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οςLUpoleus appearing at velocities of —160 to —200 kin Land —135 kis 1 are located within a few hundred parsecs of the GC. | components appearing at velocities of $-$ 160 to $-$ 200 km $^{-1}$ and $-$ 135 km $^{-1}$ are located within a few hundred parsecs of the GC. |
In the injer Galaxy. atomic gas Is most often associated with regions of molecular gas where it serves 10 shied the molecular gas agalust »hotodissociation (Dickey Lockinan 1990). | In the inner Galaxy, atomic gas is most often associated with regions of molecular gas where it serves to shield the molecular gas against photodissociation (Dickey Lockman 1990). |
Therefore. H] absorption features not described above 1uay be idenified with known GC molecular emission [ealures usiug correlatious in velocity stricture. | Therefore, HI absorption features not described above may be identified with known GC molecular emission features using correlations in velocity structure. |
The CO survey carried out by Oka et al. ( | The CO survey carried out by Oka et al. ( |
1998) usiig the Nojevauma .o-ur telescope provides the most [favorable resolution. velocity. aud spatial C"verage oL aLy σιrvey of molecular gas within the central Galaxy. | 1998) using the Nobeyama 45-m telescope provides the most favorable resolution, velocity, and spatial coverage of any survey of molecular gas within the central Galaxy. |
Iu addition. the multitude of “forbidden” (e.g. sigu opposite to galactic rotation) veουν components iu the GC region are thought to represeit the respouse of the molecular gas iu the GC to the Galaxys stroig stellar bar (Binney οἱ al. | In addition, the multitude of “forbidden” (e.g. sign opposite to galactic rotation) velocity components in the GC region are thought to represent the response of the molecular gas in the GC to the Galaxy's strong stellar bar (Binney et al. |
1991: Bally et al. | 1991; Bally et al. |
LOSS). | 1988). |
Tie. CO survey data of Oka et al. ( | The CO survey data of Oka et al. ( |
1998). illstrated that the molecular gas taced by CO elission iu the central 200 pc is organized iutο filaijentary and shell-like features. | 1998) illustrated that the molecular gas traced by CO emission in the central 200 pc is organized into filamentary and shell-like features. |
This morphology ald kijet1c stricture indicates that violent kiiletic activity (such as supernova explosiois and stellar wluds from Wolt-Bayet type stars) plays an iiiportaut role in shaping the ISAL. | This morphology and kinetic structure indicates that violent kinetic activity (such as supernova explosions and stellar winds from Wolf-Rayet type stars) plays an important role in shaping the ISM. |
In aclclition to the hadio Are reeion (where the Quiutupet aud. Arcles clusters are located). the GC region is fillec wlth sites whe‘e compact thermal radio and inid-iufrared sources have been observed (e.g. Ser B. Serie C. aud at uauvy positions along the Calaetie plane: e.g.. Laltosa et al. | In addition to the Radio Arc region (where the Quintuplet and Arches clusters are located), the GC region is filled with sites where compact thermal radio and mid-infrared sources have been observed (e.g. Sgr B, Sgr C, and at many positions along the Galactic plane; e.g., LaRosa et al. |
2000: Egan et al. | 2000; Egan et al. |
1995 al Lit is likely hat massive stars are eiher foriing or have formed in these regions. | 1998) and it is likely that massive stars are either forming or have formed in these regions. |
Iu addition. the spectrum of cli[use X-ray emission in this regiou suggests that the ISM is being strongly influence bst qnasslve staforming activities (Wang. Cothelf Lang 2002: Wane. Doug Lang 2006). | In addition, the spectrum of diffuse X-ray emission in this region suggests that the ISM is being strongly influenced by massive star-forming activities (Wang, Gotthelf Lang 2002; Wang, Dong Lang 2006). |
HI absorption toward the bright SerA ccdLiplex aud the compact SgrÁ* radio source has beet the sibjeet of a number of interferometric stidies over the last three clecacdes (Badlakrishnan et al. | HI absorption toward the bright SgrA complex and the compact $^*$ radio source has been the subject of a number of interferometric studies over the last three decades (Radhakrishnan et al. |
1972. Schwa*. Ekers Coss 1982. Liszt et al. | 1972, Schwarz, Ekers Goss 1982, Liszt et al. |
1983: Dwarakanath et al. | 1983; Dwarakanath et al. |
2001). | 2004). |
These studies illust"ate the wide variety of absorption au enission features towalc this complex. area of the Galaxy. many o “which have velocities that ineicate non-circular motions. | These studies illustrate the wide variety of absorption and emission features toward this complex area of the Galaxy, many of which have velocities that indicate non-circular motions. |
On larger scales. Laseuby. Li1361by Yusel-Zadeh (1989) carried out the first VLA compact configration HI absorption study toward the cent‘al of the QC (corresponcliug to τὸ pe at a distance c LS kpc (Bekl et al. | On larger scales, Lasenby, Lasenby Yusef-Zadeh (1989) carried out the first VLA compact configuration HI absorption study toward the central of the GC (corresponding to 75 pc at a distance of 8 kpc (Reid et al. |
1993)). cente'ed on the well-known Radio Are uonthermal filaments anc includiο the bright SerA complex. | 1993)), centered on the well-known Radio Arc nonthermal filaments and including the bright SgrA complex. |
Tle spatial rescAution was 20-70" with a veocity resolution of 10.2τν witha total velocity verage of 660L. | The spatial resolution was $\sim$ with a velocity resolution of 10.2, with a total velocity coverage of 660. |
However. tlis spatial resolution o ule Lasenby et al. ( | However, this spatial resolution of the Lasenby et al. ( |
1989) data is not equate or detailed comparisons wit1 higher frequency continttun aud recombination liue datasets the HII regins in the Radio Are (e.e.. Lang e al. | 1989) data is not adequate for detailed comparisons with higher frequency continuum and recombination line datasets of the HII regions in the Radio Arc (e.g., Lang et al. |
1997. 2001) ancl ν'elocity. inormation on the 10izing sellar clusters. | 1997, 2001) and velocity information on the ionizing stellar clusters. |
Iu. acklition. he spatial coverage cid 1ot iuclude the active Ser B region. | In addition, the spatial coverage did not include the active Sgr B region. |
Athough high spatial resolution VLA HI absorption measurements have been mace toward several indivicdtua GC sources (e.g.. Uchida e al. ( | Although high spatial resolution VLA HI absorption measurements have been made toward several individual GC sources (e.g., Uchida et al. ( |
1992) and Roy e al. ( | 1992) and Roy et al. ( |
2003)). a complete HI absorption sluly is djissiug [rom the growing canon of GC surΝΘΥΣ. | 2003)), a complete HI absorption study is missing from the growing canon of GC surveys. |
"Therefore. we have carried out an HI absorption survey of the central κου (250 x 125 pc) | Therefore, we have carried out an HI absorption survey of the central $\times$ (250 x 125 pc) |
change is very small compared to that between Galactic and SAIC’ abundanees. | change is very small compared to that between Galactic and `SMC' abundances. |
The present discussion. of the relationship between temperature and. spectral tvpe in the recuced-metallicity environment. of the SMC has immediate implications for the eriteria used. to allocate. luminosity classes. | The present discussion of the relationship between temperature and spectral type in the reduced-metallicity environment of the SMC has immediate implications for the criteria used to allocate luminosity classes. |
At given spectral twpe. the temperature of an A-type SAIC star is lower than its Galactic counterpart: as a consequence. the 115 equivalent width will be different in the SAIC star. | At given spectral type, the temperature of an A-type SMC star is lower than its Galactic counterpart; as a consequence, the $\gamma$ equivalent width will be different in the SMC star. |
For example. Figure 13. shows the model Le line for =O000K. = Z. and —8500lx. = E = 2.0). corresponding to Galactic and SAIC A2 spectra. respectively: the EI, equivalent width is some 304 larger in the SAIC case. | For example, Figure \ref{ew} shows the model $\gamma$ line for = 9000K, = $_{\odot}$ and = 8500K, = $_{\odot}$ (at = 2.0), corresponding to Galactic and SMC A2 spectra, respectively; the $\gamma$ equivalent width is some $\%$ larger in the SMC case. |
This is not (directly) a metallicity ellect. as the Ες lines for Galactic and SAIC metallicities are essentially identical at fixed temperature. | This is not (directly) a metallicity effect, as the $\gamma$ lines for Galactic and SMC metallicities are essentially identical at fixed temperature. |
Table ο summarizes the differences in H. equivalent widths for stars of spectral twpes BsAT (averaged over al a given temperature). | Table \ref{factor} summarizes the differences in $\gamma$ equivalent widths for stars of spectral types B8–A7 (averaged over at a given temperature). |
In eencral. equivalent widths are —10 30% Larger in the svnthetic SAIC spectra than in Galactic models at the same spectral type (but sof the same temperature). | In general, equivalent widths are $\sim$ $\%$ larger in the synthetic SMC spectra than in Galactic models at the same spectral type (but the same temperature). |
Note that the equivalent widths are larger in aff of the SMC spectra: in contrast to A-type dwarls where the equivalent width of the Balmer lines reaches a maximum around AO/A2. the maximum for supergiants occurs at a much later type (e.g.2). resulting in a positive ellect throughout the spectral types in Table 13.. | Note that the equivalent widths are larger in $all$ of the SMC spectra; in contrast to A-type dwarfs where the equivalent width of the Balmer lines reaches a maximum around A0/A2, the maximum for supergiants occurs at a much later type \citep[e.g.][]{h66} resulting in a positive effect throughout the spectral types in Table \ref{ew}. |
The clear implication is that if luminosity classifications are allocated from Calactic calibrations. the intrinsic brightness. of a star with a given classification cannot be assumed to be universal. | The clear implication is that if luminosity classifications are allocated from Galactic calibrations, the intrinsic brightness of a star with a given classification cannot be assumed to be universal. |
Our work has demonstrated. that accurate A-supergiant temperatures require knowledge of the metallicity of a svstem (ancl vice versa). | Our work has demonstrated that accurate A-supergiant temperatures require knowledge of the metallicity of a system (and vice versa). |
This οσο has important ramifications for studies of extragalactic A-type supergiants. | This effect has important ramifications for studies of extragalactic A-type supergiants. |
For example. from comparison with template Calactic spectra. ? assign a spectral twpe of Al la to a star in NGC 3621 (a spiral galaxy. at a distance of 6.7 Alpe). | For example, from comparison with template Galactic spectra, \citet{bk01} assign a spectral type of A1 Ia to a star in NGC 3621 (a spiral galaxy at a distance of 6.7 Mpc). |
From the spectral type they estimate a temperature (00001 £400) and then use Ixurucz model atmospheres and. the line. formation calculations of 2? το [ind the chemicalcomposition which best matches the observations: their | From the spectral type they estimate a temperature (9000K $\pm$ 400) and then use Kurucz model atmospheres and the line formation calculations of \citet{pryz02} to find the chemicalcomposition which best matches the observations; their |
hose in the first reduction method. resulting in a decrease in the number of vectors selected after error clipping. | those in the first reduction method, resulting in a decrease in the number of vectors selected after error clipping. |
The change in the errors in polarisation are due to he binning. | The change in the errors in polarisation are due to the binning. |
When the pixel size is set to3.09"... four ixels are produced. for every one when the size is6. | When the pixel size is set to, four pixels are produced for every one when the size is. |
18".. A vector is then produced for cach pixel. with the vectors or the smaller pixels being binned together adding the »olarisations together in (quacdrature to calculate the error. | A vector is then produced for each pixel, with the vectors for the smaller pixels being binned together — adding the polarisations together in quadrature to calculate the error. |
"his erroneously reduces the resultant errors. | This erroneously reduces the resultant errors. |
The observing mode used means that one independent »olarisation measurement is taken at steps of every. the results of which can be superimposed over an intensity : ↓⊔↓⋜↧⋏∙≟∢⊾≼∼↓⋅∢⊾⋜⋯⋅∠⇂∖∖⊽↓↿↓↥↶∫≻⋡∪≤⋗∢⋅∕∕ pixels. | The observing mode used means that one independent polarisation measurement is taken at steps of every, the results of which can be superimposed over an intensity image created with pixels. |
The mass of the star-forming cores can be calculated by assuming: where g is the gas-to-dust ratio. 5, is the lux.d the distance. αγ the absorption cocllicient at frequency. ος and. Dita) is the Planek function for frequceney vat a temperature of Lint. | The mass of the star-forming cores can be calculated by assuming: where $g$ is the gas-to-dust ratio, $S_{\rm \nu}$ is the flux,$d$ the distance, $\kappa_{\rm \nu}$ the absorption coefficient at frequency $\rm \nu$, and $B_{\rm \nu}(T_{\rm dust})$ is the Planck function for frequency $\rm \nu$ at a temperature of $T_{\rm dust}$. |
Using a gas-to-dust ratio of 100:1. (Hildebrand: 1983).. and an absorption coelficient of 0.15 m? ke! estimated [rom Ossenkopf&Llenning(1994) based on a numberdensity of ng 107 . thick ice mantles and a formation timescale of 107 vears. mass estimates for the cores were caleulated (listed in table 2.. along with the other parameters derived [rom the observations). | Using a gas-to-dust ratio of 100:1 \citep{hildebrand}, , and an absorption coefficient of 0.15 $^{2}$ $^{-1}$ estimated from \citet{ossen} based on a numberdensity of $_{H}$ = $^{5}$ $^{-3}$, thick ice mantles and a formation timescale of $^{5}$ years, mass estimates for the cores were calculated (listed in table \ref{tab:param}, along with the other parameters derived from the observations). |
The mass of these objects are subject to uncertainties within the used. parameters. especially any errors. in measuring the distance to the core. | The mass of these objects are subject to uncertainties within the used parameters, especially any errors in measuring the distance to the core. |
The gas-to-dust ratio. which mav be as [ow as 45:1 (AleCutcheonet also introduces an error that may be up to a factor of 2. | The gas-to-dust ratio, which may be as low as 45:1 \citep{mccutcheon} also introduces an error that may be up to a factor of 2. |
he absorption coellicient at SbOf/mi still has not been determined. precisely. (Hildebrand:1983:Chinietal.2001).. although the value adopted. in this paper from Ossenkopf&lHlenning(1994) agrees with the values determined by Bianchietal.(2008) ancl Visseretal.(2002). | The absorption coefficient at $\mu$ m still has not been determined precisely \citep{hildebrand,chini}, although the value adopted in this paper from \citet{ossen} agrees with the values determined by \citet{bianchi} and \citet{visser}. |
. The masses we determine in this paper are therefore the upper limits for the temperature of the cores. | The masses we determine in this paper are therefore the upper limits for the temperature of the cores. |
The CF relation can be used to obtain the plane of the sky average magnetic field strength. | The CF relation can be used to obtain the plane of the sky average magnetic field strength. |
This method is based on equipartition and the ability of the magnetic field to retain straight field lines under the inlluence of turbulence. | This method is based on equipartition and the ability of the magnetic field to retain straight field lines under the influence of turbulence. |
The plane of the sky. average field strength can be calculated vla where p is the mean density (g em 7). a. the line of sight velocity dispersion (cm ). ae isthe dispersion in polarisation position angles (measured cast of north) and is coprected for measurement errors (65=o7luensured6,CEPOL ) where @ is in radians. and. f. is a correction factor found to be 20.5 (Lleitschetal.2001). | The plane of the sky average field strength can be calculated via: where $\rho$ is the mean density (g $^{-3}$ ), $\sigma_{v_{\rm los}}$ the line of sight velocity dispersion (cm $^{-1}$ ), $\sigma_{\theta}$ isthe dispersion in polarisation position angles (measured east of north) and is corrected for measurement errors $\sigma^{2}_{\theta}= \sigma^{2}_{\rm measured} -
\sigma^{2}_{\rm error}$ ) where $\theta$ is in radians, and $f$ is a correction factor found to be $\sim$ 0.5 \citep{heitsch}. |
. ]5rrors on the position angle of the vectors are calculated based on the polarimetry signal-to-noise: where d89 is the error in the position angle and s, is the signal-to-noise in the polarisation. | Errors on the position angle of the vectors are calculated based on the polarimetry signal-to-noise: where $d\theta$ is the error in the position angle and $s_{\rm p}$ is the signal-to-noise in the polarisation. |
Pherefore in regions where the polarisation percentage is low (e.g. across the main core of DhR21(OLID). then σας~torr resulting in misleaclingly small dispersion. angles. and very strong magnetic fields. | Therefore in regions where the polarisation percentage is low (e.g. across the main core of DR21(OH)), then $\sigma_{meas} \sim \sigma_{err}$ resulting in misleadingly small dispersion angles, and very strong magnetic fields. |
By only selecting the vectors which have a signal-to-noise (in polarisation) of z 3. this problem is avoided. therefore all of the magnetic field strength estimates in this paper are based on vectors selected in this way. | By only selecting the vectors which have a signal-to-noise (in polarisation) of $>$ 3, this problem is avoided, therefore all of the magnetic field strength estimates in this paper are based on vectors selected in this way. |
Please note. however. as mentioned. earlier. the vectors shown in the figures are not selected in this way. as in terms of magnetic field morphology. polarisation nulls and low levels of polarisation are valid. detections. | Please note, however, as mentioned earlier, the vectors shown in the figures are not selected in this way, as in terms of magnetic field morphology, polarisation nulls and low levels of polarisation are valid detections. |
The CF method should. be used. with caution when calculating the magnetic field streneth in the plane of the sky. | The CF method should be used with caution when calculating the magnetic field strength in the plane of the sky. |
The beanrsize of the ΙΟΝΤΕ means that the small-scale taneline of the magnetic field. Geld can occur within the beam. and so the measured. vectors only represent the net magnetic field. direction. leading to over-cstimates of the Ποια strength. | The beam-size of the JCMT means that the small-scale tangling of the magnetic field field can occur within the beam, and so the measured vectors only represent the net magnetic field direction, leading to over-estimates of the field strength. |
Mocelling studies of this effect (Ποκοetal.2001) have lead to the introduction of a correction [actor f. which has been found to be ~ 0.5 (see eq. 5)). | Modelling studies of this effect \citep{heitsch} have lead to the introduction of a correction factor $f$, which has been found to be $\sim$ 0.5 (see eq. \ref{bfield}) ). |
Also. any underlving magnetic field. morphology. (c.g. intrinsic. field curvature) has not been accounted for in calculating the dispersion in position angles of the polarimetry vectors (i.e. his technique assumes that the magnetic field is uniform). | Also, any underlying magnetic field morphology (e.g. intrinsic field curvature) has not been accounted for in calculating the dispersion in position angles of the polarimetry vectors (i.e. this technique assumes that the magnetic field is uniform). |
Uneertaintics in) our estimations of the magnetic icld strength arise from calculating the density of the cores. which incorporates the errors involved in calculating he mass. they therefore. represent. the upper limits. of he magnetic field strength. | Uncertainties in our estimations of the magnetic field strength arise from calculating the density of the cores, which incorporates the errors involved in calculating the mass, they therefore represent the upper limits of the magnetic field strength. |
There are also errors in calculating the volume of the core which contribute as a spherical geometry has been assumed. for cach core (except where otherwise stated). although with no density racer information. we lack the ability to modal the threc-dimensional structure of the cores. therefore the upper limits statecl are solely for spherical geometry. | There are also errors in calculating the volume of the core which contribute as a spherical geometry has been assumed for each core (except where otherwise stated), although with no density tracer information, we lack the ability to modal the three-dimensional structure of the cores, therefore the upper limits stated are solely for spherical geometry. |
The velocity of the eas within the core introduces another error as a F\WLAL of ~2kmss 5 has been used but it may be anvwhiere between lknmss and 3 (Brandctal.2001:Thompsonet 2004). | The velocity of the gas within the core introduces another error as a FWHM of $\sim$ 2 $^{-1}$ has been used but it may be anywhere between 1 $^{-1}$ and 3 $^{-1}$ \citep{brand,thompson}. . |
. Measurement. errors are also introcuced by the angle 8. although these are relatively small in comparison to the other errors stated. | Measurement errors are also introduced by the angle $\theta$ , although these are relatively small in comparison to the other errors stated. |
Cepheus A is a well-known star forming region. | Cepheus A is a well-known star forming region. |
Located at a distance of ~730 pe (Blaauw.Hiltner&Johnson 1959).. it is the closest star-forming region in the sample. | Located at a distance of $\sim$730 pc \citep{blaauw}, , it is the closest star-forming region in the sample. |
The region | The region |
The 2010 Eruption was discovered by us (BGI and SD) as part of svstematic nightly monitoring aimed specilically at the discovery of the eruption. | The 2010 Eruption was discovered by us (BGH and SD) as part of systematic nightly monitoring aimed specifically at the discovery of the eruption. |
llarris imaged U dco al 2010 Jan 23.4385 UT (JD 2455224.9385). saw the bright star in the center of the field. and quickly realized that U Sco was in eruption. | Harris imaged U Sco at 2010 Jan 28.4385 UT (JD 2455224.9385), saw the bright star in the center of the field, and quickly realized that U Sco was in eruption. |
Her first act was to send the observation io the AAVSO. and then she telephoned Schaefer. | Her first act was to send the observation to the AAVSO, and then she telephoned Schaefer. |
Schaefer could not get confirmation from ROTSE. so he took his 6-inch telescope out into the front varcl ancl made. direct visual confirmation that U Sco was bright in eruption. | Schaefer could not get confirmation from ROTSE, so he took his 6-inch telescope out into the front yard and made direct visual confirmation that U Sco was bright in eruption. |
Independenüly. Dvorak discovered the eruption. notified the AAVSO. and started a (ime series on U Seo to cover the short {ime interval until dawn got too bright to continue. | Independently, Dvorak discovered the eruption, notified the AAVSO, and started a time series on U Sco to cover the short time interval until dawn got too bright to continue. |
These initial observations are included in Table 1. | These initial observations are included in Table 1. |
Circumstances. pictures. ancl anecdotes on (he (wo independent discoveries are eiven in Simonsen MacRobert (2010). | Circumstances, pictures, and anecdotes on the two independent discoveries are given in Simonsen MacRobert (2010). |
In practice. our organization worked perfectly. | In practice, our organization worked perfectly. |
The AAVSO automated alert svstem woke up MT and AP. | The AAVSO automated alert system woke up MT and AP. |
Within an hour of the discovery. the eruption had been confirmed and worldwide notifications were started. | Within an hour of the discovery, the eruption had been confirmed and worldwide notifications were started. |
The first was to the LAU Cirenlars (Schaefer et al. | The first was to the IAU Circulars (Schaefer et al. |
2010a). | 2010a). |
The sun had already risen in Chile. so we started wilh more western observatories as well as spacecraft, | The sun had already risen in Chile, so we started with more western observatories as well as spacecraft. |
Within two hours. BES. AP. and NT. had worked through all the long-prepared contact lists. | Within two hours, BES, AP, and MT had worked through all the long-prepared contact lists. |
The response to (hese contacts (both by members of our existing collaboration as well as by independent observers) was excellent ancl fast. | The response to these contacts (both by members of our existing collaboration as well as by independent observers) was excellent and fast. |
The discovery of the 2010 eruption was a fulfillment of the prediction in Schaefer (2005) that U Sco would next erupt in the vear 341.0. | The discovery of the 2010 eruption was a fulfillment of the prediction in Schaefer (2005) that U Sco would next erupt in the year $\pm$ 1.0. |
The eruption in 2010.1 falls well within the one-sigma region of the prediction. | The eruption in 2010.1 falls well within the one-sigma region of the prediction. |
This adds good. confidence to the physical method of summine the total accreted material based on the D-band flux in the prior inter-eruption interval. | This adds good confidence to the physical method of summing the total accreted material based on the B-band flux in the prior inter-eruption interval. |
The folded light curve (see Figure 3) shows (he primary eclipse at phases 0.0. 1.0. and 2.0. ( | The folded light curve (see Figure 3) shows the primary eclipse at phases 0.0, 1.0, and 2.0. ( |
The magnitudes are double plotted so as to make (he eclipse at phase 1.0 easily visible.) | The magnitudes are double plotted so as to make the eclipse at phase 1.0 easily visible.) |
The out-ol-eclipse brightness varies substantially. aud (his makes for a ragged eclipse light curve because each point is [rom a different epoch eclipse with a different amount of flickering lieht added. | The out-of-eclipse brightness varies substantially, and this makes for a ragged eclipse light curve because each point is from a different epoch eclipse with a different amount of flickering light added. |
The scatter around (he middle of the eclipse is much smaller than (he out-of-eclipse scatter, which implies that the fIickering region is small and centrally locatec. | The scatter around the middle of the eclipse is much smaller than the out-of-eclipse scatter, which implies that the flickering region is small and centrally located. |
No secondary eclipse is visible in the B and V bands. | No secondary eclipse is visible in the B and V bands. |
However. in the I-band. the secondary eclipse is visible with aumplitude roughly 0.3 mag. | However, in the I-band, the secondary eclipse is visible with amplitude roughly 0.3 mag. |
This is readily. understood. as | This is readily understood as |
singular. it cannot be diagonalized aud therefore x caunot be whitened. | singular, it cannot be diagonalized and therefore $\chib$ cannot be whitened. |
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