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monitoring data. | monitoring data. |
For cach simulated clata set we calculate NM suchthat NAM>AAI* for 2xiX6. thus we do not specify between which pairs of images the observed changes should be seen. | For each simulated data set we calculate $\{\Delta M\}$ suchthat $\Delta M^{i}>\Delta M^{i-1}$ for $2\leq i\leq6$, thus we do not specify between which pairs of images the observed changes should be seen. |
We calculate the probability of finding a change in the dillerence lieht-curves of AM!>ANAL, magnitudes for all £ over ο.να luring any part ofthe period). | We calculate the probability of finding a change in the difference light-curves of $\Delta M^{i}>\Delta M_{obs}^{i}$ magnitudes for all $i$ over $0.15\eta_{period}$ (during any part of the period). |
The distributions are shown in the lower panel of figure 2.. | The distributions are shown in the lower panel of figure \ref{sample_length}. |
Larger sources are less likely to exhibit the observed variation over ~15'% of a given sample length. | Larger sources are less likely to exhibit the observed variation over $\sim$ of a given sample length. |
For example. while model source sizes of S£;0.0515. always exhibit the observed. level of microlensing variation over sample lengths z105,. the S=1.65, source attains these values less than of the time over a sample length of ~15015... | For example, while model source sizes of $S\la0.05\eta_{o}$ always exhibit the observed level of microlensing variation over sample lengths $\ga10\eta_o$, the $S=1.6\eta_o$ source attains these values less than of the time over a sample length of $\sim150\eta_o$. |
DUM]LAALosSnui) is convolved with Pyloss]9) to find This function is shown in the right-hand. panel of figure 3.. | $P_m(\{\Delta M\}>\{\Delta M_{obs}\}|S,\eta_{period})$ is convolved with $p_{\eta}(\eta_{period}|S)$ to find This function is shown in the right-hand panel of figure \ref{rad_prob}. |
We find that the large. rapid changes in the image magnitudes limit the source to be smaller than 0.25, at the level. | We find that the large, rapid changes in the image magnitudes limit the source to be smaller than $0.2\eta_o$ at the level. |
We note that the caleulation of the probabilities POAAM]LAMSUUS) assumes that £2,,({AAL}:NMUSnues) and puGtussud]9) ave independent. | We note that the calculation of the probabilities $P(\{\Delta M\}>\{\Delta M_{obs}\}|S)$ assumes that $P_m(\{\Delta M\}>\{\Delta M_{obs}\}|S,\eta_{period})$ and $p_{\eta}(\eta_{period}|S)$ are independent. |
This is à false assumption since the two functions have been calculated from the same data set; | This is a false assumption since the two functions have been calculated from the same data set. |
However. the observation of the Large scale variation (in the OGLE data) introduces largeB derivatives which increases the estimate of sample1 length.ὃν (over the estimate that would. be made from. the pre 1996 data alone. sealed by the relative monitoring periods). | However, the observation of the large scale variation (in the OGLE data) introduces large derivatives which increases the estimate of sample length (over the estimate that would be made from the pre 1996 data alone, scaled by the relative monitoring periods). |
In the case of a longer sample length. a source has more caustic network over which to undergo large-scale mücrolensing variation. | In the case of a longer sample length, a source has more caustic network over which to undergo large-scale microlensing variation. |
This results in the inference of a larger upper limit on source size than would be expected if the sampling length: were deduced. from. the. pre-1996 data alone. | This results in the inference of a larger upper limit on source size than would be expected if the sampling length were deduced from the pre-1996 data alone. |
Any bias introduced. by. the co-dependence of PAM]LAM ΓΡ. therefore results in more conservative (ie. | Any bias introduced by the co-dependence of $P_m(\{\Delta M\}>\{\Delta M_{obs}\}|S,\eta_{period})$ and $p_{\eta}(\eta_{period}|S)$ therefore results in more conservative (ie. |
larger) source-size limits than the case where the sample length and L[arge-scale variation were measured from cillerent data-sets. | larger) source-size limits than the case where the sample length and large-scale variation were measured from different data-sets. |
We have used. the distribution of microlensed. light-curve derivatives to find. probability. functions for the length. of caustic structure sampled: by monitoring observations of 2237|0305 as a function of assumed source size. | We have used the distribution of microlensed light-curve derivatives to find probability functions for the length of caustic structure sampled by monitoring observations of Q2237+0305 as a function of assumed source size. |
“Phe 1988 ight-curve peak had a height larger than 0.2 magnitudes. and a duration less than 0.02 of the monitoring period. | The 1988 light-curve peak had a height larger than 0.2 magnitudes, and a duration less than 0.02 of the monitoring period. |
At the level such a short peak can only be explained or à source with dimensions smaller than —0.0255,. | At the level such a short peak can only be explained for a source with dimensions smaller than $\sim$ $\eta_{o}$. |
In addition. monitoring by OGLE shows changes in dillerence ight-curves ranging from QO.S.—1.5 magnitudes over 2154 ol the monitoring period. | In addition, monitoring by OGLE shows changes in difference light-curves ranging from $\sim0.8-1.5$ magnitudes over $\sim$ of the monitoring period. |
We find that such rapid large scale changes can only be explained by à source that is smaller han ~0.25, confidence). | We find that such rapid large scale changes can only be explained by a source that is smaller than $\sim0.2\eta_{o}$ confidence). |
Lmportantly. these limits are independent of any assumption about mean microlens mass or galactic transverse velocity. | Importantly, these limits are independent of any assumption about mean microlens mass or galactic transverse velocity. |
The Einstein radius of the average microlens mass (n in Q2237|0305 is n,~1017Jimem. | The Einstein radius of the average microlens mass $\langle m\rangle$ in Q2237+0305 is $\eta_o\sim 10^{17}\sqrt{\langle m\rangle}\,cm$. |
In combination with our limits in 5. the assumption of stellar mass microlenses therefore.B impose. a limit+ ofB <2».10l21075em on the continuum. source size (consistent with the typical scale-size expected for à continuum emitting accretion disc | In combination with our limits in $S$ , the assumption of stellar mass microlenses therefore impose a limit of $\la 2\times10^{15}-2\times10^{16}\,cm$ on the continuum source size (consistent with the typical scale-size expected for a continuum emitting accretion disc |
our model to the measurement of the tangential shear in gravitational lensing. | our model to the measurement of the tangential shear in gravitational lensing. |
Finally, we discuss and summarize the main conclusions in Section 5. | Finally, we discuss and summarize the main conclusions in Section 5. |
Let us start with a brief review of the NFW approximation for DM haloes in cosmological N-body simulations (see also e.g. ?)). | Let us start with a brief review of the NFW approximation for DM haloes in cosmological $N$ -body simulations (see also e.g. \citealt{Lo01}) ). |
This is a simple function which provides a good description for the density profile inside the virial radius. | This is a simple function which provides a good description for the density profile inside the virial radius. |
Yet, it turns out to give wrong results for the external regions since it does not take into account the mean matter density of the Universe, which is the main contribution at large distances from the halo centre (see ?)). | Yet, it turns out to give wrong results for the external regions since it does not take into account the mean matter density of the Universe, which is the main contribution at large distances from the halo centre (see \citealt{Pr06}) ). |
The analytic expression for the NFW density profile is: 'This formula describes the internal profile region quite well (up to one virial radius approximately) and depends on two parameters: the characteristic density o" and the characteristic scale radius r;. | The analytic expression for the NFW density profile is: This formula describes the internal profile region quite well (up to one virial radius approximately) and depends on two parameters: the characteristic density $\rho_{s}^{\rmn{NFW}} $ and the characteristic scale radius $r_{s} $. |
The latter is the radius in which r?-pyrw(r) reaches its local maximum, i.e. S —2, and the former is just given by ps"=4pnrw(rs). | The latter is the radius in which $r^2\cdot\rho_{\rmn{NFW}}(r) $ reaches its local maximum, i.e. $ \frac{d \ \ln\rho(r)}{d \ln r}=-2$ , and the former is just given by $\rho_{s}^{\rmn{NFW}}=4\rho_{\rmn{NFW}}(r_s)$. |
mee)The NFW profile may also be described in terms of the virial mass Myir=M(<Ryir), and the concentration parameter c=Ryir/rs. | The NFW profile may also be described in terms of the virial mass $M_{\rmn{vir}}=M(<R_{\rmn{vir}}) $, and the concentration parameter $c \equiv R_{\rmn{vir}}/r_{s} $. |
The quantity Ey is the virial radius of the halo, defined as the radius of a sphere enclosing a given overdensity, the value adopted here is A= 340. | The quantity $R_{\rmn{vir}}$ is the virial radius of the halo, defined as the radius of a sphere enclosing a given overdensity, the value adopted here is $\Delta=340$ . |
Hence, the relation between the virial radius and the virial mass is Myir=7340ρRA. | Hence, the relation between the virial radius and the virial mass is $M_{\rmn{vir}}=\frac{4\pi}{3} 340 \ \bar{\rho} \ R_{\rmn{vir}}^3$. |
The NFW profile can now be written as follows: where s is the radial coordinate scaled to Ri, i.e. Ry. | The NFW profile can now be written as follows: where $s$ is the radial coordinate scaled to $R_{\rmn{vir}}$, i.e. $s \equiv r/R_{\rmn{vir}}$ . |
Note that ps*™ is now a function (in general) of both c and M,ir. | Note that $\rho_{s}^{\rmn{NFW}}$ is now a function (in general) of both $c$ and $M_{\rmn{vir}}$. |
In order to find this function, let us calculate the halo enclosed mass from the density NFW profile: Since My, is defined as the mass inside the virial radius, we have, It is straightforward to derive the expression for the characteristic density in terms of c and Miyi. | In order to find this function, let us calculate the halo enclosed mass from the density NFW profile: Since $M_{\rmn{vir}}$ is defined as the mass inside the virial radius, we have, It is straightforward to derive the expression for the characteristic density in terms of $c$ and $M_{\rmn{vir}}$. |
It turns out that pS*™ is actually a function of the concentration parameter only, i.e.: where the function g is defined as follows: Therefore, the mass inside a sphere of a given radius is completely given by the virial mass of the halo and its concentration: To describe the external regions of DM haloes, it is essential to decide the kind of function that must be added to the NFW approximation, in such a way that its contribution can be neglected in the inner parts. | It turns out that $\rho_{s}^{\rmn{NFW}}$ is actually a function of the concentration parameter only, i.e.: where the function $g$ is defined as follows: Therefore, the mass inside a sphere of a given radius is completely given by the virial mass of the halo and its concentration: To describe the external regions of DM haloes, it is essential to decide the kind of function that must be added to the NFW approximation, in such a way that its contribution can be neglected in the inner parts. |
A first attempt to improve this fit is proposed in ?.. | A first attempt to improve this fit is proposed in \citet{Pr06}. |
At very large radii the DM density profile should not tend to zero as the NFW profile does, but instead it should tend to the mean matter density of the Universe. | At very large radii the DM density profile should not tend to zero as the NFW profile does, but instead it should tend to the mean matter density of the Universe. |
Then, the modified profile is: The parameter p? is no longer given by Eq. ( | Then, the modified profile is: The parameter $\rho_{s}^{\rmn{mod}}$ is no longer given by Eq. ( |
5). | 5). |
If we use the condition (4) we obtain in this case: In addition, cosmological DM halo density profiles show a tiny or null influence on the concentration parameter at large distances (r> Rvir), so that the density profile in the halo outskirts can only depend on the remaining parameter Myi.. | If we use the condition (4) we obtain in this case: In addition, cosmological DM halo density profiles show a tiny or null influence on the concentration parameter at large distances $r>R_{\rmn{vir}}$ ), so that the density profile in the halo outskirts can only depend on the remaining parameter $M_{\rmn{vir}}$. |
Therefore, in order to approximate the transition to the outer regions we add a function f which depends only on s (i.e. on the virial radius, but not on the concentration). | Therefore, in order to approximate the transition to the outer regions we add a function $f$ which depends only on $s$ (i.e. on the virial radius, but not on the concentration). |
This makes Λάνιν theonly relevant parameter at largedistances from the halo centre. | This makes $M_{\rmn{vir}}$ theonly relevant parameter at largedistances from the halo centre. |
The new density profile approximation that we propose here is a simple extension of the NFW formula, i.e., | The new density profile approximation that we propose here is a simple extension of the NFW formula, i.e., |
predominantly determined by the intensity J, which is proportional to the absorbance of the structure. | predominantly determined by the intensity $I$, which is proportional to the absorbance of the structure. |
Then, the contribution of a given structure, at a given wavelength, is the product of the corresponding line intensity, J, in its spectrum, with a multiplying factor, f, representing its relative abundance in the dust. | Then, the contribution of a given structure, at a given wavelength, is the product of the corresponding line intensity, $I$, in its spectrum, with a multiplying factor, $f$, representing its relative abundance in the dust. |
The same factor applies to all members of a given family of structures, and the concatenation of these products constitute the model spectrum. | The same factor applies to all members of a given family of structures, and the concatenation of these products constitute the model spectrum. |
Taking as a benchmark the spectrum of NGC 1482 displayed in Smith et al. (2007), | Taking as a benchmark the spectrum of NGC 1482 displayed in Smith et al. \cite{smi07}, |
, and the nominal feature wavelengths listed by the same authors, we arrived, by trial and error, at the f factors in the last column of Table 1. | and the nominal feature wavelengths listed by the same authors, we arrived, by trial and error, at the $f$ factors in the last column of Table 1. |
The concatenated spectrum obtained in this way is presented in fig. | The concatenated spectrum obtained in this way is presented in fig. |
12, for the case where f(concatenated structures 3)=0. | 12, for the case where $f$ (concatenated structures 3)=0. |
For the sake of clarity, the maximum wavelength was limited at 20 jum and the line width was uniformly set at ~ 0.2um. Most lines then overlap their neighbours. | For the sake of clarity, the maximum wavelength was limited at 20 $\mu$ m and the line width was uniformly set at $\sim0.2 \mu$ m. Most lines then overlap their neighbours. |
It must be stressed that the software used here was optimised for small hydrocarbon molecules and, therefore, does not pretend to a wavelength accuracy better than a few percent, especially when applied to large structures, and when heavy heteroatoms are included. | It must be stressed that the software used here was optimised for small hydrocarbon molecules and, therefore, does not pretend to a wavelength accuracy better than a few percent, especially when applied to large structures, and when heavy heteroatoms are included. |
The study of galaxy groups can provide essential insight into galaxy formation. particularly because many groups are niuch less dvnamically evolved (han rich clusters and tius are closer to their earliest. conditions. | The study of galaxy groups can provide essential insight into galaxy formation, particularly because many groups are much less dynamically evolved than rich clusters and thus are closer to their earliest conditions. |
The densitv of formation environment. affects the dynamical evolution of galaxies: for example. the Iuminositv. and color distributions of galaxies differ in [ied versus group environments (Girardietal.2003). | The density of formation environment affects the dynamical evolution of galaxies; for example, the luminosity and color distributions of galaxies differ in field versus group environments \citep{girardi03}. |
. Furthermore. lor groups with large central members. (he properties of (he central galaxy. correlate. with properties of their | Furthermore, for groups with large central members, the properties of the central galaxy correlate with properties of their |
2002). | . |
. Its optical counterpart. wilh V~26 mae. was found (Walter&Matthews1997).. but no radio counterpart has been observed. | Its optical counterpart, with $\sim$ 26 mag, was found \citep{Walter97}, but no radio counterpart has been observed. |
A 505-ks observation revealed a featureless spectrum which can be well fitted by a blackbody. with apparent radius. εἰς— 4.4 km and temperature Z4,— 63 eV (Durwitzelal.2003).. and no N-rav modulation being found. | A 505-ks observation revealed a featureless spectrum which can be well fitted by a blackbody, with apparent radius = 4.4 km and temperature = 63 eV \citep{Burwitz03}, and no X-ray modulation being found. |
Ransometal.(2002) setted an upper limit on the pulsed fraction of ~4.5% confidence) for frequency < 50 Lz and frequency derivative —5x10!Ilsσσ !. whereas Burwilzetal.(2003) obtained an upper limit of (20 confidence)) on the pulsed fraction in the frequency range (10—50) Hz using data. | \citet{Ransom02} setted an upper limit on the pulsed fraction of $\sim$ confidence) for frequency $\lesssim$ 50 Hz and frequency derivative $-5\times10^{10}{\rm ~Hz~s^{-1}} \leq f \leq 0 {\rm
~Hz~s^{-1}}$ , whereas \citet{Burwitz03} obtained an upper limit of $\sigma$ confidence) on the pulsed fraction in the frequency range $(10^{-3}-50)$ Hz using data. |
Various efforts have been made to explain the observations inthe regime of normal neulron star. such as a two-component blackbody CIrümperetal.2003).. a neutron star with reflective surface (Burwitzetal.2003).. a magnetar with high kiek-velocityRuderman 2003).. à naked neutron star (Turollaetal.2004)... and a surface with strong magnetic field (vanAdelsbergοἱal.2005:Pérez-Azorin.Miralles&Pons2005). | Various efforts have been made to explain the observations inthe regime of normal neutron star, such as a two-component blackbody \citep{trumper03}, a neutron star with reflective surface \citep{Burwitz03}, a magnetar with high kick-velocity\citep{Mori03}, a naked neutron star \citep{tzd04}, and a surface with strong magnetic field \citep{vanA05,pmp05}. |
. But these models are [ar away [rom fitting the real data with reasonable emissivity. | But these models are far away from fitting the real data with reasonable emissivity. |
Summarily. several difficulties are in the normal neutron star models. ( | Summarily, several difficulties are in the normal neutron star models. ( |
1) Featureless spectrum could be hard to reproduce by a neutron star will an atmosphere of normal matter. | 1) Featureless spectrum could be hard to reproduce by a neutron star with an atmosphere of normal matter. |
Though strong magnetic liekl may smear oul some spectral features (Lai2001).. Cae consequent large spin down luminosity is not observed. ( | Though strong magnetic field may smear out some spectral features \citep{Lai01}, the consequent large spin down luminosity is not observed. ( |
2) Special geometry is needed (ο explain the noanodulation observation the pulsar should be aligned or we are situated al the stars polar direction. ( | 2) Special geometry is needed to explain the no-modulation observation — the pulsar should be aligned or we are situated at the star's polar direction. ( |
3) A normal neutron star of radius 17 km in the two-component moclel requires a very low-mass about 0.4M... | 3) A normal neutron star of radius 17 km in the two-component model requires a very low-mass about $0.4\msun$. |
The mechanism to form such a normal neutron star is still unknown. | The mechanism to form such a normal neutron star is still unknown. |
Alternatively. the X-ray observation alone may be understood by assiuning RN J1856 to be a low-mass bare strange quark star. aud Zhang.Nu&Zhang(2004) fitted well the X-ray data will a phenomenological spectral emissivity in a solid quark star model. | Alternatively, the X-ray observation alone may be understood by assuming RX J1856 to be a low-mass bare strange quark star, and \citet{zxz04} fitted well the X-ray data with a phenomenological spectral emissivity in a solid quark star model. |
However. the UV-optical observations revealed a seven times brighter source comparing to (hat derived from: X-ray observation. | However, the UV-optical observations revealed a seven times brighter source comparing to that derived from X-ray observation. |
What's missed here? | What's missed here? |
To overcome these difficulties. we present a model under low-mass quark star regime. | To overcome these difficulties, we present a model under low-mass quark star regime. |
A boundary laver around RA 195560 is proposed in this paper. which is optically thick for UV-optical radiation but is optically thin for N-ravy radiation. | A boundary layer around RX J1856 is proposed in this paper, which is optically thick for UV-optical radiation but is optically thin for X-ray radiation. |
We can obtain consistency with the observational data. as well as strong constrains on the stars magnetic field strength and spin period. through this approach. | We can obtain consistency with the observational data, as well as strong constrains on the star's magnetic field strength and spin period, through this approach. |
We consider the star to be a bare quark star which would be indicated by the featureless spectrum οί (he 505-ks Chandra data (Nu 2002).. | We consider the star to be a bare quark star which would be indicated by the featureless spectrum from the 505-ks data \citep{xu02}. . |
Since a bare quark star have quark | Since a bare quark star have quark |
direction of LBN 679, another PÀ structure Is located at about ἐξ1401235.0=—2:00. | direction of LBN 679, another $PA$ structure is located at about $\ell = 141\fdg35, b = -2\fdg60$. |
found that the northern part of LBN 677 1s associated with the exciting star HD 19820 at 1 kpe distance. | found that the northern part of LBN 677 is associated with the exciting star HD 19820 at 1 kpc distance. |
0.8 kpe distance were quoted for associated CO-emission(2). which we adopt in the following discussion. | 0.8 kpc distance were quoted for associated CO-emission, which we adopt in the following discussion. |
A circular average is difficult to apply to the large area of LBN 677 due to significant variations and the non-symmetric distribution of PA. | A circular average is difficult to apply to the large area of LBN 677 due to significant variations and the non-symmetric distribution of $PA$. |
Different signs of PA in different areas indicate changing properties throughout the entire region. | Different signs of $PA$ in different areas indicate changing properties throughout the entire region. |
We select the western part of LBN 677. where PA changes smoothly for modeling. | We select the western part of LBN 677, where $PA$ changes smoothly for modeling. |
Based on the central five pixels average. the best fit (Fig. 12) | Based on the central five pixels average, the best fit (Fig. ) |
gives a RM;« value of -150440 rad πι. | gives a $RM_{FS}$ value of $-150\pm$ 40 rad $^{-2}$. |
69% of the total polarized emission originates in the foreground. | 69% of the total polarized emission originates in the foreground. |
The depolarization factor ts f = 0.88. | The depolarization factor is $\mathit{f}$ = 0.88. |
The 2° diameter source gives a depth of 28 pe assuming a spherical shape. | The $\degr$ diameter source gives a depth of 28 pc assuming a spherical shape. |
With the 16 em brightness temperature of about 20 mK Ty we calculate EM = 137 pe em. | With the $\lambda$ 6 cm brightness temperature of about 20 mK $\rm T_{B}$ we calculate $EM$ = 137 pc $^{-6}$. |
Bj then is —3.0 uG and n, about 2.2 cm™. | $B_{\parallel}$ then is $-3.0~\mu$ G and $n_{e}$ about 2.2 $^{-3}$. |
The reddening measurement of the exciting star HD 19820 (£=I40@:12.b 1254) is about 0.82(2). | The reddening measurement of the exciting star HD 19820 $\ell = 140\fdg12, b = 1\fdg54$ ) is about 0.82. |
The Ha intensity is about 14 Rayleigh after subtracting a background level of 11 Rayleigh. | The $\alpha$ intensity is about 14 Rayleigh after subtracting a background level of 11 Rayleigh. |
We obtain £M as 233 pe οι by Eq. | We obtain $EM$ as 233 pc $^{-6}$ by Eq. |
3. | 3. |
Then By reduces to -2.3 wG and n, increases to 2.9 em7*. | Then $B_{\parallel}$ reduces to $-2.3~\mu$ G and $n_{e}$ increases to 2.9 $^{-3}$. |
The physical parameters from both methods are similar. | The physical parameters from both methods are similar. |
The best fit of P/;, for LBN 676 and LBN 679 ts around 70%. | The best fit of $PI_{fg}$ for LBN 676 and LBN 679 is around 70%. |
We found almost the same value also for LBN 677. which is unexpected in view of their different distances. | We found almost the same value also for LBN 677, which is unexpected in view of their different distances. |
If the polarized emissivity in this direction ts fairly constant. this may indicate that LBN 677 is also at about 2 kpe distance. | If the polarized emissivity in this direction is fairly constant, this may indicate that LBN 677 is also at about 2 kpc distance. |
For this distance By will change to —1.9 uG and n, to 14 em7. | For this distance $B_{\parallel}$ will change to $-1.9~\mu$ G and $n_{e}$ to 1.4 $^{-3}$. |
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