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Specifically. t10 οbservec pulse width | in Eq. (1)) | Specifically, the observed pulse width $W$ in Eq. \ref{equ:smin}) ) |
is often likeY to |ο greaer than the itriusic whth Wine cluitted at fhe pulum because of the SCterme and clispersio iof]ulses 1w free electrous iu the interstellar iiecium. aux by t16 post-detection integratiou pertor1ued in the receiver. | is often likely to be greater than the intrinsic width $W_{\rm int}$ emitted at the pulsar because of the scattering and dispersion of pulses by free electrons in the interstellar medium, and by the post-detection integration performed in the receiver. |
The sampled pulse profile is the convolution of the intrinsic o»ilse width aud broadening functions due to dispersion. scattering aud integration aud is estimated from the followi19 quadrature sunm: where fiuup is the data saupling interval. fpx, is the dispersion broadeuing across one filterbank channel aud faan Is the imterstellar scatter broadeniug. | The sampled pulse profile is the convolution of the intrinsic pulse width and broadening functions due to dispersion, scattering and integration and is estimated from the following quadrature sum: where $t_{\rm samp}$ is the data sampling interval, $t_{\rm DM}$ is the dispersion broadening across one filterbank channel and $t_{\rm
scatt}$ is the interstellar scatter broadening. |
To lighlieht the effects of pulse broadoeni1 ο sensitivitv. im Fig. | To highlight the effects of pulse broadening on sensitivity, in Fig. |
2. we present the effective scusitivity as a function of period for a hypothetical pulsar with an intrinsic duty cvele of for asstmed DMsx of 0. 128 and 512 ?ppe. | \ref{fig:smin} we present the effective sensitivity as a function of period for a hypothetical pulsar with an intrinsic duty cycle of for assumed DMs of 0, 128 and 512 $^{-3}$ pc. |
The scaHops in the curves at short periods reflect the reduction in sensitivity due to the loss of higher-order harmonics in the Fourier spectrun (see | The scallops in the curves at short periods reflect the reduction in sensitivity due to the loss of higher-order harmonics in the Fourier spectrum (see |
with the closest angular approach between lens and source star being for a small 4. which occurs at epoch /o. | with the closest angular approach between lens and source star being for a small $\varphi$, which occurs at epoch $t_0$. |
Therefore. the signal of eclipsing microlensing resembles an normal. extended-source standard microlensing light curve. described by the + parameters fe. fo. vo. and py. | Therefore, the signal of eclipsing microlensing resembles an normal extended-source standard microlensing light curve, described by the 4 parameters $t_\rmn{E}$, $t_0$, $u_0$, and $\rho_\star$. |
For reference. the light curve of a binary system with the parameters of AJ=8.5ΔΙ. a main sequence star with the mass of m,=0.85 M..«=1Tau and y=0.33” is shown in Fig. 2.. | For reference, the light curve of a binary system with the parameters of $M = 8.5~M_\odot$, a main sequence star with the mass of $m_\star = 0.35~M_\odot$, $a= 17~\mbox{au}$ and $\varphi =
0.33\arcsec$ is shown in Fig. \ref{fig2}. |
This system has the tinite-size parameter p,=0.51 and the period of this system is about 23 years. | This system has the finite-size parameter $\rho_\star = 0.81$ and the period of this system is about $23$ years. |
Main-sequence stars are again disfavoured due to their long periods in detectable systems. whereas substantial signals can arise in systems with white dwarfs with much shorter periods. | Main-sequence stars are again disfavoured due to their long periods in detectable systems, whereas substantial signals can arise in systems with white dwarfs with much shorter periods. |
Let us now investigate the prospects for detecting compact objects by means of binary self-lensing for specitic observational strategies. | Let us now investigate the prospects for detecting compact objects by means of binary self-lensing for specific observational strategies. |
Modelled upon the characteristics of current. or upcoming microlensing campaigns. and giving us a hint on the roles of both photometric accuracy and sampling rate. we consider regular monitoring with the following parameters (seealso2): (a) 5 per cent photometric accuracy at 15 min cadence. indicative for high-cadence ground-based surveys (22). (b) 2. per cent accuracy at 2 hr cadence. roughly representative. of current. follow-up monitoring programmes (2).. and (ο) 0.3 per cent photometric accuracy at [5-min cadence. reflecting the coming state-of-the-art. including lucky-imaging or spaced-based observations (222). | Modelled upon the characteristics of current or upcoming microlensing campaigns, and giving us a hint on the roles of both photometric accuracy and sampling rate, we consider regular monitoring with the following parameters \citep[see also][]{rah}: (a) 5 per cent photometric accuracy at 15 min cadence, indicative for high-cadence ground-based surveys \citep{Sumi:planet,KMTNet}, (b) 2 per cent accuracy at 2 hr cadence, roughly representative of current follow-up monitoring programmes \citep{PLANET:EGS}, and (c) 0.3 per cent photometric accuracy at 15-min cadence, reflecting the coming state-of-the-art, including lucky-imaging or spaced-based observations \citep{Uffe:planets,Bennett:space1,Bennett:space2}. |
For main-sequence stars. we adopt the mass function £n.)οgin./M.)] proposed by ?.. namely which covers the range of ni,0.1.2]A.. while we assume a mass-radius relation 2,//2.o(m,/M.7 (2).. | For main-sequence stars, we adopt the mass function $\xi(m_\star) =
dN/d[\lg (m_\star/M_\odot)]$ proposed by \citet{chab03}, namely which covers the range of $m_\star\in[0.1,2]~ M_\odot$, while we assume a mass-radius relation $R_\star/R_\odot\simeq(m_\star/M_\odot)^{0.8}$ \citep{rmr}. |
For the compact objects. we adopt the product of the evolution of the zero-age mass function to the final stage of stars (2). with the mass range of AL¢1.2.15]AZ.. | For the compact objects, we adopt the product of the evolution of the zero-age mass function to the final stage of stars \citep{bel02}
with the mass range of $M\in[1.2,15]~M_\odot$. |
To estimate the fraction of binary systems with one compact object and one main sequence star. we do a rough calculation for stars in the binaries with the initial masses in the range of AJ«LA/. for the first star and McSAL. for the companion star. | To estimate the fraction of binary systems with one compact object and one main sequence star, we do a rough calculation for stars in the binaries with the initial masses in the range of $M<1 M_\odot$ for the first star and $M> 8M_\odot$ for the companion star. |
Star with the larger mass has a relative short life time and will evolve to a compact object while the smaller star stays in the main sequence if we don't have mass transfer between the two stars. | Star with the larger mass has a relative short life time and will evolve to a compact object while the smaller star stays in the main sequence if we don't have mass transfer between the two stars. |
For the binaries located far enough distance from each other (i.e. stellar size should be smaller than the roche lobe). we obtain almost 0.4 per cent of the stars will end to the binary systems with one compact object and a companion main sequence star, | For the binaries located far enough distance from each other (i.e. stellar size should be smaller than the roche lobe), we obtain almost $0.4$ per cent of the stars will end to the binary systems with one compact object and a companion main sequence star. |
For the orbital distance within the binary system. we assume a logarithmic distribution in the range of «0.01.50]au. in accordance with Oppik’s law. while the inclination angle is drawn uniformly from y©0.2]. | For the orbital distance within the binary system, we assume a logarithmic distribution in the range of $a\in [0.01,50]~\mbox{au}$, in accordance with Öppik's law, while the inclination angle is drawn uniformly from $\varphi \in [0,\upi/2]$. |
Using these parameter distributions. we generated synthetic light curves by means of Monte-Carlo simulations. where Figure 3 shows an example. | Using these parameter distributions, we generated synthetic light curves by means of Monte-Carlo simulations, where Figure \ref{lc_sim} shows an example. |
With a detection criterion of three consecutive data point being larger than three times of the standard deviation from the base line. we not only obtain the fraction of systems for which the compact object is detectable. but also the distribution of parameters of the expected eclipsing microlensing events. | With a detection criterion of three consecutive data point being larger than three times of the standard deviation from the base line, we not only obtain the fraction of systems for which the compact object is detectable, but also the distribution of parameters of the expected eclipsing microlensing events. |
Figure 4. shows the detection efticiency for the three considered monitoring strategies. | Figure \ref{effms} shows the detection efficiency for the three considered monitoring strategies. |
One finds that it depends only weakly on the mass of the lens. | One finds that it depends only weakly on the mass of the lens. |
This is a consequence of the relation between the lens mass A/ and the event time-scale fp=με ο. | This is a consequence of the relation between the lens mass $M$ and the event time-scale $t_\rmn{E} = R_\rmn{E}/v$ . |
With RexVM and epxomn,|M. one finds a weakly-varying fpxVM(AL|m,). | With $R_\rmn{E} \propto \sqrt{M}$ and $v_\perp \propto \sqrt{m_\star+M}$, one finds a weakly-varying $t_\rmn{E} \propto \sqrt{{M}/{(M + m_\star})}$. |
A larger mass m, of the main-sequence source star implies a larger radius //,. which diminishes the magnification due to the finite-size effect. | A larger mass $m_\star$ of the main-sequence source star implies a larger radius $R_\star$, which diminishes the magnification due to the finite-size effect. |
Moreover. the event time-scale becomes smaller. | Moreover, the event time-scale becomes smaller. |
On the other hand. a larger source radius /?, enables us to get a signal from a wider range of inclination angles. and the effective signal duration is increased. | On the other hand, a larger source radius $R_\star$ enables us to get a signal from a wider range of inclination angles, and the effective signal duration is increased. |
The gain from a longer signal duration plays a larger role for sparser | The gain from a longer signal duration plays a larger role for sparser |
higher annihilation cross sections or a lower particlemasses!?., a larger radius and a lower density are needed to balance the DM heating and the stellar luminosity (which scales as 17). | higher annihilation cross sections or a lower particle, a larger radius and a lower density are needed to balance the DM heating and the stellar luminosity (which scales as $R^2$ ). |
During the early stages of the DS evolution the dependence of the adiabatically contracted DM density on the concentration parameter is very small at least for the range we have considered here. | During the early stages of the DS evolution the dependence of the adiabatically contracted DM density on the concentration parameter is very small at least for the range we have considered here. |
As it can be seen from Fig.7.. prior to the onset of the KH contraction phase, the central baryon densities for models with different values of the concentration parameter have similar baryon density and DM density as well. | As it can be seen from \ref{bcd}, prior to the onset of the KH contraction phase, the central baryon densities for models with different values of the concentration parameter have similar baryon density and DM density as well. |
Models with a larger concentration parameter have slightly more dark matter, have slightly lower central DM densities, and are also more extended. | Models with a larger concentration parameter have slightly more dark matter, have slightly lower central DM densities, and are also more extended. |
Before the contraction phase, the central DM density of the c.=5 case’s density is lower than the c=2 case. | Before the contraction phase, the central DM density of the $c=5$ case's density is lower than the $c=2$ case. |
The radius is larger. | The radius is larger. |
Models with ditferent concentration parameters only begin to dramatically diverge once the star begins to contract and enters its Kelvin-Helmholz contraction phase. | Models with different concentration parameters only begin to dramatically diverge once the star begins to contract and enters its Kelvin-Helmholz contraction phase. |
At this point, the star begins to shrink, which cause the DM densities to increase dramatically. | At this point, the star begins to shrink, which cause the DM densities to increase dramatically. |
DS in halos with a larger concentration parameter have more DM and thus delay the onset of the KH phase. | DS in halos with a larger concentration parameter have more DM and thus delay the onset of the KH phase. |
For c=2, the contraction phase begins at /~0.23 Myr; See Fig.4. | For $c=2$, the contraction phase begins at $t\sim 0.28$ Myr; See \ref{radius}. |
. At this time, the stellar mass has reached ~1003... | At this time, the stellar mass has reached $\sim 700\msun$. |
For e=3.5 and 5, the contraction phase begins later. | For $c=3.5$ and 5, the contraction phase begins later. |
In the case of ¢=5, the star has a mass of ~8503.. | In the case of $c=5$, the star has a mass of $\sim850\msun$. |
Thus the contraction begins once the star is more massive. | Thus the contraction begins once the star is more massive. |
At à fixed stellar mass, the DM densities will differ dramatically between models which are in the contraction phase compared to those which are not contacting. | At a fixed stellar mass, the DM densities will differ dramatically between models which are in the contraction phase compared to those which are not contacting. |
For instance, let us consider à 150.U.. DS. | For instance, let us consider a $750 \msun$ DS. |
In the case of e=2, the star has entered the contraction phase. | In the case of $c=2$, the star has entered the contraction phase. |
While the cases with a larger concentration parameter (3.5.5) have yet to begin their contraction phase. | While the cases with a larger concentration parameter (3.5,5) have yet to begin their contraction phase. |
Hence the stars with a lareer concentration, have a lower DM density andare more extended, which can be seen in Fig. 9.. | Hence the stars with a larger concentration, have a lower DM density andare more extended, which can be seen in Fig. \ref{dmdens}. |
Finally, in Fig. | Finally, in Fig. |
11. we have plotted the amount of adiabatically contracted DM inside the DS as a function of time. | \ref{DM} we have plotted the amount of adiabatically contracted DM inside the DS as a function of time. |
One can also see that DM densities are many orders of magnitude lower than their baryonic counterparts at all times. | One can also see that DM densities are many orders of magnitude lower than their baryonic counterparts at all times. |
Although the amount of DM never exceeds 0.4... , | Although the amount of DM never exceeds $0.4 \msun$ , |
to the reference curve, the and the flow speed show conspicuous stepwise changes intensityassociated with the flare. | to the reference curve, the intensity and the flow speed show conspicuous stepwise changes associated with the flare. |
The rapid changes during the flare occur in as short as 40 minutes or less with change rates much larger than general evolution. | The rapid changes during the flare occur in as short as 40 minutes or less with change rates much larger than general evolution. |
The mean horizontal flow speed averaged in the ROI increases from 330+3.1 to 403+4.6ms!,, where the values and the errors are the mean and the standard deviation, respectively, of 9 data points in the time profile immediately before and after the flare. | The mean horizontal flow speed averaged in the ROI increases from $\pm$ 3.1 to $\pm$ 4.6, where the values and the errors are the mean and the standard deviation, respectively, of 9 data points in the time profile immediately before and after the flare. |
The difference of 73 iis more than 15 times the standard deviation of the data. | The difference of 73 is more than 15 times the standard deviation of the data. |
The changed sunspot structure and the enhanced sheared Evershed flow last for at least 1 hour with the available data indicating a permanent rather than a transient change as a result of the flare. | The changed sunspot structure and the enhanced sheared Evershed flow last for at least 1 hour with the available data indicating a permanent rather than a transient change as a result of the flare. |
It is worthwhile to point out that there is a noticeable increase of the sheared Evershed flow speed (from 303+4.0 to 330+3.1 ms!)) at 18:00 UT about 40 minutes before the flare. | It is worthwhile to point out that there is a noticeable increase of the sheared Evershed flow speed (from $\pm$ 4.0 to $\pm$ 3.1 ) at 18:00 UT about 40 minutes before the flare. |
We also examined the Michelson Doppler Imager (MDI) 96-min LOS magnetograms and found no increase of the total unsigned magnetic flux in the active region during and after the flare. | We also examined the Michelson Doppler Imager (MDI) 96-min LOS magnetograms and found no increase of the total unsigned magnetic flux in the active region during and after the flare. |
It implies that no considerable new flux emergence was involved in this flare. | It implies that no considerable new flux emergence was involved in this flare. |
We have presented the rapid stepwise sunspot structure change and enhancement of the sheared Evershed flow along the flaring neutral line associated with the X6.5 flare. | We have presented the rapid stepwise sunspot structure change and enhancement of the sheared Evershed flow along the flaring neutral line associated with the X6.5 flare. |
These are in the sense that they last for at least 1 changeshour after the permanentflare. | These changes are permanent in the sense that they last for at least 1 hour after the flare. |
Since no signature of new flux emergence was found throughout the event, we exclude the possibility that the enhancement of the sheared Evershed flow may be caused by emerging flux near the neutral line. | Since no signature of new flux emergence was found throughout the event, we exclude the possibility that the enhancement of the sheared Evershed flow may be caused by emerging flux near the neutral line. |
Considering that the penumbral structure and Evershed flow are strongly controlled by magnetic inclination or horizontal magnetic field, we attribute the observed rapid changes of sunspot structure and surface flow to photospheric magnetic restructuring due to the flare. | Considering that the penumbral structure and Evershed flow are strongly controlled by magnetic inclination or horizontal magnetic field, we attribute the observed rapid changes of sunspot structure and surface flow to photospheric magnetic restructuring due to the flare. |
The central enhanced sheared Evershed flow manifests a more horizontal sheared magnetic field in the photosphere near the flared neutral line. | The central enhanced sheared Evershed flow manifests a more horizontal sheared magnetic field in the photosphere near the flared neutral line. |
The decayed outer penumbrae indicate the weakening of the horizontal field in the outer region. | The decayed outer penumbrae indicate the weakening of the horizontal field in the outer region. |
HH images evidence that the originally fanning out field lines at the two sides of the neutral line get connected and contracted over the central region after the flare, which naturally results in overall weakening/strengthening of horizontal magnetic field in the outer/central region and consequently the decay/enhancement of the outer/central | H images evidence that the originally fanning out field lines at the two sides of the neutral line get connected and contracted over the central region after the flare, which naturally results in overall weakening/strengthening of horizontal magnetic field in the outer/central region and consequently the decay/enhancement of the outer/central penumbrae. |
Although the highly sheared horizontal fields in penumbrae.the photosphere that give rise to the sheared Evershed flow in the ROI are barely observed in HH images, the strengthening and contraction of the newly formed fields could be an indicator of the overalloverlying trend ofpotential the magnetic fields near the neutral line that become more horizontal after the flare. | Although the highly sheared horizontal fields in the photosphere that give rise to the sheared Evershed flow in the ROI are barely observed in H images, the strengthening and contraction of the newly formed overlying potential fields could be an indicator of the overall trend of the magnetic fields near the neutral line that become more horizontal after the flare. |
In summary, the observations fit well to the reconnection picture presented in Liuetal.(2005,Fig.12) and are consistent with recent magnetic observations and theoretical predictions of induced photospheric magnetic field change. | In summary, the observations fit well to the reconnection picture presented in \citet[][Fig.12]{LiuC+etal2005ApJ...622..722L} and are consistent with recent magnetic observations and theoretical predictions of flare-induced photospheric magnetic field change. |
Using GONG LOS magnetograms, Petrie&Sudol(2010) found that this X6.5 flare was associated with the most impressive stepwise magnetic flux changes and Lorentz force budget in their 77 flare samples studied. | Using GONG LOS magnetograms, \citet{Petrie+Sudol2010ApJ...724.1218P} found that this X6.5 flare was associated with the most impressive stepwise magnetic flux changes and Lorentz force budget in their 77 flare samples studied. |
Moreover, the spatial distribution of their estimated Lorentz force changes (Petrie&Sudol2010,Fig.16) is co-spatial with the decayed outer penumbral and the enhanced central neutral line regions as illustrated in this letter. | Moreover, the spatial distribution of their estimated Lorentz force changes \citep[][Fig. 16]{Petrie+Sudol2010ApJ...724.1218P} is co-spatial with the decayed outer penumbral and the enhanced central neutral line regions as illustrated in this letter. |
Their analysis of the direction of the Lorentz force change does suggest a contraction of the side field lines toward the neutral line resulting in a more horizontal magnetic field in the central region. | Their analysis of the direction of the Lorentz force change does suggest a contraction of the side field lines toward the neutral line resulting in a more horizontal magnetic field in the central region. |
Since larger flares tend to produce stronger field configuration changes that eventually result in stronger changes in WL structure and surface flow (e.g.,Liuetal.2005;Chenetal.2007;Petrie&Sudol 2010), we have not found other smaller Hinode observed events that show enhancement of the central sheared Evershed flow as prominent as this event so far, although some of them do show changes in direction or speed in some areas. | Since larger flares tend to produce stronger field configuration changes that eventually result in stronger changes in WL structure and surface flow \citep[e.g.,][]{LiuC+etal2005ApJ...622..722L, ChenW+etal2007ChJAA...7..733C, Petrie+Sudol2010ApJ...724.1218P}, we have not found other smaller Hinode observed events that show enhancement of the central sheared Evershed flow as prominent as this event so far, although some of them do show changes in direction or speed in some areas. |
For the 2006 December 13 X3.4 flare occurred in the same AR but in the southern part where sheared penumbral flows are also present, Tanetal.(2009) found, however, no increase of the shear flow after the flare. | For the 2006 December 13 X3.4 flare occurred in the same AR but in the southern part where sheared penumbral flows are also present, \citet{Tan+etal2009ApJ...690.1820T} found, however, no increase of the shear flow after the flare. |
The X3.4 event is different from the X6.5 event presented in this letter in many aspects. | The X3.4 event is different from the X6.5 event presented in this letter in many aspects. |
For the X3.4 event, the central sheared penumbrae involve complex “magnetic channel" structure (Wangetal.2008),, sunspot rotation, and new flux emergence, which make their structure and flow complicated, thus difficult to interpret. | For the X3.4 event, the central sheared penumbrae involve complex “magnetic channel” structure \citep{WangH+etal2008ApJ...687..658W}, sunspot rotation, and new flux emergence, which make their structure and flow complicated, thus difficult to interpret. |
With ground observation, Dengetal.(2006) detected clues of enhanced shear flow along the flaring neutral line right after the X10 flare on 2003 October 29 in NOAA AR 10486 using limited 18 minutes post-flare data. | With ground observation, \citet{Deng+etal2006ApJ...644.1278D} detected clues of enhanced shear flow along the flaring neutral line right after the X10 flare on 2003 October 29 in NOAA AR 10486 using limited 18 minutes post-flare data. |
Different from the sheared Evershed flow presented in this letter that mainly flows in one direction, the sheared penumbral flows in NOAA AR 10486 flow in opposite directions at the two sides of the neutral line. | Different from the sheared Evershed flow presented in this letter that mainly flows in one direction, the sheared penumbral flows in NOAA AR 10486 flow in opposite directions residing at the two sides of the neutral line. |
The anti-parallel or residingone-directional sheared penumbral flow depends on whether both umbrae of | The anti-parallel or one-directional sheared penumbral flow depends on whether both umbrae of |
and velocity. dispersions of early-type galaxies. which we postpone to future work. | and velocity dispersions of early-type galaxies, which we postpone to future work. |
Instead. the aim here is to show the what we can learn from the simultaneous comparison with the size and mass distribution of early-type galaxies. | Instead, the aim here is to show the what we can learn from the simultaneous comparison with the size and mass distribution of early-type galaxies. |
The orange. green. and blue contour levels in Figure 3 indicate the region of the size-mass plane containing68/A..95'4.. and of the whole SDSS sample of local carly- galaxies. respectively. | The orange, green, and blue contour levels in Figure \ref{fig|SizeMassRelation} indicate the region of the size-mass plane containing, and of the whole SDSS sample of local early-type galaxies, respectively. |
All the contour levels have been weighted by the appropriate Έως. as in 7. ancl ?.. | All the contour levels have been weighted by the appropriate $1/V_{\rm max}$ , as in \citet{Bernardi09} and \citet{ShankarBernardi}. |
The evan. vellow. and red contour levels contain the99.7%... and of the corresponding mock sample of local carly-tvpe galaxies [rom ?.. | The cyan, yellow, and red contour levels contain the, and of the corresponding mock sample of local early-type galaxies from \citet{Bower06}. |
Figure 3. plots the ? sample. and therefore. for consistency. we only adopt mock galaxies with DTor0.7. | Figure \ref{fig|SizeMassRelation}
plots the \citet{Hyde09a} sample, and therefore, for consistency, we only adopt mock galaxies with $B/T>0.7$. |
We have also checked that the mean trend and scatter in the predicted size-mass relation does not change significantly when adopting lower limits of the bulge component. such as 2/70.5. | We have also checked that the mean trend and scatter in the predicted size-mass relation does not change significantly when adopting lower limits of the bulge component, such as $B/T>0.5$. |
Ehe solid squares with error bars show the predicted 7median and. variances of the sizes at fixed stellar mass for the models. | The solid squares with error bars show the predicted median and variances of the sizes at fixed stellar mass for the models. |
We find that the mocel predicts an increasing size when moving from the lower to the highest masses up to Aa210M... | We find that the model predicts an increasing size when moving from the lower to the highest masses up to $\sim 2\times 10^9$. |
However. as seen in the Figure. at stellar masses above Maio210" M... at variance. with the data the model. prediets a strong Lattening in the predicted. size-mass relation. while ab Mau30771L AL... the sizes. start increasing. again. with. increasing stellar mass. | However, as seen in the Figure, at stellar masses above $\sim 2\times 10^9$ , at variance with the data the model predicts a strong flattening in the predicted size-mass relation, while at $\sim 3 \times 10^{11}$ , the sizes start increasing again with increasing stellar mass. |
Similar findings were also recently discussed by. 2.. | Similar findings were also recently discussed by \citet{GonzalezSAM08}. |
Not. only the observed ancl predicted: size-niass distributions differ in slope and zero point. but— also the predicted: scatter. (in. size at fixed. stellar mass or vice versa). is much larger than the observed. one. | Not only the observed and predicted size-mass distributions differ in slope and zero point, but also the predicted scatter (in size at fixed stellar mass or vice versa), is much larger than the observed one. |
Figure 32 clearly highlights the problem in the predicted: size-mass relation. already. noticed by some previous studies (c.e.. ?.. 2009a)). | Figure \ref{fig|SizeMassRelation} clearly highlights the problem in the predicted size-mass relation, already noticed by some previous studies (e.g., \citealt{GonzalezSAM08}, ). |
We will show below that despite some possible improvements towards reproducing the size and mass Functions. the Full match to the size-mass relation remains an extremely non-trivial task for the mocel. | We will show below that despite some possible improvements towards reproducing the size and mass functions, the full match to the size-mass relation remains an extremely non-trivial task for the model. |
The blue area in Figure 4 shows the ο predicted.size distribution forcarly- galaxies computed by counting the number of sources | The blue area in Figure \ref{fig|Models} shows the \citet{Bower06}
predictedsize distribution forearly-type galaxies computed by counting the number of sources |
continuum by 10 Jy at all frequencies to give a better fit to the spectrum calibrated from the telescope. | continuum by 10 Jy at all frequencies to give a better fit to the spectrum calibrated from the telescope. |
Reapplying a calibration file derived from this model of Uranus to Neptune shows that the Neptune measurement agrees with, the model to within across the full SPIRE band. | Reapplying a calibration file derived from this model of Uranus to Neptune shows that the Neptune measurement agrees with the model to within across the full SPIRE band. |
The Vesta model as provided by Mueller was shown to be lower than the measurement calibrated using Neptune and so we have increased the model spectrum that is used in the derivation of the spectrometer pipeline calibration by 1.2. | The Vesta model as provided by Mueller was shown to be lower than the measurement calibrated using Neptune and so we have increased the model spectrum that is used in the derivation of the spectrometer pipeline calibration by 1.2. |
We discuss the accuracy of the pipeline derived spectra further in Sect. 10.. | We discuss the accuracy of the pipeline derived spectra further in Sect. \ref{conclusions}. |
The measurement of the beam size of the photometer has been discussed in Sect. 2.. | The measurement of the beam size of the photometer has been discussed in Sect. \ref{initial}. |
The average beam derived for the three arrays has a near Gaussian core with a width of 18.1, 25.2 and 36.6 arcsec respectively all with an uncertainty of +5%.. | The average beam derived for the three arrays has a near Gaussian core with a width of 18.1, 25.2 and 36.6 arcsec respectively all with an uncertainty of $\pm$. |
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