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brielituess being within 1” of oue of the 128 GCs ij 2410 7. | brightness being within $''$ of one of the 428 GCs is $\times$ $^{-5}$. |
We present the I magnitude. LK. colours. nüasses ages and |Fe/II| metalicities of the four GCs suspected of hosting new BIICs in Table 2.. along with the two M31 GC BICS already identified: the magnitudes were obtained from he RBC: the masses. ages and mectalicitics were drawn from ? and 7. | We present the I magnitude, I-K colours, masses ages and [Fe/H] metalicities of the four GCs suspected of hosting new BHCs in Table \ref{gcprops}, along with the two M31 GC BHCs already identified; the magnitudes were obtained from the RBC; the masses, ages and metalicities were drawn from \citet{caldwell09} and \citet{caldwell11}. |
Comparison with the xoperties of the general GC population presentect we? sneeests that the GCs harboring BITC are nore luassive (brighter). aud redder / more metal rich than the general population. | Comparison with the properties of the general GC population presented by \citet{peacock10} suggests that the GCs harboring BHCs are more massive (brighter), and redder / more metal rich than the general population. |
We preseut iu Fie. | We present in Fig. |
5 the I vs. LK color magnitude diagram or MOI GCs: points represeu the whole GC xopulation with I aud Is maguitudes. open circles represent GCs in our field with associated X-rav endsson (see Barnard ο al. | \ref{ikcd} the I vs. I-K color magnitude diagram for M31 GCs; points represent the whole GC population with I and K magnitudes, open circles represent GCs in our field with associated X-ray emission (see Barnard et al., |
im prep). and filled’ circles represeut the six M31 GCs harboring DIICs: the mean of the whole CC population is represented by a star. the mean of the non-DIIC: N-ray GCs bv a triangle. aud the mean of the DIIC GCs is represented by a square. | in prep), and filled circles represent the six M31 GCs harboring BHCs; the mean of the whole GC population is represented by a star, the mean of the non-BHC X-ray GCs by a triangle, and the mean of the BHC GCs is represented by a square. |
It appears hat the BUC GCs are a rather massive and rec subset of the GCs associated with N-rav sources. | It appears that the BHC GCs are a rather massive and red subset of the GCs associated with X-ray sources. |
While all of the BIC GCs are 214 times more netal rich than the mean ΑΟ CC metalicity of L.08 fouud by ?.. ancl iore massive thau : he CC population. only Bo 163 is particularly nassive and ictal rich. | While all of the BHC GCs are 2–14 times more metal rich than the mean M31 GC metalicity of $-$ 1.08 found by \citet{caldwell11}, and more massive than of the GC population, only Bo 163 is particularly massive and metal rich. |
Bo 82 is the 1th mos nassive of the 379 CC's analysed by οον, but only he LO2ud most metal rh. | Bo 82 is the 4th most massive of the 379 GCs analysed by \citet{caldwell09,caldwell11}, but only the 102nd most metal rich. |
Do TLL is the 139th nost massive. but the LOth richest: indeed. it is supersolar. aud richer than any Galactic GC (?).. | Bo 144 is the 139th most massive, but the 10th richest; indeed, it is supersolar, and richer than any Galactic GC \citep{caldwell11}. |
Do 153 is the 87th most massive. but the 36th richest. | Bo 153 is the 87th most massive, but the 36th richest. |
Bo 163 is the 20th mos Πιννο aud the 2ist richest. | Bo 163 is the 20th most massive and the 21st richest. |
Bo 185 is the 53d most massive aud the 75th richest. | Bo 185 is the 53rd most massive and the 75th richest. |
Ποιος GCs that are either lassive or metal rich are able o produce bright N-rav sources. as well as CC's that are both. | Hence GCs that are either massive or metal rich are able to produce bright X-ray sources, as well as GCs that are both. |
Despite carly indications for an absence of stellar mass black hole binarics in elobular clusters. they are becoming increasingly common. | Despite early indications for an absence of stellar mass black hole binaries in globular clusters, they are becoming increasingly common. |
Out of the 35 XN-rav sources associated with elobular clusters in the central region of MOI. 5 harbor DIICs. | Out of the 35 X-ray sources associated with globular clusters in the central region of M31, 5 harbor BHCs. |
Four of these appear to be persüsteutlv bright. aud are consisteut with the theoretical predictions of ? τον binaries formed bw tidal capture of a main sequence star. or for ultra-compact black hole | white dwarf binaries (?7).. | Four of these appear to be persistently bright, and are consistent with the theoretical predictions of \citet{kalogera04} for binaries formed by tidal capture of a main sequence star, or for ultra-compact black hole + white dwarf binaries \citep{ivanova10}. |
However. NB1I63 is a recurring transient. and provides the first test of the theoretical predictions of ? reearding binaries formed by exchanec. | However, XB163 is a recurring transient, and provides the first test of the theoretical predictions of \citet{kalogera04} regarding binaries formed by exchange. |
We fud that the GCs that are metal rich or nassive are able to produce bright N-rav sources. in addition to GCs that are both. | We find that the GCs that are metal rich or massive are able to produce bright X-ray sources, in addition to GCs that are both. |
We observed 5 outbursts in the Chandra aud NADENewton observations of NB163 over ~ 1000 days: however. the large off-axis angle for NB163 in these observations mcaus that further outbursts nav have been missed. | We observed 5 outbursts in the Chandra and XMM-Newton observations of XB163 over $\sim$ 4000 days; however, the large off-axis angle for XB163 in these observations means that further outbursts may have been missed. |
Four of the outbursts occurred over LLOO davs. | Four of the outbursts occurred over 1100 days. |
Furthermore. 7?— found 3 outbursts within LOO davs in the ROSAT observations. | Furthermore, \citet{trudolyubov04} found 3 outbursts within 400 days in the ROSAT observations. |
Such behavior may be cousisteut with a black hole | main sequence star formed by exchange ?.. or due to the complex behaviour of a lack hole | white dwarf binary in a hierarchical riple svsteni. as cuvisioucd by ?.. | Such behavior may be consistent with a black hole + main sequence star formed by exchange \citet{kalogera04}, or due to the complex behaviour of a black hole + white dwarf binary in a hierarchical triple system, as envisioned by \citet{ivanova10}. |
We shall now discuss alternative explanations or the observed behaviour. | We shall now discuss alternative explanations for the observed behaviour. |
We shall discuss whether they are colucideut Ανα οσα Cluission frou multiple sources. or neutron star iuaries with beamed eniüssion. | We shall discuss whether they are coincident AGNs, blended emission from multiple sources, or neutron star binaries with beamed emission. |
As discussed in the previous section. the xobabilitv of cach source being an ACN that is coincident with one of the GCs iu our field is already simall. | As discussed in the previous section, the probability of each source being an AGN that is coincident with one of the GCs in our field is already small. |
The probability that NBOs2. XDB153. X185 and NBII ave all coincident ACNs within 1" of a CC is «10 78. since the X- LDhuninosities observed in the NAIVENewton observations used to obtain the spectra were each ower than the peak observed luuinosity iu the Chandra data. | The probability that XB082, XB153, X185 and XB144 are all coincident AGNs within $''$ of a GC is $<$ $^{-20}$, since the X-ray luminosities observed in the XMM-Newton observations used to obtain the spectra were each lower than the peak observed luminosity in the Chandra data. |
We shall now consider he possibility that the DIICs in our field are instead blends of multiple N-rav sources: dl4 dt AD. neutron star binaries accreting at Eddiustou would be required o produce the observed NMBMNE-Newton spectra of NBOS2. ND153 and XD185. aud most would rave to be persistent to account for the Chiudra σμήνος, | We shall now consider the possibility that the BHCs in our field are instead blends of multiple X-ray sources; 4–14 1.4 $_{\odot}$ neutron star binaries accreting at Eddington would be required to produce the observed XMM-Newton spectra of XB082, XB153 and XB185, and most would have to be persistent to account for the Chandra lightcurves. |
We find that XDOS2 varied by: 107 org Liu 9 days. XB153 varied by 1075 ere s+ in 2 days. and NBISh varied by ~3\10°" cre 1 OVCT ~ 2 hours. | We find that XB082 varied by $^{38}$ erg $^{-1}$ in 9 days, XB153 varied by $^{38}$ erg $^{-1}$ in 2 days, and XB185 varied by $\sim3\times 10^{37}$ erg $^{-1}$ over $\sim$ 2 hours. |
Such variation is more Likely to come from a single source than the concerted variation | Such variation is more likely to come from a single source than the concerted variation |
temporal filtering was required; however, both the MOS and pn data trom the second observation suffered from a large flare at the start of the observation, which rendered the pn data unusable and required the MOS data to be filtered using a count rate threshold of 0.5 counts !. | temporal filtering was required; however, both the MOS and pn data from the second observation suffered from a large flare at the start of the observation, which rendered the pn data unusable and required the MOS data to be filtered using a count rate threshold of 0.5 counts $^{-1}$. |
The resulting clean, merged data had a duration of 9700 s (MOS) and 6314 s (pn). | The resulting clean, merged data had a duration of 9700 s (MOS) and 6314 s (pn). |
The data were used primarily in our study of the nucleus and the extended, low surface brightness diffuse emission from the group. | The data were used primarily in our study of the nucleus and the extended, low surface brightness diffuse emission from the group. |
The SHS was detected in these observations, the NHS was not. | The SHS was detected in these observations, the NHS was not. |
The larger PSF (relative to Chandra) provides no additional structural constraints, so we use only the data in our study of the hot spots. | The larger PSF (relative to ) provides no additional structural constraints, so we use only the data in our study of the hot spots. |
We present data from threeSpitzer observations of 3C 33, two data sets taken from the public archive (one IRAC and one MIPS observation, both pointed towards the SHS - program ID 3327), and an additional IRAC observation (program ID 3418) centered on the host galaxy taken by the 3CRR low-z consortium (Birkinshaw 2007. in preparation). | We present data from three observations of 3C 33, two data sets taken from the public archive (one IRAC and one MIPS observation, both pointed towards the SHS - program ID 3327), and an additional IRAC observation (program ID 3418) centered on the host galaxy taken by the 3CRR low-z consortium (Birkinshaw 2007, in preparation). |
The IRAC observations were made on July 23. 2004 (3327). and January 6, 2005 (3418). with observations times of 96 and 360 seconds, respectively. | The IRAC observations were made on July 23, 2004 (3327), and January 6, 2005 (3418), with observations times of 96 and 360 seconds, respectively. |
The MIPS (24 jim only) observation was made on December 23, 2004 (3327) with an observation time of 200 seconds. | The MIPS (24 $\mu$ m only) observation was made on December 23, 2004 (3327) with an observation time of 200 seconds. |
The images used were produced by the data analysis pipeline version 14.1.0. | The images used were produced by the data analysis pipeline version 14.1.0. |
The SHS is detected in all four IRAC bands and the MIPS image. | The SHS is detected in all four IRAC bands and the MIPS image. |
The NHS is only contained within theSpitzer field of view in the 2005 IRAC observation and the MIPS image, and is detected in all four IRAC bands and the MIPS 24 jim band, although there is some confusion from adjacent stars. | The NHS is only contained within the field of view in the 2005 IRAC observation and the MIPS image, and is detected in all four IRAC bands and the MIPS 24 $\mu$ m band, although there is some confusion from adjacent stars. |
We also use archivalHST (WFPC and WEPC?) and VLA data in this paper. | We also use archival (WFPC and WFPC2) and VLA data in this paper. |
The SHS was observed for 2400 s with the HS7/WFPC2 instrument in 1995 as part of the HST survey of hot spots (PI: P. Crane) using the F702W filter (pivot wavelength of 6919 A)), and for 1800 s with the HS7/WEPC instrument using the F606W filter (pivot wavelength of 5888 A)) 1992). | The SHS was observed for 2400 s with the /WFPC2 instrument in 1995 as part of the survey of radio-galaxy hot spots (PI: P. Crane) using the F702W filter (pivot wavelength of 6919 ), and for 1800 s with the /WFPC instrument using the F606W filter (pivot wavelength of 5888 ) \citep{cra92}. |
. There have been noHST observations of the NHS. | There have been no observations of the NHS. |
We obtained the reprocessed data of the SHS from theHST archive and used the IRAFsvaipAiot package to apply photometric calibrations. | We obtained the reprocessed data of the SHS from the archive and used the IRAF package to apply photometric calibrations. |
The fluxes were reddening-corrected using the dust maps of (1998). | The fluxes were reddening-corrected using the dust maps of \citet{sch98}. |
. The correction to the flux densities is ~25% in the visual. | The correction to the flux densities is $\sim$ in the visual. |
A 1.5-GHz radio map with a resolution of 4.0 arcsec was obtained from the 3CRRAtlas!:: this is the image of (1991). | A 1.5-GHz radio map with a resolution of 4.0 arcsec was obtained from the 3CRR: this is the image of \citet{lp91}. |
. At higher frequencies, we used 4.9 and 15-GHz data trom the VLA public archive. | At higher frequencies, we used 4.9 and 15-GHz data from the VLA public archive. |
Details of the VLA data used and the maps made from them are given in Table |.. | Details of the VLA data used and the maps made from them are given in Table \ref{vla}. |
The data were calibrated and reduced in the standard manner using AIPS. | The data were calibrated and reduced in the standard manner using AIPS. |
Results from analyses of these data have been previously published in Rudnick(1988) and Rudnick&Anderson(1990). | Results from analyses of these data have been previously published in \citet{rud88} and \citet{rud90}. |
. Finally, we also examined the Optical Monitor (UVM? filter) data and archivalGALEX images of 3C 33. | Finally, we also examined the Optical Monitor (UVM2 filter) data and archival images of 3C 33. |
The hot spots were not detected inany of the UV images. | The hot spots were not detected inany of the UV images. |
The observation | The observation |
planets within our chosen M,a parameter space and v And has three (Figure 3). | planets within our chosen $M,a$ parameter space and $\upsilon$ And has three (Figure 3). |
'These data do not support the idea that accreting planets have swept up much of the disc. | These data do not support the idea that accreting planets have swept up much of the disc. |
In particular, only one system in Figure 3 (HIP 14810) appears to have a ‘starved’ outer planet and both bodies ending up near the star. | In particular, only one system in Figure 3 (HIP 14810) appears to have a `starved' outer planet and both bodies ending up near the star. |
Also, 5/11 of the systems have outer planets that are more massive than the inner planet, contradictory to the idea of sweeping through already-depleted regions of the disc. | Also, 5/11 of the systems have outer planets that are more massive than the inner planet, contradictory to the idea of sweeping through already-depleted regions of the disc. |
From a theoretical perspective, a further problem with the idea that migration can aid planet-building is that most of the gas accretion occurs in a runaway phase, with a timescale much shorter than typical migration timescales (Pollacketal.1996;Ikoma2000;Bryden 2000). | From a theoretical perspective, a further problem with the idea that migration can aid planet-building is that most of the gas accretion occurs in a runaway phase, with a timescale much shorter than typical migration timescales \citep{pollack, ikoma00, bryden00}. |
. Migration is thus implausible as a mechanism that allows a planet to sweep up its bulk in gas from a large region of the disc. | Migration is thus implausible as a mechanism that allows a planet to sweep up its bulk in gas from a large region of the disc. |
However, migration could aid in the growth of the solid planetary core (Hourigan&Ward1984;Riceetal. 2003),, and this could allow the core to reach a critical mass to attract an atmosphere, while there is still sufficient gas in the disc. | However, migration could aid in the growth of the solid planetary core \citep{hourigan,rice03}, and this could allow the core to reach a critical mass to attract an atmosphere, while there is still sufficient gas in the disc. |
While migration is thus still important to planetary evolution, neither theory or observational constraints suggest that it solves the mass’ problem of discs. | While migration is thus still important to planetary evolution, neither theory or observational constraints suggest that it solves the `missing-mass' problem of discs. |
Small corrections for opacity are known to be needed when converting millimetre dust emission from T Tauri discs into masses. | Small corrections for opacity are known to be needed when converting millimetre dust emission from T Tauri discs into masses. |
Andrews&Williams(2007b) estimate that the ratio of optically thick to optically thin submillimetre emission is typically around 0.3, as more opacity would result in flattening of the spectrum. | \citet{aw07b} estimate that the ratio of optically thick to optically thin submillimetre emission is typically around 0.3, as more opacity would result in flattening of the spectrum. |
However, if the discs have a massive central inner region, on unresolved scales of tens of AU or less, then this could be much more optically thick — contributing significant mass, but little extra millimetre signal. | However, if the discs have a massive central inner region, on unresolved scales of tens of AU or less, then this could be much more optically thick – contributing significant mass, but little extra millimetre signal. |
Zhuetal.(2009);Rice&Armitage(2009) have recently shown that if discsare massive with respect to the star, then transport of angular momentum through disc self-gravity does in fact lead to a pile-up of material at smaller radii. | \citet{zhu09,rice09} have recently shown that if discs massive with respect to the star, then transport of angular momentum through disc self-gravity does in fact lead to a pile-up of material at smaller radii. |
A quasi-steady-state is reached in which ~80 of the disc mass ends up within 10-20 AU of the star, with a drop to lower surface densities in the model outer disc extending to 50 AU. | A quasi-steady-state is reached in which $\sim 80$ of the disc mass ends up within 10-20 AU of the star, with a drop to lower surface densities in the model outer disc extending to 50 AU. |
There is thus a physical basis for the idea of a central mass concentration, at scales relevant to planet formation. | There is thus a physical basis for the idea of a central mass concentration, at scales relevant to planet formation. |
Figure 5 shows representative spectral energy distributions (SED) of the star plus disc system -- generated using the HO-CHUNK: 3D radiation transfer code (Whitneyetal.2003) - for a standard power-law distribution of disc mass (top panel), and a case where more material has been artifically added inside 10 AU to double the total disc material (bottom panel). | Figure 5 shows representative spectral energy distributions (SED) of the star plus disc system – generated using the HO-CHUNK: 3D radiation transfer code \citep{whitney03} – for a standard power-law distribution of disc mass (top panel), and a case where more material has been artifically added inside 10 AU to double the total disc material (bottom panel). |
There is very little difference in the SED of the power-law and centrally-enhanced discs, especially in the millimetre regime that is canonically ‘mass tracing’. | There is very little difference in the SED of the power-law and centrally-enhanced discs, especially in the millimetre regime that is canonically `mass tracing'. |
In fact, the centrally condensed disc has a submillimetre flux that is slightly lower than that from the lower-mass, power-law disc. | In fact, the centrally condensed disc has a submillimetre flux that is slightly lower than that from the lower-mass, power-law disc. |
Therefore, if real discs are in fact massive, a central pile-up would be both theoretically predicted (Rice&Armitage2009) and not detected in millimetre images where the inner disc is unresolved. | Therefore, if real discs are in fact massive, a central pile-up would be both theoretically predicted \citep{rice09} and not detected in millimetre images where the inner disc is unresolved. |
This provides a potential solution to the missing mass, at least for discs with moderately high mass estimates already. | This provides a potential solution to the missing mass, at least for discs with moderately high mass estimates already. |
The standard ACDAL cosmological model has been very successful in accouuting for observations on scales larger than around a Mpc. | The standard $\Lambda$ CDM cosmological model has been very successful in accounting for observations on scales larger than around a Mpc. |
However. it appears that this model faces difficulties on the scales of ealaxies auc dwarf galaxies ((van 2000). | However, it appears that this model faces difficulties on the scales of galaxies and dwarf galaxies \markcite{2000AJ....119.1579V}( 2000). |
One such problem is that CDM. simulations of the local group of galaxies predict an order of magnitude more ciwart galaxy halos with masses ereater than ~10°AL. than there are observed satellites of the Milly Way (ATW) Galaxy aud M21 ((Moore 1999: 1999: 1998). | One such problem is that CDM simulations of the local group of galaxies predict an order of magnitude more dwarf galaxy halos with masses greater than $\sim 10^7\,\msun$ than there are observed satellites of the Milky Way (MW) Galaxy and M31 \markcite{1999ApJ...524L..19M,1999ApJ...522...82K,1998ARA&A..36..435M}( 1999; 1999; 1998). |
These simulations predict that of the virial mass of a galaxy. halo is dnosubstruetmres of nass 2LOM... | These simulations predict that of the virial mass of a galaxy halo is in substructures of mass $\simgt 10^7\msun$. |
This over prediction of dwarf halos could be a sign that there is something fundamentally wrong with the CDM model. | This over prediction of dwarf halos could be a sign that there is something fundamentally wrong with the CDM model. |
Proposed explanations iuclude wart dark matter (DM) which simoothes out small scale structure in the carly universe {ίοιο,Bode.Ostriker. 2001). unorthodox inflation models which break scale invariance ((Ilxanionukowski Liddle 2000) and seltiuteractiug dark matter which causes substructures to evaporate within larger halos ((Spergel 2000). | Proposed explanations include warm dark matter (WDM) which smoothes out small scale structure in the early universe \markcite{2001ApJ...556...93B}( (e.g., 2001), unorthodox inflation models which break scale invariance \markcite{2000PRL.Kamionkowski}( (Kamionkowski Liddle 2000) and self-interacting dark matter which causes substructures to evaporate within larger halos \markcite{2000PhRvL..84.3760S}( 2000). |
Alternatively, CDM could be correct and the sanall Dark Matter (DM) clumps could exist. but not contain stars. so as to escape detection as observable dwarf galaxies. | Alternatively, CDM could be correct and the small Dark Matter (DM) clumps could exist, but not contain stars, so as to escape detection as observable dwarf galaxies. |
This situation can casily. perhaps inevitably, come about through the action of feedback | This situation can easily, perhaps inevitably, come about through the action of feedback |
confirmed RR Lyrae stars,30 were RRab stars, 11 were RRc stars, and 8 were RRd's. | confirmed RR Lyrae stars,$30$ were RRab stars, $11$ were RRc stars, and $8$ were RRd's. |
The RRd variable stars are discussed separately in section 3.2.. | The RRd variable stars are discussed separately in section \ref{sec:rrd}. |
Figures 2--5 show the light curves for the RRab, RRc, and the other variable stars. | Figures \ref{abcurves}- \ref{othercurves} show the light curves for the RRab, RRc, and the other variable stars. |
Table 1 lists the identified variable stars, except for the RRd stars, as well as their classification, period, V and B amplitudes, intensity-weighted V and B mean magnitudes, and magnitude-weighted mean B—V color. | Table \ref{vartable} lists the identified variable stars, except for the RRd stars, as well as their classification, period, $V$ and $B$ amplitudes, intensity-weighted $V$ and $B$ mean magnitudes, and magnitude-weighted mean $B-V$ color. |
The intensity-weighted mean magnitudes and the magnitude-weighted mean color were obtained through the fitting of the light curves with template light curves (Layden1998).. ( | The intensity-weighted mean magnitudes and the magnitude-weighted mean color were obtained through the fitting of the light curves with template light curves \citep{ly98}. ( |
For the relation between these average quantities and the color of the equivalent static star, the reader is referred to Bono et al. | For the relation between these average quantities and the color of the equivalent static star, the reader is referred to Bono et al. |
1995.) | 1995.) |
Notes on some of the individual stars are in the following subsections. | Notes on some of the individual stars are in the following subsections. |
Table 2 contains the photometric data for the variable stars. | Table \ref{phottable} contains the photometric data for the variable stars. |
We use a naming system that is an extension of the one used in Wesselink (1971).. | We use a naming system that is an extension of the one used in \citet{we71}. . |
Walker identified the variable stars found by Wesselink by their number in that paper, | Walker identified the variable stars found by Wesselink by their number in that paper, |
physical) means surface mass density perturbations in the two coupled discs are in-phase. | physical) means surface mass density perturbations in the two coupled discs are in-phase. |
Stationary surface mass density perturbations in both clises scale in the forms of -xpreLid in azimuthal angle 6. | Stationary surface mass density perturbations in both discs scale in the forms of $\propto\mu e^{-\hbox{i}m\theta}$ in azimuthal angle $\theta$. |
For aligned perturbations. we have further taken fox where 5 is a positive/negative constant exponent. | For aligned perturbations, we have further taken $\mu\propto r^{-\varepsilon}$ where $\varepsilon$ is a positive/negative constant exponent. |
For example in subsection. 3.1. we have chosen 5;=a1|24 for coplanar perturbations carrying the same radial power-LIaw dependence of the background equilibrium disc svstem. | For example in subsection 3.1, we have chosen $\varepsilon=\alpha=1+2\beta$ for coplanar perturbations carrying the same radial power-law dependence of the background equilibrium disc system. |
On the other hand. for ¢ being a complex constant exponent. perturbations would appear in spiral forms. namely. the so-called logarithmic spiral ppxrNPexpi3s)Inr] where We) and Be) are the real and imaginary parts ος. | On the other hand, for $\varepsilon$ being a complex constant exponent, perturbations would appear in spiral forms, namely, the so-called logarithmic spiral $\mu\propto r^{-\Re(\varepsilon)}\exp
[-\hbox{i}\Im(\varepsilon)\ln r]$ where $\Re(\varepsilon)$ and $\Im(\varepsilon)$ are the real and imaginary parts of $\varepsilon$. |
To ensure the gravitational potential perturbation arising [ron this perturbed surface mass density as computed by Poisson integral (4)) being finite requires mlsm2 (Qian 1992). | To ensure the gravitational potential perturbation arising from this perturbed surface mass density as computed by Poisson integral \ref{fish}) ) being finite requires $-m+1<\Re(\varepsilon)<m+2$ (Qian 1992). |
Without loss of generality. we assume a set of logarithmic spiral density perturbations and the resulting eravitational potential perturbation in a mathematically consistent (Ixalnajs 1971: Sver Premaine: Shu et al. | Without loss of generality, we assume a set of logarithmic spiral density perturbations and the resulting gravitational potential perturbation in a mathematically consistent (Kalnajs 1971; Syer Tremaine; Shu et al. |
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Data Introduction
Over 1.5 Million synthetically generated ground-truth/OCR pairs for post correction tasks from our paper "Large Synthetic Data from the ar𝜒iv for OCR Post Correction of Historic Scientific Articles".
Synthetic ground truth (SGT) sentences have been mined from the ar𝜒iv Bulk Downloads source documents, and Optical Character Recognition (OCR) sentences have been generated with the Tesseract OCR engine on the PDF pages generated from compiled source documents.
SGT/OCR pairs come from astronomy articles in the years 1991-2011.
No page augmentation has been applied to any of the PDF documents (i.e. these are "clean" pages without warping, dust, etc.)
Resources
Dataset Versions
- V0 (original released with original paper) is available here
Citation
Please reference the following if you make use of this dataset:
@inproceedings{10.1007/978-3-031-43849-3_23,
author = {Naiman, J. P. and Cosillo, Morgan G. and Williams, Peter K. G. and Goodman, Alyssa},
title = {Large Synthetic Data From the arχiv For OCR Post Correction Of Historic Scientific Articles},
year = {2023},
isbn = {978-3-031-43848-6},
publisher = {Springer-Verlag},
address = {Berlin, Heidelberg},
url = {https://doi.org/10.1007/978-3-031-43849-3_23},
doi = {10.1007/978-3-031-43849-3_23},
abstract = {Historical scientific articles often require Optical Character Recognition (OCR) to transform scanned documents into machine-readable text, a process that often produces errors. We present a pipeline for the generation of a synthetic ground truth/OCR dataset to correct the OCR results of the astrophysics literature holdings of the NASA Astrophysics Data System (ADS). By mining the arχiv we create, to the authors’ knowledge, the largest scientific synthetic ground truth/OCR post correction dataset of 203,354,393 character pairs. Baseline models trained with this dataset find the mean improvement in character and word error rates of 7.71\% and 18.82\% for historical OCR text, respectively. Interactive dashboards to explore the dataset are available online: , and data and code, are hosted on GitHub: .},
booktitle = {Linking Theory and Practice of Digital Libraries: 27th International Conference on Theory and Practice of Digital Libraries, TPDL 2023, Zadar, Croatia, September 26–29, 2023, Proceedings},
pages = {265–274},
numpages = {10},
keywords = {scholarly document processing, optical character recognition, astronomy},
location = {Zadar, Croatia}
}
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