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The EIwnamicalstructural’ estimates are reasonably consistent Wwith {1ο “starburst” ages. indicating a relatively voung age | The `dynamical/structural' estimates are reasonably consistent with the `starburst' ages, indicating a relatively young age |
We performed the simulations with a mocilied and tested version of the Gadget-2 code (Springel2005). | We performed the simulations with a modified and tested version of the Gadget-2 code \citep{springel2005}. |
. As discussed in our previous papers (Drandao&deAraujo2010a.b.c).. (his choice is based on the collisionless nature of galaxies modeled by particles. and the method used by Gadget-2 to build the recursive tree in order to compute forces and potentials. | As discussed in our previous papers \citep{ca2009a,ca2009b,ca2009c}, this choice is based on the collisionless nature of galaxies modeled by particles, and the method used by Gadget-2 to build the recursive tree in order to compute forces and potentials. |
We have modified the Gadget-2 and replaced the Newtonian potential ancl acceleration bv (he expressions given by Ecuations (3)) aud (4)) just in the respective cocle’s instructions. | We have modified the Gadget-2 and replaced the Newtonian potential and acceleration by the expressions given by Equations \ref{moffat_equation2}) ) and \ref{moffat_aceleration2}) ) just in the respective code's instructions. |
We have extensively tested the code efficiency (ο calculate potentials via the tree method. using a (vpical initial snapshot composed by a disk embedded in a dark matter halo. | We have extensively tested the code efficiency to calculate potentials via the tree method, using a typical initial snapshot composed by a disk embedded in a dark matter halo. |
lt is worth noting that we included a halo only (o test the code accuracy. since in the probes of the ability of the DM gravity to generate spiral galaxies with flat rotation curves. without dark matter. the halo is not included in the simulations. | It is worth noting that we included a halo only to test the code accuracy, since in the probes of the ability of the BM gravity to generate spiral galaxies with flat rotation curves, without dark matter, the halo is not included in the simulations. |
The Newtonian and the Molfatian codes were set up with the tolerance parameter 9=0.8. maximizing the tree code's performance ancl softening length αμ=0.33 kpe for the dark halo aud /;=0.15 kpe for the barvonic disk. | The Newtonian and the Moffatian codes were set up with the tolerance parameter $\theta=0.8$, maximizing the tree code's performance and softening length $l_{\rm{dh}} = 0.33$ kpc for the dark halo and $l_{\rm{d}} = 0.15$ kpc for the baryonic disk. |
This set of softening lengths. vields conservation of the total energy better than other sets. | This set of softening lengths yields conservation of the total energy better than other sets. |
The procedure to choose the values for 8. fay, and /4, adopted here is analog to (hat used in our previous papers references therein). | The procedure to choose the values for $\theta$, $l_{\rm{dh}}$ and $l_{\rm{d}}$ adopted here is analog to that used in our previous papers \citep[][ and references therein]{ca2009a}. |
We have studied (μου models: model I à (vpical exponential-Spilzer disk with a clark | We have studied three models: model I a typical exponential-Spitzer disk with a dark |
certainly includes some "cosmic" With (V—Do at hand. M; was derived using equation (1)). which is calibration case A). | certainly includes some “cosmic” With $(V-I)_{\rm 0}$ at hand, $\overline{M}_I$ was derived using equation \ref{sbfrel}) ), which is calibration case A). |
Together with the measured 77;. this yielded the "null hypothesis" distance modulus (71—M)4. see Table l.. | Together with the measured $\overline{m}_I$, this yielded the “null hypothesis” distance modulus $(m-M)_A$ , see Table \ref{sbfresults}. |
Fig. | Fig. |
4 shows thumbnail images illustrating the SBF measurement procedure for two out of the 28 dEs with clear SBF signal. | \ref{thumbnails} shows thumbnail images illustrating the SBF measurement procedure for two out of the 28 dEs with clear SBF signal. |
25 of the 28 investigated galaxies had S/N>3 and entered our subsequent analysis. | 25 of the 28 investigated galaxies had $S/N>3$ and entered our subsequent analysis. |
Their absolute brightnesses are in the range —16.5«My<-I1.2 mag. their central surface brightnesses cover the regime 20.3<pay24.6 nag/aresec. | Their absolute brightnesses are in the range $-16.5<M_V<-11.2$ mag, their central surface brightnesses cover the regime $20.3<\mu_V<24.6$ $^2$. |
They occupy a colour range 0.8«(V—Dy1.10 nag. ideally suited for extending the Tonry colour range to the blue. | They occupy a colour range $0.8<(V-I)_0<1.10$ mag, ideally suited for extending the Tonry colour range to the blue. |
In Fig. | In Fig. |
5. we show that the null hypothesis SBF distance modulus does not correlate with the S/N of the SBF neasurement nor with the amount of background fluctuations BG. | \ref{biastest} we show that the null hypothesis SBF distance modulus does not correlate with the S/N of the SBF measurement nor with the amount of background fluctuations $BG$. |
ote the large range of BG values in Fig. 5.. | Note the large range of $BG$ values in Fig. \ref{biastest}. . |
This has three reasons: The first and main reason is related to the fact that BG is determined by fitting equation (3)) to the normalised sky background PS. | This has three reasons: The first and main reason is related to the fact that $BG$ is determined by fitting equation \ref{azimut2}) ) to the normalised sky background PS. |
For this fitting we have to exclude the same low wavenumber regime that is excluded for fitting the galaxy SBF amplitude Po. | For this fitting we have to exclude the same low wavenumber regime that is excluded for fitting the galaxy SBF amplitude $P_0$. |
Since BG is only a fraction of Po. this exclusion of low wavenumbers has a stronger effect on the fitting precision for BG than for fitting Po. | Since $BG$ is only a fraction of $P_0$, this exclusion of low wavenumbers has a stronger effect on the fitting precision for $BG$ than for fitting $P_0$. |
Indeed. the negative value for BG that is measured for FCC 215 (see Table 1. and Fig. 5)) | Indeed, the negative value for $BG$ that is measured for FCC 215 (see Table \ref{sbfresults} and Fig. \ref{biastest}) ) |
is a consequence of this low wavenumber exclusion. | is a consequence of this low wavenumber exclusion. |
The background PS in the remaining wavenumbers is predominantly noisedominated such that a formally negative value for BG ts fitted. | The background PS in the remaining wavenumbers is predominantly noisedominated such that a formally negative value for $BG$ is fitted. |
As a consequence of that. the SBF data with poor seeing (FWHM>0.85”") show a scatter in BG of 0.16 mag which ts almost twice as large as the scatter of 0.09 mag for the data with good seeing (FWHM<0.85”). see Fig. 5.. | As a consequence of that, the SBF data with poor seeing $>$ $''$ ) show a scatter in $BG$ of 0.16 mag which is almost twice as large as the scatter of 0.09 mag for the data with good seeing $<$ $''$ ), see Fig. \ref{biastest}. |
The second reason for the variation of BG is that the galaxies investigated span a considerable range in surface brightness (> 4 mag). | The second reason for the variation of $BG$ is that the galaxies investigated span a considerable range in surface brightness $>$ 4 mag). |
This leads to varying relative amounts of BG. given that the SBF signal in lower surface brightness regions is more strongly affected by sky background fluctuations. | This leads to varying relative amounts of $BG$, given that the SBF signal in lower surface brightness regions is more strongly affected by sky background fluctuations. |
The third reason is the somewhat varying fringing amplitude. both between different chips and different nights. see for example Fig. 2.. | The third reason is the somewhat varying fringing amplitude, both between different chips and different nights, see for example Fig. \ref{fringing}. |
We finally note that the sky background of the galaxy SBF data is done by the sky background PS image from the normalised galaxy light PS image. | We finally note that the sky background of the galaxy SBF data is done by the sky background PS image from the normalised galaxy light PS image. |
Only the 1s achieved by a PS. | Only the is achieved by a PS. |
To take the uncertainty arising from. the power-spectrum fit and from the sky fluctuation variability into account. we adopt the scatter of Py resulting from the subtraction of three different sky background PS images as error estimate of the SBF measurement. see the following Sect. 9.2... | To take the uncertainty arising from the power-spectrum fit and from the sky fluctuation variability into account, we adopt the scatter of $P_0$ resulting from the subtraction of three different sky background PS images as error estimate of the SBF measurement, see the following Sect. \ref{sbferrors}. |
The error of (1—M) has two equally important contributions: uncertainty in (V—Ὀρ and Po. The uncertainty in (V.—Do of 0.058 mag (see above) translates into a 0.26 mag distance uncertainty in the case of the empirically calibrated slope The error of Po was estimated in two I. | The error of $(m-M)$ has two equally important contributions: uncertainty in $(V-I)_{\rm 0}$ and $P_{\rm 0}$ The uncertainty in $(V-I)_0$ of 0.058 mag (see above) translates into a 0.26 mag distance uncertainty in the case of the empirically calibrated slope The error of $P_{\rm 0}$ was estimated in two 1. |
based on the Monte Carlo simulations presented in Mieske et al. (2003a)). | based on the Monte Carlo simulations presented in Mieske et al. \cite{Mieske03a}) ). |
For the median seeing of our data (0.75" ), interpolation of the simulation results for 0.5 and 1.0” for Fornax dEs and | hour integration yields the following uncertainties: 0.37 mag in the range -I]>My—-13 mag. 0.27 mag in the range -13>My-14.5 mag. and 0.20 mag in the range My<—14.5 mag. | For the median seeing of our data $''$ ), interpolation of the simulation results for 0.5 and $''$ for Fornax dEs and 1 hour integration yields the following uncertainties: 0.37 mag in the range $-11>M_V>-13$ mag, 0.27 mag in the range $-13>M_V>-14.5$ mag, and 0.20 mag in the range $M_V<-14.5$ mag. |
Note that the simulation errors are calculated for images of the same pixel scale than the one used here. | Note that the simulation errors are calculated for images of the same pixel scale than the one used here. |
The fainter VLT-FORS zero points assumed in the simulations are practically compensated by the larger integration times of our Magellan-IMACS 2. | The fainter VLT-FORS zero points assumed in the simulations are practically compensated by the larger integration times of our Magellan-IMACS 2. |
from the scatter of the fitted values for Po when subtracting the three different sky background power spectra. | from the scatter of the fitted values for $P_{\rm 0}$ when subtracting the three different sky background power spectra. |
This was an important double-check of the errors adopted from the simulations. because the fringing of the IMACS data represent an additional uncertainty source. apart from the photon noise and background galaxy fluctuations which had been included in the The maximum of both error estimates was adopted as error in Po. | This was an important double-check of the errors adopted from the simulations, because the fringing of the IMACS data represent an additional uncertainty source, apart from the photon noise and background galaxy fluctuations which had been included in the The maximum of both error estimates was adopted as error in $P_{\rm 0}$. |
For seven out of the 25 dEs investigated. the scatter from background subtraction was larger than the Monte Carlo estimate. see Table 1.. | For seven out of the 25 dEs investigated, the scatter from background subtraction was larger than the Monte Carlo estimate, see Table \ref{sbfresults}. |
The resulting mean error of 6—M) is 0.4] mag when adopting calibration case A). | The resulting mean error of $(m-M)$ is 0.41 mag when adopting calibration case A). |
There are four galaxies in the range —16.5<My-11.5 mag which were imaged twice in the course of our survey since they were located in the overlap of adjacent fields. | There are four galaxies in the range $-16.5<M_V<-11.5$ mag which were imaged twice in the course of our survey since they were located in the overlap of adjacent fields. |
The differences in Gn—M) between those double measurements ranged between 0.10 and 0.35 mag. | The differences in $(m-M)$ between those double measurements ranged between 0.10 and 0.35 mag. |
This is encouragingly low. indicating that our uncertainty estimates are on the conservative side. | This is encouragingly low, indicating that our uncertainty estimates are on the conservative side. |
A final test for observational biases before coming to the calibration is to look at the measured SBF amplitude 77; as a function of seeing. see Fig. 6.. | A final test for observational biases before coming to the calibration is to look at the measured SBF amplitude $\overline{m}_I$ as a function of seeing, see Fig. \ref{seeing}. |
Those two observables should be independent of each other. | Those two observables should be independent of each other. |
However. we do find a 2σ significant correlation inthe sense that bad seeing data have stronger 77. | However, we do find a $\sigma$ significant correlation inthe sense that bad seeing data have stronger $\overline{m}_I$ . |
We neither find a correlation between seeing and the background fluctuation amplitude BG nor between seeing and galaxy One possibility to qualitatively explain the trend of seeing with 77;is that a fit to the same seeing power spectrum yields | We neither find a correlation between seeing and the background fluctuation amplitude $BG$ nor between seeing and galaxy One possibility to qualitatively explain the trend of seeing with $\overline{m}_I$is that a fit to the same seeing power spectrum yields |
at any altitude. | at any altitude. |
Avila&Cuevas(2009)| demonstrated that this overestimation might be negligible or relevant stronely depending on the selected observational parameters namely telescope diameter. double-star angular separation and analysis. plane conjugation altitude. | \cite{avila09} demonstrated that this overestimation might be negligible or relevant strongly depending on the selected observational parameters – namely telescope diameter, double-star angular separation and analysis plane conjugation altitude. |
An analytical expression to caleulate the actual errors. induced. during eeneralized-SCLDATU data processing as well as a procedure for the correct. recalibration of CX. profiles. derived. from generalized-SCLDAR. observations were also provided. in Avila&Cuevas(2009). | An analytical expression to calculate the actual errors induced during generalized-SCIDAR data processing as well as a procedure for the correct recalibration of $_N^2$ profiles derived from generalized-SCIDAR observations were also provided in \cite{avila09}. |
.. This procedure has been alreacy applied. to. re-calibrate atmospheric optical turbulence profiles retrieved in Mt Graham (Masciadrietal.|2010)... Ll Teide (García-Lorenzo&Fucnsalicda 2011).. and San Pedro Alárrtir (Αναetal.POLL) observatories. | This procedure has been already applied to re-calibrate atmospheric optical turbulence profiles retrieved in Mt Graham \citep{masciadri10}, El Teide \citep{garcia11}, , and San Pedro Márrtir \citep{avila11} observatories. |
The atmospheric optical turbulence monitoring progranune at the Roque de los Aluchachos —Observatory (ORAL hereafter) started in 2004. | The atmospheric optical turbulence monitoring programme at the Roque de los Muchachos Observatory (ORM hereafter) started in 2004. |
The classical data processing (dIxluckersetal.L998) sce e.g.] was performed to retrieved the CS profiles from the generalized-SCIDAT observations assuming negligible errors induced in the data treatment. | The classical data processing \citep{kluckers98}[ [see e.g.] was performed to retrieved the $_N^2$ profiles from the generalized-SCIDAR observations assuming negligible errors induced in the data treatment. |
Results derived. from the CX. profiles in. the ORAL database: were already published: (Castro-Almazan6al.2007:Fuensalicdaet2007.2004a.b) before the Avila&Cuevas(2009) work. | Results derived from the $_N^2$ profiles in the ORM database were already published \citep{castro09, garcia09b, garcia07, salida07, salida04a, salida04b} before the \cite{avila09} work. |
In this paper. we present the database of atmospheric optical turbulence profiles recorded at the ORAL through eeneralized-SCLDAR. observations. the argest database of (hb) for an astronomical site that has oen published: so far. | In this paper, we present the database of atmospheric optical turbulence profiles recorded at the ORM through generalized-SCIDAR observations, the largest database of $_N^2$ (h) for an astronomical site that has been published so far. |
We also perform the recalibration of the CX profiles in the ORAL database to compensate or the errors introduced. curing data. processing. | We also perform the recalibration of the $_N^2$ profiles in the ORM database to compensate for the errors introduced during data processing. |
We analyze the implications in the statistical results. cerived rom this database before and. after. the recalibration. | We analyze the implications in the statistical results derived from this database before and after the recalibration. |
Section. 822 presents the database of CX profiles. derived rom egeneralized-SCTIHDATi measurements at the ORAL | Section 2 presents the database of $_N^2$ profiles derived from generalized-SCIDAR measurements at the ORM. |
Me also calculate the impact of the cata processing error on retrieved. CX. profiles and. re-calibratethe full database ollowing the proposed procedure in Avila&Cuevas(2009). | We also calculate the impact of the data processing error on retrieved $_N^2$ profiles and re-calibratethe full database following the proposed procedure in \cite{avila09}. |
. Section 833 analvzes the implications of the CX. database recalibration on results derived. (rom. profiles. | Section 3 analyzes the implications of the $_N^2$ database recalibration on results derived from profiles. |
Conclusions are summarized in section S44. | Conclusions are summarized in section 4. |
The ORAL is located. at an altitude of ~2396 meters above sea level(asf hereafter). at. latitude 28°46’ N and longitude 17753! W on the island. of La Palma (Canary Islands. Spain). | The ORM is located at an altitude of $\sim2396$ meters above sea level hereafter), at latitude $28^0 46'$ N and longitude $17^0 53'$ W on the island of La Palma (Canary Islands, Spain). |
"This astronomical site was one of the final candidates to locate the European Extremely. Large Telescope. (432m-EIZLT). | This astronomical site was one of the final candidates to locate the European Extremely Large Telescope (42m-EELT). |
X monitoring program of the atmospheric turbulence structure at the ORAL began. in 2004 using the egeneralized-SCIDAR. technique. | A monitoring program of the atmospheric turbulence structure at the ORM began in 2004 using the generalized-SCIDAR technique. |
The 1-m Jacobus Ixaptevn Telescope was used. in combination with the Cute-SCIDAIC instrument (llocecmannοἱal.2004:Fuensalidactal.2004¢) developed at the Instituto cde Astrofissica cle Canarias (Tenerife. Canary Islancls. Spain). | The 1-m Jacobus Kapteyn Telescope was used in combination with the Cute-SCIDAR instrument \citep{ho04, salida04c} developed at the Instituto de sica de Canarias (Tenerife, Canary Islands, Spain). |
Each detector pixel. of οουσΗΛ instrument covers a square 1.9035 cm in size on the l1-m Jacobus lxaptevn Telescope pupil. | Each detector pixel of Cute-SCIDAR instrument covers a square 1.935 cm in size on the 1-m Jacobus Kapteyn Telescope pupil. |
Phe gencralized-SCIDAR data were processed using the traditional procedure (IxIuckersetal.1998). see e.g.] of deriving the normalized autocovariance [rom a series of scintillation patterns (1000 images in ORAL case). | The generalized-SCIDAR data were processed using the traditional procedure \citep{kluckers98}[ [see e.g.] of deriving the normalized autocovariance from a series of scintillation patterns (1000 images in ORM case). |
The autocovariance peaks allow the determination of CX 1) using a numerical inversion. | The autocovariance peaks allow the determination of $_N^2$ (h) using a numerical inversion. |
The CX(h) svsteniatic campaigns at ORAL were carried out from February 2004 to October 2006 and from January 2008 to August 2009 with a requeney of about 4-6 nights per month. | The $_N^2$ (h) systematic campaigns at ORM were carried out from February 2004 to October 2006 and from January 2008 to August 2009 with a frequency of about 4-6 nights per month. |
Useful generalizedSCIDAR. observations were obtained in 211 nights during hese campaiüns and 197035 individual C3- proliles constitute he database of turbulence profiles at ORAL (see table 13). he largest Cx. database published until now. | Useful generalized-SCIDAR observations were obtained in 211 nights during these campains and 197035 individual $_N^2$ profiles constitute the database of turbulence profiles at ORM (see table \ref{tab1}) ), the largest $_N^2$ database published until now. |
The dome and mirror turbulence contribution was removed from all the wofiles using the procedure in Fuensalidaetal.(2008). | The dome and mirror turbulence contribution was removed from all the profiles using the procedure in \cite{salida08}. |
. AX set of 19 clouble-stars (see table 2)) were selected ο carry out the eeneralized-SCIDAR. observations at. the ORAL | A set of 19 double-stars (see table \ref{stars}) ) were selected to carry out the generalized-SCIDAR observations at the ORM. |
The double-stars selection was based on: (1) apparent magnitude of the primary star brighter. than 6.5 and double-star magnitude cillerence smaller than 2.5. in order to garantce an appropiate signal-to-noise in the autocovariance peaks: (2) double-star angular separations in the range [rom 4.2 to 10 aresec. to ensure that the SCLDAR maximum altitude is high. enough to detect all turbulent lavers. | The double-stars selection was based on: (1) apparent magnitude of the primary star brighter than 6.5 and double-star magnitude difference smaller than 2.5, in order to garantee an appropiate signal-to-noise in the autocovariance peaks; (2) double-star angular separations in the range from 4.2 to 10 arcsec, to ensure that the SCIDAR maximum altitude is high enough to detect all turbulent layers. |
After a few months of operations showing that most of the turbulence was concentrated in low-altituce lavers. we increase the range of double-star angular separation to 16.5 aresec to better sample low-altitude turbulence structure: (3) clouble-star declination in the range between 2 anc 56 degrees. allowing generalized οςΗΛ measurements at zenith angles shorter than 30": and (4) a variety of double-star right ascension. to allow a Lull monitoring of the atmospheric turbulence structure along seasons. | After a few months of operations showing that most of the turbulence was concentrated in low-altitude layers, we increase the range of double-star angular separation to 16.5 arcsec to better sample low-altitude turbulence structure; (3) double-star declination in the range between 2 and 56 degrees, allowing generalized SCIDAR measurements at zenith angles shorter than $^0$; and (4) a variety of double-star right ascension, to allow a full monitoring of the atmospheric turbulence structure along seasons. |
The selected double-star svstems allow to retrieved CX(Bh) with vertical resolutions (Avilaetal.1998). κου c.g. at groumn (GNIQO)) that ranges from ~195 to ~1314 meters. | The selected double-star systems allow to retrieved $_N^2$ (h) with vertical resolutions \citep{avila98}[ [see e.g.] at ground $\Delta H$ (0)) that ranges from $\sim$ 195 to $\sim$ 1314 meters. |
The typical AZI(0) for Generalized SCIDAIU observations is about 1000 meters. | The typical $\Delta H(0)$ for Generalized SCIDAR observations is about 1000 meters. |
The observations carried. out at ORA are split. in two groups according to AZL(0). | The observations carried out at ORM are split in two groups according to $\Delta H(0)$. |
Lerealter Generalized οςΕΛ observations obtained with a 2N(0) ower and higher than 500 meters will be referred. to as ugh- and low-resolution modes. respectively. | Hereafter Generalized SCIDAR observations obtained with a $\Delta H(0)$ lower and higher than 500 meters will be referred to as high- and low-resolution modes, respectively. |
Generalized SCIDAR. data recorded using hieh vertical resolution are limited. to turbulence structures up to ~17 km (only ~17% of the profiles were obtained in high-vertical resolution mode). while data obtain in low vertical resolution (AZO)c 500 meters) reaches well above 20 km at the dem Jacobus Ixaptevn telescope (constituting ~s83% of the woliles in the ORAL database). | Generalized SCIDAR data recorded using high vertical resolution are limited to turbulence structures up to $\sim17$ km (only $\sim$ of the profiles were obtained in high-vertical resolution mode), while data obtain in low vertical resolution $\Delta H(0)>$ 500 meters) reaches well above 20 km at the 1-m Jacobus Kapteyn telescope (constituting $\sim$ of the profiles in the ORM database). |
Due to the shift between the pupil footprints of the two stars on the detector (see Fig. | Due to the shift between the pupil footprints of the two stars on the detector (see Fig. |
| in Garcta-Lorenzo&Fucn-salida (2011))) during eeneralized-SCIDAR. observations. the derived CX. intensities are indeed. an overestimation of the actual turbulence streneth (Avila&Cuevas 2009).. | 1 in \cite{garcia11}) ) during generalized-SCIDAR observations, the derived $_N^2$ intensities are indeed an overestimation of the actual turbulence strength \citep{avila09}. . |
This overstimation is induced during data processing and strongly depends. on the selected: cdouble-stars ancl the analysis planes combinations as well as on the telescope diameter. | This overstimation is induced during data processing and strongly depends on the selected double-stars and the analysis planes combinations as well as on the telescope diameter. |
‘Table 2shows the different observational configurations of the eeneralized-SCLDAR. observations carried oul at the Lm Jacobus Kaptevn telescope and. | Table \ref{stars} shows the different observational configurations of the generalized-SCIDAR observations carried out at the 1-m Jacobus Kapteyn telescope and, |
and interpulse. within (he measurement error. | and interpulse, within the measurement error. |
It may be of interest to note that in the X-ray pulse profile the (railing edees of the pulse as well as the interpulse are distinctly. steeper than their leading edges. | It may be of interest to note that in the X-ray pulse profile the trailing edges of the pulse as well as the interpulse are distinctly steeper than their leading edges. |
This does not appear to be the case for the optical interpulse. | This does not appear to be the case for the optical interpulse. |
If the X-rav (o radio lag were a true phase lag. attributable to the (radial) energy distribution across a cone. will the pulses occurring near the cone edges. one would expect ihe placement to be symmetrical. ie.. one X-ray pulse to be leading. the other trailing. | If the X-ray to radio lag were a true phase lag, attributable to the (radial) energy distribution across a cone, with the pulses occurring near the cone edges, one would expect the placement to be symmetrical, i.e., one X-ray pulse to be leading, the other trailing. |
As ib stands. both. X-ray. pulses are leading by (he same amounl. | As it stands, both X-ray pulses are leading by the same amount. |
The simplest explanation for (his phenomenon is that we are dealing with a time delay reflecting a pathleneth difference: (he radio pulses originate approximately LOO km closer to the surface of (he neutron star. as already suggested by Masnouetal.(1994). | The simplest explanation for this phenomenon is that we are dealing with a time delay reflecting a pathlength difference: the radio pulses originate approximately 100 km closer to the surface of the neutron star, as already suggested by \citet{masn1994}. |
. We 5gratefully acknowledge5 the efforts of Edward Morgan5 ancl Robert Shirev to keep up wilh constructing pulsar fold mode configurations as the pulsar slowed down. | We gratefully acknowledge the efforts of Edward Morgan and Robert Shirey to keep up with constructing pulsar fold mode configurations as the pulsar slowed down. |
We are indebted to the RNTE-GOF for maintaining the RATE fine clock correction file. tde.cdat. | We are indebted to the RXTE-GOF for maintaining the RXTE fine clock correction file, tdc.dat. |
We are 5grateful to Robert Pritehard and Mark Roberts for maintaining5 the Jodrell Bank Crab (timing5 ephemerides. | We are grateful to Robert Pritchard and Mark Roberts for maintaining the Jodrell Bank Crab timing ephemerides. |
We (hank | We thank |
radial wave number &Cr.7.0) from the corresponding equation of motion: where ry=2M is the ratio of the event horizon. | radial wave number $k(r,l,\omega)$ from the corresponding equation of motion: where $r_H=2M$ is the ratio of the event horizon. |
Now. let us derive the temperature of the black hole firstly. | Now, let us derive the temperature of the black hole firstly. |
Using the S-wave approximation correspouding to eq.(15)). we lave We should derive the outgoing wave function of o in both outside and inside of the black hole. | Using the S-wave approximation corresponding to \ref{k}) ), we have We should derive the outgoing wave function of $\phi$ in both outside and inside of the black hole. |
The incoming wave function of o reads Iu the above expression. the iutegration nrieμάτισαμιςrg) is actually of the so called the tortoise coordinate 5/7=r|πμανμέν) used in τοῦ, expect an muimportant coustant. | The incoming wave function of $\phi$ reads In the above expression, the integration $\int^r_c r/(r-r_H)
dr=r-c+r_H\ln ((r-r_H)/(c-r_H))$ is actually of the so called the tortoise coordinate $r^\ast=r+r_H\ln ((r-r_H)/r_H)$ used in , expect an unimportant constant. |
We set £4forfarμα=v which is like the usual L..advanced Eddingtion-Fiukelsteiu coordiautes. | We set $t+\int^r_c r/(r-r_H) dr=\nu $ which is like the usual advanced Eddingtion-Finkelstein coordiantes. |
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