included all observations regardless of Hubble's quality flag (“good", “fair", or “poor") but we did not digitize observations where the star was below the faintest camparison, or
lnass rage. we use the Press Schechter formalisin ()..
mass range, we use the Press Schechter formalism \cite{ps74}.
The total mass (dark matter) coutaied per uuit comoving volume within collapsed objects of (οσαο). mass range (InM.InCM.|dÀZ3) is given by where py is the mean comoving density of the universe.
The total mass (dark matter) contained per unit comoving volume within collapsed objects of (logarithmic) mass range $(\ln M, \ln(M+\de M))$ is given by where $\rho_0$ is the mean comoving density of the universe.
The other quautities are defined as The quantity v is defined as Pox(kh) is the normalised dark matter power spectra. D(:)is the erowth factor for density perturbations and d, is the critical density. usually 1.69 for Q,,=1 flat universe.
The other quantities are defined as The quantity $\nu$ is defined as $P_{\rm DM}(k)$ is the normalised dark matter power spectrum, $D(z)$ is the growth factor for density perturbations and $\delta_c$ is the critical density, usually 1.69 for $\Omega_m=1$ flat universe.
The corresponding O is given by 00 where p,=2.8«1012?M. P isthe present critical deusitv of the universe aud O,,=po/pe-
The corresponding $\Omega$ is given by = where $\rho_c=2.8 \times 10^{11} h^2 ~ M_{\odot}$ $^{-3}$ is the present critical density of the universe and $\Omega_m=\rho_0/\rho_c$.
We shall now calculate the total mass contributed bybaryons m the collapsed lalocs within the logarithmic mass range.
We shall now calculate the total mass contributed by in the collapsed haloes within the logarithmic mass range.
Iu order to do this. we assume that the barvonic fraction of matter in each halo is same as the global value.
In order to do this, we assume that the baryonic fraction of matter in each halo is same as the global value.
Then the € contributed by barvous in collapsed haloes within a logarithinic mass rauge (luAW.ΔΕαλ} is giveu by We now have the total barvouic O84) contained within collapsed dark iatter haloes of mass Af at a eiven epoch.
Then the $\Omega$ contributed by baryons in collapsed haloes within a logarithmic mass range $(\ln M, \ln(M+\de M))$ is given by We now have the total baryonic $\Omega_{M,b}^{\rm halo}$ contained within collapsed dark matter haloes of mass $M$ at a given epoch.
We will assume that all the barvous are either converted into luminous stars. or they fori gaseous clouds.
We will assume that all the baryons are either converted into luminous stars, or they form gaseous clouds.
Mathematically. this cau be expressed as It is believed that the damped Lya systems are mainly contributed bv the gaseous cloudsvirialised dark matter haloes.
Mathematically, this can be expressed as (z) = + _*(z) It is believed that the damped $\alpha$ systems are mainly contributed by the gaseous clouds dark matter haloes.
IIeuce. one shouldnot iuclude the low coluuu deusitv svsteiis in this analysis. which are believed to be density perturbations within a diffuse iutergalactie iiecium (ICMD ἐν)..
Hence, one should include the low column density systems in this analysis, which are believed to be density perturbations within a diffuse intergalactic medium (IGM) \cite{cps01,csp01}.
It is clear that once we obtain the quantity Ὃν contained in stars. we can estimate Open. from the above relation.
It is clear that once we obtain the quantity $\Omega_*$ contained in stars, we can estimate $\Omega_{M,{\rm gas}}$ from the above relation.
To calculate O« from observational data. we proceed as follows: The star formation rate (SFR) (dp.fdt)=p.(f) is defined as the rate at which baryoulc mass is converted iuto stars per unit (comoving) volume.
To calculate $\Omega_*$ from observational data, we proceed as follows: The star formation rate (SFR) $(\de \rho_*/\de t) \equiv \dot{\rho_*}(t)$ is defined as the rate at which baryonic mass is converted into stars per unit (comoving) volume.
Given this quantity. we can obtain the total density of matter contained within stars af a particular f bu uou) or. in terms of redshift The correspoudius O is One can determine ος(0) from observations. which cau then be iuteerated to eive Q.(2).
Given this quantity, we can obtain the total density of matter contained within stars at a particular $t$ _0^t t (t) or, in terms of redshift z (z) z The corresponding $\Omega$ is One can determine $\dot{\rho_*}(t)$ from observations, which can then be integrated to give $\Omega_*(z)$.
It is well known that uot all the eas which is turned into stars is removed from the easeous phase forever.
It is well known that not all the gas which is turned into stars is removed from the gaseous phase forever.
Actually. some of the stellar material is returned bv stellar winds ancl supernovac.
Actually, some of the stellar material is returned by stellar winds and supernovae.
ILowever. we shall ignore this contribution for the following reasons: (1) It is difficult to iiplemoent this feedback effect iu our model without introducing more free parameters ()..
However, we shall ignore this contribution for the following reasons: (i) It is difficult to implement this feedback effect in our model without introducing more free parameters \cite{efstathiou00}.
This spoils the simplicity as well as the predictive capacity of our miodel. (
This spoils the simplicity as well as the predictive capacity of our model. (
i) The SER has large uncertainties at high redshifts due to extiuction (see below).
ii) The SFR has large uncertainties at high redshifts due to extinction (see below).
The correction due the feedback through stellar winds aud superuovae is less than this uncertainty in the SFR. aud cau be ignored as a first approximation.
The correction due the feedback through stellar winds and supernovae is less than this uncertainty in the SFR, and can be ignored as a first approximation.
To compare our results with observations. or to discuss any observational consequences of our mocdol. it is better to work in terius of the circular velocities (ο) of the collapsed haloes. rather thanin terms of their masses.
To compare our results with observations, or to discuss any observational consequences of our model, it is better to work in terms of the circular velocities $v_c$ ) of the collapsed haloes, rather thanin terms of their masses.
The mass AM and e. can be related to each other using spherical collapse model.
The mass $M$ and $v_c$ can be related to each other using spherical collapse model.
The relevant equatious for a universe with cosmolocical constant are () aud where Aqu) is the virial density of the collapsed halo at redshift + aud ry is the correspoucding virial radius.
The relevant equations for a universe with cosmological constant are \cite{sp99} and where $\Delta_{\rm vir}(z)$ is the virial density of the collapsed halo at redshift $z$ and $r_{\rm vir}$ is the corresponding virial radius.
The circular velocity is calculated asstuuing that the virialised halo has a sinenlar isothermal deusity profile p(r)xr 7.
The circular velocity is calculated assuming that the virialised halo has a singular isothermal density profile $\rho(r) \propto r^{-2}$ .
Fig.
Fig.
6 illustrates the spectral decomposition for the — region.
\ref{fig:sepavis} illustrates the spectral decomposition for the – region.
Although different values of A (or μ) are found at different epochs, the extracted spectra are remarkably consistent.
Although different values of $A$ (or $\mu$ ) are found at different epochs, the extracted spectra are remarkably consistent.
The microlensed part of the spectrum, Fy,, contains the continuum with the full absorption profiles as well as a small contribution from the core (not the wings) of the emission profiles.
The microlensed part of the spectrum, $F_{M\mu}$, contains the continuum with the full absorption profiles as well as a small contribution from the core (not the wings) of the emission profiles.
The bulk of the emission lines appears in the macrolensed-only part of the spectrum Fy, clearly showing a two-peak structure in (at 5350 aand 5500 À).
The bulk of the emission lines appears in the macrolensed-only part of the spectrum $F_{M}$, clearly showing a two-peak structure in (at 5350 and 5500 ).
Recall that Fy shows the flux emitted from a large region of the quasar (much larger than the Einstein radius of the microlens) whereas Fy, shows the flux emitted from a smaller region (comparable to and smaller than the Einstein radius).
Recall that $F_M$ shows the flux emitted from a large region of the quasar (much larger than the Einstein radius of the microlens) whereas $F_{M\mu}$ shows the flux emitted from a smaller region (comparable to and smaller than the Einstein radius).
Interestingly enough, the small part of the emission profile observed in Fy, is the core, i.e. the low-velocity part.
Interestingly enough, the small part of the emission profile observed in $F_{M\mu}$ is the core, i.e. the low-velocity part.
The temporal variations of the absorption are particularly well seen in the Fy, spectrum of iv.
The temporal variations of the absorption are particularly well seen in the $F_{M\mu}$ spectrum of .
The rest-frame UV spectra, and more particularly the Ίνα + region, are similarly analyzed (Fig. 7)).
The rest-frame UV spectra, and more particularly the $\alpha$ + region, are similarly analyzed (Fig. \ref{fig:sepauv}) ).
Although the decomposition is less accurate due to structures in the continuum blueward of Lya (possibly due to narrow absorption features and inaccuracies in the wavelength calibration), the extracted spectra F,,, and Fy show the same qualitative behavior asobserved in the and line profiles.
Although the decomposition is less accurate due to structures in the continuum blueward of $\alpha$ (possibly due to narrow absorption features and inaccuracies in the wavelength calibration), the extracted spectra $F_{M\mu}$ and $F_{M}$ show the same qualitative behavior asobserved in the and line profiles.
Fig.
Fig.