ReadingTimeMachine/rtm-sgt-ocr-v1 · Datasets at Hugging Face

The simulations are all in reasonable agreement with the analytical mocdel.

The simulations are all in reasonable agreement with the analytical model.

The agreement is especially good with Zahnοἱal. (2007).. where the typical error in As) is ~10% although it ranges up to ~ 25%.

The agreement is especially good with \citet{zahn}, , where the typical error in $\Delta_{21}$ is $\sim 10\%$ although it ranges up to $\sim 25\%$ .

The agreement with Lievοἱ is good at >= 12. when density [uctuations are completely dominant. but. later curing reionization a 25% dilference is typical. with the simulation curves showing a somewhat dillerent shape that includes a decrease with & at hk Lh/Alpe.

The agreement with \citet{iliev} is good at $z=12$ , when density fluctuations are completely dominant, but later during reionization a $25\%$ difference is typical, with the simulation curves showing a somewhat different shape that includes a decrease with $k$ at $k \ga 1h$ /Mpc.

There is good agreement (typically ~ 1054)

There is good agreement (typically $\sim 10\%$ )

integrations at fixed positions 1n the disk.

integrations at fixed positions in the disk.

This enabled us to achieve good sensitivity but was at the cost of undersampling the source.

We obtained deep observations at nine positions of the galaxy with a total on source integration time of 11 hours (Figure 1).

The observations were frequency switched.

The intrinsic velocity resolution was 2.7 km s!: the data was then smoothed using a Hanning squared function.

The intrinsic velocity resolution was 2.7 km $^{-1}$; the data was then smoothed using a Hanning squared function.

We reduced the data using the CLASS software of the GILDAS package by fitting a first order baseline to all spectra within a window going from -400 to ss! about the galaxys’ systemic velocity of 13830 km s7!.

We reduced the data using the CLASS software of the GILDAS package by fitting a first order baseline to all spectra within a window going from -400 to $^{-1}$ about the galaxys' systemic velocity of 13830 km $^{-1}$.

This window was the same for all nine spectra.

The noise level is not the same for all receivers: the lowest is 0.7mK and the highest is 1.6 mK in the 10.9 km/s channels.

The noise level is not the same for all receivers; the lowest is 0.7mK and the highest is 1.6 mK in the 10.9 km/s channels.

The noise is also not uniform across the band.

Hence we computed the baseline and the noise in the -400 +400 window using emission free channels only.

All the details are given in Table 2.

The conversion factor from K to Jy is 8.6 Jy ΚΙ.

The conversion factor from K to Jy is 8.6 Jy $^{-1}$.

To convert from the antenna temperature scale 71 to the main beam temperature Τρ we multiplied 7) by the factor F;;;/B,;;=1.67 where F,;, is the forward beam efficiency and δι, is the main beam efficiency.

To convert from the antenna temperature scale $T_A^*$ to the main beam temperature $T_{mb}$ we multiplied $T_A^*$ by the factor $F_{eff}/B_{eff}~=~1.67$ where $F_{eff}$ is the forward beam efficiency and $B_{eff}$ is the main beam efficiency.

We have detected CO(2-1) emission from several positions in the disk as well as from the center of Malin 2.

In the following paragraphs we present our results and discuss their FFigure 2 shows the CO(2-1) emission spectra observed from nine locations across Malin 2.

In the following paragraphs we present our results and discuss their Figure 2 shows the CO(2-1) emission spectra observed from nine locations across Malin 2.

The offsets from the galaxy center are indicated in each box.

CO(2-1) emission was detected from four out of nine positions at line intensities above 3c.

CO(2-1) emission was detected from four out of nine positions at line intensities above $3\sigma$.

The line at (-24. 24) 1s a a hint of emission rather than a sure detection.

The line at (-24, 24) is a a hint of emission rather than a sure detection.

At (0. 0) the line is broad but ts a 3c detection.

At (0, 0) the line is broad but is a $3\sigma$ detection.

We estimated the line parameters (flux. width and central velocity) by fitting à gaussian to each spectrum.

We estimated the line parameters (flux, width and central velocity) by fitting a gaussian to each spectrum.

We determined the noise level for each of the nine positions.

The results are listed in Table 2 and the best fit gaussians are overlaid on the spectra in Figure 2.

Molecular gas has been detected earlier in this. galaxy by Das et al. (

Molecular gas has been detected earlier in this galaxy by Das et al. (

2006) with the IRAM 30m telescope and the BIMA array.

However. due to a correlator setup problem the BIMA map was incomplete. it was covering a velocity range corresponding to CO(I-0) line emission from the east side of the galaxy only.

However, due to a correlator setup problem the BIMA map was incomplete, it was covering a velocity range corresponding to CO(1–0) line emission from the east side of the galaxy only.

In addition. the 30m telescope was pointed toward two directions only at 7" and ~35” east of the nucleus (see 11).

In addition, the 30m telescope was pointed toward two directions only at $''$ and $\sim$ $''$ east of the nucleus (see 1).

Although the source was observed simultaneously at GGHz and 230GGHz with the 30m telescope. only CO(1-0) emission was detected: the CO(2-I) line was not detected from either positions.

Although the source was observed simultaneously at GHz and GHz with the 30m telescope, only CO(1–0) emission was detected; the CO(2--1) line was not detected from either positions.

Our present observations cover the CO emission over a wider velocity and spatial extent than these previous observations and hence give a better idea of the distribution of molecular gas in the inner disk of Malin 2.

These observations are also the first detections of the CO(2-1) πο in Malin 2.

These observations are also the first detections of the CO(2–1) line in Malin 2.

Our detection lies below the detection limit of the older observations of Das et al. (

2006).

Their CO(2-1) emission spectrum had a noise (rms) of 2.6 mK whereas our line detections have a peak of 2 to 3 mK (Figure 2).

Their CO(2–1) emission spectrum had a noise (rms) of 2.6 mK whereas our line detections have a peak of 2 to 3 mK (Figure 2).

Near the galaxy center. where there is overlap with the previous CO detection. the CO line velocities are in the same direction and are similar in shape and in width.

Near the galaxy center, where there is overlap with the previous CO detection, the CO line velocities are in the same direction and are similar in shape and in width.

Close to the center of the galaxy the CO(I-0) line as detected by Das et al. (

Close to the center of the galaxy the CO(1–0) line as detected by Das et al. (

2006) is broad (~200kkmss~') and asymmetric with the red side being slightly more prominent than the blue side.

2006) is broad $\sim$ $^{-1}$ ) and asymmetric with the red side being slightly more prominent than the blue side.

The CO(2A-1) line detected at the center of the galaxy by our new HERA observations is 243+76Kms! wide and at a centroid position offset by 77+34kins! relative to the systemic velocity given in Table |.

The CO(2Â-1) line detected at the center of the galaxy by our new HERA observations is $243\pm76~km~s^{-1}$ wide and at a centroid position offset by $77\pm34~km~s^{-1}$ relative to the systemic velocity given in Table 1.

—Investigating the cause of this offset would require interferometric observations.

Investigating the cause of this offset would require interferometric observations.

As the beams and pointing directions are different (23” for the CO(I—O0) line and 11 for the CO(2-1) line) the fluxes cannot be directly compared.

As the beams and pointing directions are different $''$ for the CO(1--0) line and $''$ for the CO(2–1) line) the fluxes cannot be directly compared.

But if the molecular gas were uniformly distributed we would expect a line ratio in temperature scale close m the range of values found by Braine Combes (1992) with the same telescope te.. 0.4 to 1.2.

But if the molecular gas were uniformly distributed we would expect a line ratio in temperature scale close in the range of values found by Braine Combes (1992) with the same telescope i.e., 0.4 to 1.2.

We checked this for the HERA central beam whose pointing. direction is the closest to the central pointing of Das et al (2006).

We checked this for the HERA central beam whose pointing direction is the closest to the central pointing of Das et al (2006).

⋀∣⋪∪∐∶↔⊺∣↴∁⋂⋯∣⊃⋯⋪≣⋯∏∪↑↴↾∣↴⊜⇂↴∣⋪≣∶↔⊺∣⇈∏⊖⋋⋋≣∏∣⊔∣∖↗∣∖⊳⋯⊳√∶↔⊺≣∖⇁⊖⋋ ∣ ∣⊂⊲≺≻≼∶⊣⊳∕∣⊂⊲≺≻≼⊢⋯∶∩↜−↓∍∕⊔∥∶↭↜−↓∍⋖∖∖⇁∣↴⊜∣⋪⊜⋔⊜⊂↻⋖⊐∣−⊓∥∏⊜ intensity from the HERA central pointing is 0.43 and the CO(1—0) intensity from IRAM ts 1.01).

A rough comparison of the brightness in $mK~km~s^{-1}$ gives $I_{\rm CO(2-1)}/I_{\rm CO(1-0)}$ = 0.43/1.01 = 0.43 (where the CO(2–1) line intensity from the HERA central pointing is 0.43 and the CO(1–0) intensity from IRAM is 1.01).

This value is at the lower end of the line ratio range for most galaxies but given the uncertainties (e.g. gas distribution). the value shows that

This value is at the lower end of the line ratio range for most galaxies but given the uncertainties (e.g. gas distribution), the value shows that

Tt should be noted that the nuuvey of stars decreases rapidly with the increasing &á—/ colour.

It should be noted that the number of stars decreases rapidly with the increasing $r'-i'$ colour.

A slight chanee in the zero point of the photometric calibration in r or may change slightly our couclusiois.

A slight change in the zero point of the photometric calibration in $r'$ or $i'$ may change slightly our conclusions.

We estimate from Tables 4. 5 aud 6 that a systematic slift of 0.05 magnitude ine’/ would produce a chiuse of about 0.5 on the slope a.

We estimate from Tables 4, 5 and 6 that a systematic shift of 0.05 magnitude in $r'-i'$ would produce a change of about 0.5 on the slope $\alpha$.

IHowever such a shift is iuprobab eas it would be seen also at the blue cud of the sequence (7.7= 0) which is not the case. ax seen in Figure 9.

However such a shift is improbable as it would be seen also at the blue end of the sequence $r'-i'=0$ ) which is not the case, as seen in Figure 9.

Zheng et al. (2001))

Zheng et al. \cite{Zheng}) )

determined the luminosity function fromn a sample of about 11400 NI dwurfs iu 118 fields using the WEC?2 aud 162 fields frou PCT with the UST.

determined the luminosity function from a sample of about 1400 M dwarfs in 148 fields using the WFC2 and 162 fields from PC1 with the HST.

Their sample is characterized by a mean height above the plane of 1.5 kpe. with very few stars at vertical height «1 kpe.

Their sample is characterized by a mean height above the plane of 1.5 kpc, with very few stars at vertical height $<$ 1 kpc.

They derive their LF aud IME taking iuto account a probable metallicity eradieut. by adopting a metallicitv of 0.5 dex at 1.5 kpc. aud a colom-absolute

They derive their LF and IMF taking into account a probable metallicity gradient, by adopting a metallicity of –0.5 dex at 1.5 kpc, and a colour-absolute

1n contrast with the methods based on integral transformation techniques. πο formalism developed here does not require that the mass density has an analytic continuation to complex arguments.

In contrast with the methods based on integral transformation techniques, the formalism developed here does not require that the mass density has an analytic continuation to complex arguments.

Indeed. this is the principal disadvantage involved in such methods.

Indeed, this is the principal disadvantage involved in such methods.

Moreover. our fractional derivative approach can be regarded as a general method that contains. as particular cases. the results obtained by Fricke (1952)... IXalnajs(1976) and Jiang&Ossipkov(2007).

Moreover, our fractional derivative approach can be regarded as a general method that contains, as particular cases, the results obtained by \cite{fricke}, , \cite{kal} and \cite{jiang}.

. The method developed here can be applied to a wider variety of axisvmmetrie models. due to the generic form of the density as a function.

The method developed here can be applied to a wider variety of axisymmetric models, due to the generic form of the density as a function.

Another advantage of this formalism is that it can be applied directly both to tridimensional svstenis and to [lat systems. without the implementation of a pseudo-volume density.

Another advantage of this formalism is that it can be applied directly both to tridimensional systems and to flat systems, without the implementation of a pseudo-volume density.

Therefore. taking into account all the above statements. the present formalism represents a powerful tool on the construction of self-consistent stellar models.

Therefore, taking into account all the above statements, the present formalism represents a powerful tool on the construction of self-consistent stellar models.

J. IC. wants to thank the financial support from.Académica. Vniversidad Industrial deSantander.

J. R-C. wants to thank the financial support from, Universidad Industrial deSantander.

The results thus obtained are shown in Table 2 and the fit itself is compared to the data in Figure 2..

The results thus obtained are shown in Table \ref{tab:results} and the fit itself is compared to the data in Figure \ref{fig:fit}.

The reduced chi-squared for this fit is 0.63. which suggests we have slightly overestimated the uncertainties in our data.

The reduced chi-squared for this fit is 0.63, which suggests we have slightly overestimated the uncertainties in our data.

Thus the uncertainties in our results are somewhat conservative.

We also note that there are unavoidable correlations between some parameters.

Besides the exc ccorrelation mentioned in section ??.. the strongest of these are between aH,. b and FfI.

Besides the $e$ correlation mentioned in section \ref{subsec:fitting}, the strongest of these are between $a/\rs$, $b$ and $\rp/\rs$.

Phere are also significant correlations between aandz.. and also between A,ήδη and the normalisation actor For the LO data.

There are also significant correlations between and, and also between $\rp/\rs$ and the normalisation factor for the IGO data.

The uncertainties in results include he effects of all these correlations.

The uncertainties in results include the effects of all these correlations.

Since we used the values of the period (121). eccentricity (c) ancl argument of periastron (a)) from LOO as clirect constraints in the Gt. we obtained results that agree with hose values.

Since we used the values of the period ), eccentricity $e$ ) and argument of periastron ) from L09 as direct constraints in the fit, we obtained results that agree with those values.

We did find a larger uncertainty foro. but a more precise value for the eccentricity.

We did find a larger uncertainty for, but a more precise value for the eccentricity.

Our results also agree well with the parameters reported x POO. GOO and WO09.

Our results also agree well with the parameters reported by P09, G09 and W09.

Phe only significant exception to this is the period. where our result is 37 smaller than the other analyses.

The only significant exception to this is the period, where our result is $3\sigma$ smaller than the other analyses.

We note. however. that we have essentially forced our simulations to agree with the period reported by LOO.

We note, however, that we have essentially forced our simulations to agree with the period reported by L09.

If we repeat our fit without the direct constraints onL?.. ¢ and ((see section 22)). the best-fit period is almost unchanged. but the uncertainty in its value is four times ereater.

If we repeat our fit without the direct constraints on, $e$ and (see section \ref{subsec:fitting}) ), the best-fit period is almost unchanged, but the uncertainty in its value is four times greater.

“This means our photometric cata are in fact consistent with the period reported by POO. CO9 ancl WOO.

This means our photometric data are in fact consistent with the period reported by P09, G09 and W09.

We also find a planet-to-star radius ratio that is marginally smaller (by 1.80) than the values reported. by WO09 and. GOO.

We also find a planet-to-star radius ratio that is marginally smaller (by $1.8\sigma$ ) than the values reported by W09 and G09.

A possible cause for this is the nature of our data from the LOO. which contains the majority. of the in-transit points. but. no out-of-transit. points on the same night.

A possible cause for this is the nature of our data from the IGO, which contains the majority of the in-transit points, but no out-of-transit points on the same night.

This means the normalisation of those data is not strongly constrained. ancl leads to the correlation noted above.

This means the normalisation of those data is not strongly constrained, and leads to the correlation noted above.

In. addition. the LOO cata appear to show a significant svstematic trend in the middle of the transit. which we were unable to remove by de-correlation against anv physical paramctrers of the observations (such as airmass or position on the CCD).

In addition, the IGO data appear to show a significant systematic trend in the middle of the transit, which we were unable to remove by de-correlation against any physical parametrers of the observations (such as airmass or position on the CCD).

We have obtained multi-site observations of a transit ingress and a complete transit. of LID SOGOG b. across. its. host star.

We have obtained multi-site observations of a transit ingress and a complete transit of HD 80606 b across its host star.

We analvsed. these data independently of any other photometric data. and found system parameters consistent with previously reported values.

We analysed these data independently of any other photometric data, and found system parameters consistent with previously reported values.

These observations were made using four telescopes at different sites.

This allowed: us to obtain near-continuous coverage of this 12-hour event.

This allowed us to obtain near-continuous coverage of this 12-hour event.

However. the cillerences between the instruments. telescopes ancl time-allocation procedures were. t0 an extent. limitations on our ability to obtain a uniform data set.

However, the differences between the instruments, telescopes and time-allocation procedures were, to an extent, limitations on our ability to obtain a uniform data set.

In the near future. the completion of LCOC'TE's network of Im robotic telescopes (Brownetal.

In the near future, the completion of LCOGT's network of 1m robotic telescopes \citep{Brown2010}

then became globally stable.

A well studied case in which both conditions could be satisfied. is in self-gravitating protoplanetary disks where the heating is due to gravito-driven turbulence.

A well studied case in which both conditions could be satisfied, is in self-gravitating protoplanetary disks where the heating is due to gravito-driven turbulence.

Gane (2001) showed that. turbulence heat the gas such the svstem becomes stable on all scales (Q > 1). when tooo> Stan. being toooandtay, the cooling and orbital times.

Gammie (2001) showed that turbulence heat the gas such the system becomes stable on all scales (Q $>$ 1), when $\rm t_{cool} \, > \, 3 \, t_{dyn}$ , being $\rm t_{cool} \,\, and \,\, t_{dyn}$ the cooling and orbital times.

Such disk is in an equilibrium state (so-called qreveitoturbulence ) that experiences sienilicant fluctuations. but the disk is stable against fragmentation and maintains itself in the brink of instability (Ralikov 2009) Galaxies are indeed observed (o be close to equilibrium (Martin Kennicutt 2001: Downes Solomon 1998). with observed Toomre Q parameters never too [ar from 1 (averaged over the whole svstem and using the turbulent version of (he Toomre parameter: Qua,=μμ GM).

Such disk is in an equilibrium state (so-called $gravitoturbulence$ ') that experiences significant fluctuations, but the disk is stable against fragmentation and maintains itself in the brink of instability (Rafikov 2009) Galaxies are indeed observed to be close to equilibrium (Martin Kennicutt 2001; Downes Solomon 1998), with observed Toomre Q parameters never too far from 1 (averaged over the whole system and using the turbulent version of the Toomre parameter; $\rm Q_{turb} = v_{\rm turb} \kappa / \pi G \Sigma$ ).

This is due (to sell-regulation heating/cooling processes: if Qiu22 1. in the absence of heating driven by instabilities the disk will cool rapidly and the svstem will eventually become unstable. while if μι<< 1. then the sell-gravityv. aud star formation feedback will be so efficient that will produce enough turbulence to heat the disk towards Qi,7 1.

This is due to self-regulation heating/cooling processes: if $\rm Q_{turb} >>$ 1, in the absence of heating driven by instabilities the disk will cool rapidly and the system will eventually become unstable, while if $\rm Q_{turb} <<$ 1, then the self-gravity and star formation feedback will be so efficient that will produce enough turbulence to heat the disk towards $\rm Q_{turb} \sim$ 1.

llowever. galaxies are in au state that departs somewhat from the ‘gracvilolurbulent one found by Ganmamie (2001).

However, galaxies are in an state that departs somewhat from the $gravitoturbulent$ ' one found by Gammie (2001).

Because in galaxies only the turbulent Q Toonmre parameter is close to one. not the thermal Q which is the one that guarantees stability (like in grevitoturbulent state).

Because in galaxies only the turbulent Q Toomre parameter is close to one, not the thermal Q which is the one that guarantees stability (like in $gravitoturbulent$ ' state).

Galaxies are only close to stability. the runaway. growth of density [Inetuations is nol suppressed and the formation of bound objects on different scales is ongoing (i.e. star formation. GAIC formation. etc).

Galaxies are only close to stability, the runaway growth of density fluctuations is not suppressed and the formation of bound objects on different scales is ongoing (i.e. star formation, GMC formation, etc).

They are probably oscillating around marginal stability due to the sell-regulation feedback process. in a more dynamical fashion (and with larger oscillations) than the one studied in Gammie (2001).

They are probably oscillating around marginal stability due to the self-regulation feedback process, in a more dynamical fashion (and with larger oscillations) than the one studied in Gammie (2001).

Besides this more complex behavior of ISM in galaxies compared. with the classical sell-regulated *qrevitoturbulent! state studied in protoplanetary disks. (he threshold is still well defined ancl there is sell-regulation processes toward (his marginal state.

Besides this more complex behavior of ISM in galaxies compared with the classical self-regulated $gravitoturbulent$ ' state studied in protoplanetary disks, the threshold is still well defined and there is self-regulation processes toward this marginal state.

The marginal stability is well defined at thermal Q=1 and this happens when the following two conditions are salisfied: Qj,~1 and to;>Usa.

The marginal stability is well defined at thermal Q=1 and this happens when the following two conditions are satisfied: $\rm Q_{turb} \sim 1$ and $\rm t_{cool} > t_{heat}$.

Besides most disks in galaxies are in the same state of being close to marginal Toomre stability. still some disks like nucleardisks in starbursts are able to be much more turbulent

Besides most disks in galaxies are in the same state of being close to marginal Toomre stability, still some disks like nucleardisks in starbursts are able to be much more turbulent

short time-scale (~ 1 vr).

short time-scale $\sim$ 1 Gyr).

During the second one. the thin clise is formed. on a much longer time-scale (being 7 Civr at the solar ring and increasing with increasing CalactocentLic distance) oul of matter of primordial chemical composition plus traces of halo gas.

During the second one, the thin disc is formed, on a much longer time-scale (being $\sim$ 7 Gyr at the solar ring and increasing with increasing Galactocentric distance) out of matter of primordial chemical composition plus traces of halo gas.

For a complete. description of the model basic assumptions and equations we address the interested reader to Chiappini et al. (

For a complete description of the model basic assumptions and equations we address the interested reader to Chiappini et al. (