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of these wave phenomena, we utilized advanced magneto-hydrodynamic (MHD) simulations.
of these wave phenomena, we utilized advanced two-dimensional magneto-hydrodynamic (MHD) simulations.
two-dimensionalThese simulations were performed using the Lare2D code (Arberetal. where a spicule was modelled as a density enhancement,2001),, embedded in a straight, uniform magnetic field.
These simulations were performed using the Lare2D code \citep[][]{Arb01}, where a spicule was modelled as a density enhancement, embedded in a straight, uniform magnetic field.
The spicule density has a symmetric Epstein profile (Nakariakov&Roberts in the transverse direction, with a peak density 100 1995)times the background value, and a diameter of approximately 600 km (upper-left panel of Fig 4)).
The spicule density has a symmetric Epstein profile \citep[][]{Nak95} in the transverse direction, with a peak density 100 times the background value, and a diameter of approximately 600 km (upper-left panel of Fig \ref{fig4}) ).
The magnetic field strength is chosen to give an external Alfvénn speed of 362 kms~!, and an Alfvénn speed of 36.2 kms"! at the centre of the spicule.
The magnetic field strength is chosen to give an external Alfvénn speed of 362 $^{-1}$, and an Alfvénn speed of 36.2 $^{-1}$ at the centre of the spicule.
A temperature profile is chosen to give a plasma £8=1, where efficient mode coupling is expected to occur (DeMoorteletal.
A temperature profile is chosen to give a plasma $\beta=1$, where efficient mode coupling is expected to occur \citep[][]{DeM04}.
The simulation has a resolution of 600x2000 grid 2004)..points, providing a numerical domain size of 4000x20000 km?.
The simulation has a resolution of $600\times2000$ grid points, providing a numerical domain size of $4000\times20000$ $^{2}$.
For the purposes of this investigation, only effects up to a few thousand km a region incorporating the photosphere and chromosphere)(ie. will be considered.
For the purposes of this investigation, only effects up to a few thousand km (i.e. a region incorporating the photosphere and chromosphere) will be considered.
An artificial driver is applied at the lower boundary in the form of a longitudinal velocity component.
An artificial driver is applied at the lower boundary in the form of a longitudinal velocity component.
This is consistent with the observational interpretation that the driver arises from a global p-mode oscillation.
This is consistent with the observational interpretation that the driver arises from a global p-mode oscillation.
The coherent driver is applied across the diameter of the spicule, with a periodicity of 215 s, and à maximum amplitude of 12.5 kms~!.
The coherent driver is applied across the diameter of the spicule, with a periodicity of 215 s, and a maximum amplitude of 12.5 $^{-1}$.
However, to remain consistent with parameters derived from the observational time series, one side of the simulated MBP has a phase difference of 90 degrees with respect to the other left panel of Fig. 4)).
However, to remain consistent with parameters derived from the observational time series, one side of the simulated MBP has a phase difference of 90 degrees with respect to the other (upper-left panel of Fig. \ref{fig4}) ).
As the driver is longitudinal (upper-and compressive, a 90 degree phase shift creates transverse across the gradients in pressure which displace(i.e. the spicule spicule)axis, generating the kink mode, in addition to producing periodic compressions and rarefactions (sausage mode).
As the driver is longitudinal and compressive, a 90 degree phase shift creates transverse (i.e. across the spicule) gradients in pressure which displace the spicule axis, generating the kink mode, in addition to producing periodic compressions and rarefactions (sausage mode).
These periodic pressure differences, across the body of the spicule, also induce a frequency doubling of the coupled transverse wave, visible in the upper-right panel of Figure 4 by a change from a purely sinusoidal waveform.
These periodic pressure differences, across the body of the spicule, also induce a frequency doubling of the coupled transverse wave, visible in the upper-right panel of Figure \ref{fig4} by a change from a purely sinusoidal waveform.
Both transverse kink and sausage modes are readily apparent in the lower panels of Figure 4,, where time-distance cuts of observational, and simulated data, are displayed (see also Supplementary Movies 3 4).
Both transverse kink and sausage modes are readily apparent in the lower panels of Figure \ref{fig4}, where time-distance cuts of observational, and simulated data, are displayed (see also Supplementary Movies 3 4).
In our simulations, the magnitude of the excited kink mode is smaller than the amplitude of the input longitudinal driver.
In our simulations, the magnitude of the excited kink mode is smaller than the amplitude of the input longitudinal driver.
This is a consequence of the uniform magnetic field strength used.
This is a consequence of the uniform magnetic field strength used.
In the real solar atmosphere, the magnetic field strength decreases rapidly with height, which is a likely contributor to the more prominent increase in kink amplitude seen in current ground- and space-based observations of chromospheric spicules (e.g.Heetal. 2009).
In the real solar atmosphere, the magnetic field strength decreases rapidly with height, which is a likely contributor to the more prominent increase in kink amplitude seen in current ground- and space-based observations of chromospheric spicules \citep[e.g.][]{He09}.
. Nevertheless, the upper-right panel of Figure 4 indicates that the longitudinal-to-transverse mode-coupling mechanism present in our MHD simulations does promote a progressive increases in kink amplitude as a function of atmospheric height.
Nevertheless, the upper-right panel of Figure \ref{fig4} indicates that the longitudinal-to-transverse mode-coupling mechanism present in our MHD simulations does promote a progressive increases in kink amplitude as a function of atmospheric height.
By combining observed photospheric periodicities
By combining observed photospheric periodicities
allows to ignore beam filling effects. to first order.
allows to ignore beam filling effects, to first order.
Note that the absolute untensity. reduced by the fraction of stemming from the rregion. agrees well with the best fitting solution. indicating a bbeam filling factor of about 1.
Note that the absolute intensity, reduced by the fraction of stemming from the region, agrees well with the best fitting solution, indicating a beam filling factor of about 1.
The rather poor fit of the intensity ratios towards the He peak shows the short comings of a plane-parallel single density PDR model.
The rather poor fit of the intensity ratios towards the $\alpha$ peak shows the short comings of a plane-parallel single density PDR model.
First tests using ΚΟΡΜΑ-τ PDR models Rólligetal.(2006) of spherical clumps with density gradients reconcile better to the observations.
First tests using $\tau$ PDR models \citet{Roellig2006} of spherical clumps with density gradients reconcile better to the observations.
This indicates strong density gradients along the line of sight.
This indicates strong density gradients along the line of sight.
In à second paper. we shall include new HIFI ddata along two cuts through the 3302 region. and explore detailed PDR models. which include the effects of geometry and sub-solar metallicity.
In a second paper, we shall include new HIFI data along two cuts through the 302 region and explore detailed PDR models, which include the effects of geometry and sub-solar metallicity.
Mapping observations of the northern inner arm of 333222 at an unprecedented spatial resolution of 50 pe have revealed details of the distribution of the various components of the interstellar medium and their contribution to the [Cu]↴
Mapping observations of the northern inner arm of 33 at an unprecedented spatial resolution of 50 pc have revealed details of the distribution of the various components of the interstellar medium and their contribution to the emission.
aat 155 iis one of the major cooling lines of the interstellar gas.
at 158 is one of the major cooling lines of the interstellar gas.
Thus irrespective of whether hydrogen is atomic or molecular. the lline emission is expected to be strong wherever there is warm and photodissociated gas.
Thus irrespective of whether hydrogen is atomic or molecular, the line emission is expected to be strong wherever there is warm and photodissociated gas.
We have identified emission towards the rregion as well as from the spiral arm seen in the continuum. and from a region outside of the well-defined spiral arm.
We have identified emission towards the region as well as from the spiral arm seen in the continuum, and from a region outside of the well-defined spiral arm.
eemission is strongly correlated with the He and. dust continuum emission, while there is little correlation with CO. and even less withHr.
emission is strongly correlated with the $\alpha$ and dust continuum emission, while there is little correlation with CO, and even less with.
This suggests that the cold neutral medium (CNM:Wolfireetal.1995). does not contribute significantly to the eemission in the 3302 region.
This suggests that the cold neutral medium \citep[CNM;][]{Wolfire1995} does not contribute significantly to the emission in the 302 region.
Recently. (2010) found a similar poor correlation between παπά eemission in a sample of 29 diffuse clouds using HIFI.
Recently, \citet{langer2010} found a similar poor correlation between and emission in a sample of 29 diffuse clouds using HIFI.
The lack of correlation between aand CO found in 3302. may indicate that significant parts of the molecular gas are not traced by CO because it is photo-dissociated in the low-metallicity environment of M33.
The lack of correlation between and CO found in 302, may indicate that significant parts of the molecular gas are not traced by CO because it is photo-dissociated in the low-metallicity environment of M33.
This interpretation is consistent with both theoretical models developed by Bolattoetal.(1999) and recent observational studies of diffuse clouds in the Milky Way by Langer (2010).. and of dwarf galaxies by Maddenetal.(2011).
This interpretation is consistent with both theoretical models developed by \citet{bolatto1999} and recent observational studies of diffuse clouds in the Milky Way by \citet{langer2010}, and of dwarf galaxies by \citet{madden2011}.
. Comparison of the first velocity-resolved sspectrum of M33 (at the ppeak of 3302) with CO line profiles show that the pprofile is much broader. by a factor of ~1.6. and slightly shifted in velocity. by ~1.6s!..
Comparison of the first velocity-resolved spectrum of M33 (at the peak of 302) with CO line profiles show that the profile is much broader, by a factor of $\sim1.6$, and slightly shifted in velocity, by $\sim 1.6$.
Compared to the lline. at the same angular resolution. the line is less broad by a factor ~1.3 and shifted by ~4.4s.
Compared to the line, at the same angular resolution, the line is less broad by a factor $\sim 1.3$ and shifted by $\sim 4.4$.
These findings indicate that the line is not completely mixed with the CO emitting gas. but rather traces a different more turbulent outer layer of gas with slightly different systemic velocities. which ts associated with the 1onized gas.
These findings indicate that the line is not completely mixed with the CO emitting gas, but rather traces a different more turbulent outer layer of gas with slightly different systemic velocities, which is associated with the ionized gas.
Interestingly. recent HHIFI observations of Galactic star. forming. regions (Ossenkopfetal.2010:Joblin2010) also show broadened and slightly shifted lline profiles relative to CO.
Interestingly, recent HIFI observations of Galactic star forming regions \citep{Ossenkopf2010,Joblin2010} also show broadened and slightly shifted line profiles relative to CO.
The two major cooling lines of PDRs are the lline at m and the um line.
The two major cooling lines of PDRs are the line at $\mu$ m and the $\mu$ m line.
The intensity ratios [OIJ/[CIHI] and ([OI]-[|CIHD) vs. the TIR continuum. have been used extensively to estimate the density and FUV field of the emitting regions.
The intensity ratios [OI]/[CII] and ([OI]+[CII]) vs. the TIR continuum, have been used extensively to estimate the density and FUV field of the emitting regions.
Using ISO/LWS. Higdonetal.(2003) observed the far-infrared spectra of the nucleus and six giant rregions in 333. not including 3302. but including 6604. 1142. and 5595 shown in verview..
Using ISO/LWS, \citet{higdon2003} observed the far-infrared spectra of the nucleus and six giant regions in 33, not including 302, but including 604, 142, and 595 shown in \\ref{fig_overview}.
The O/LWSbeamcorrespondbeamcorrespondsto285 sto285ppcandthere ppc foresamplescimixturecre foresamplesamixtur
The ISO/LWS beam corresponds to pc and therefore samples a mixture of the different ISM phases.
eoeemission. llineratiosintherange0.7tol.3. similartotherangeo f values foundinthecen rregionBCLMP
They find line ratios in the range 0.7 to 1.3, similar to the range of values found in the center and spiral arm positions of M83 and M51 \citep{kramer2005}.
3302inthenortherninnerarimof 333. wemeasuremuchk rratiosbetweenQ.] ——0.4.
Towards the region 302 in the northern inner arm of 33, we measure much lower ratios between 0.1–0.4.
Theseratioslietoweardsthelowerendofthevalues and 2.
These ratios lie towards the lower end of the values found by \citet{malhotra2001} in their ISO/LWS study of the unresolved emission of 60 galaxies who find values between $\sim0.2$ and 2.
Similarly low values of down to 0.16 are found e.g. in the Galactic star forming regions 221 and W3IIRS5 (Jakobetal.2007;Kramer2004).
Similarly low values of down to 0.16 are found e.g. in the Galactic star forming regions 21 and IRS5 \citep{jakob2007,kramer2004}.
. Comparison with the PDR models of Kaufmanetal.(1999,Fig.4) and (2006) show that the um line becomes stronger than the eemission in regions of high densities of more than about 10*em™.
Comparison with the PDR models of \citet[][Fig.\,4]{Kaufman1999} and \citet{Roellig2006} show that the $\,\mu$ m line becomes stronger than the emission in regions of high densities of more than about $10^4$.
. At the ppeak position in 3302. we observed a ratio of 0.4. after correcting Που the contribution from the ionized gas.
At the peak position in 302, we observed a ratio of 0.4, after correcting for the contribution from the ionized gas.
This ratio indicates lower densities and a ΕΙΝ field of less than about GGo reftig,? fipdrmod)).
This ratio indicates lower densities and a FUV field of less than about $_0$ \\ref{fig_hifipdrmod}) ).
S tilllowerratios. indicatelowerimpingingF UV fields
Still lower ratios, indicate lower impinging FUV fields.
The ratio of eemission over the FIR continuum. is à good measure of the total cooling of the gas relative to the cooling of the dust. reflecting the ratio of FUV energy heating the gas to the FUV energy heating the grams. and hence the grain heating efficiency. re. the efficiency of the photo-electric (PE) effect (Rubinetal.2009).
The ratio of emission over the FIR continuum, is a good measure of the total cooling of the gas relative to the cooling of the dust, reflecting the ratio of FUV energy heating the gas to the FUV energy heating the grains, and hence the grain heating efficiency, i.e. the efficiency of the photo-electric (PE) effect \citep{rubin2009}.
. Efficiencies of up to about are still consistent- with FUV heating. te. with emission from PDRs (Bakes&Tielens1994;Kaufmanetal.1999).
Efficiencies of up to about are still consistent with FUV heating, i.e. with emission from PDRs \citep{bakestielens1994,Kaufman1999}.
. The PE heating efficiency is a function of FUV field. electron density. and temperature.
The PE heating efficiency is a function of FUV field, electron density, and temperature.
A high FUV field leads to a large fraction of ionized dust particles. lowering the efficiency.
A high FUV field leads to a large fraction of ionized dust particles, lowering the efficiency.
On the other hand. low metallicities naturally lead to increased efficiencies
On the other hand, low metallicities naturally lead to increased efficiencies
4959 line due to the relative proximity of the Io line.
4959 line due to the relative proximity of the $\beta$ line.
The distribution of the wavelength separation between (he centroids of both lines has a rms of 0.11.As this indicates that the main factor broadening the distribution of the centroids of the ΟΠΗ lines are absolute spectral shifts which mostly reflect the kinematics (<150 km !) of the narrow line clouds where the [OIL] originates.
The distribution of the wavelength separation between the centroids of both lines has a rms of 0.11; this indicates that the main factor broadening the distribution of the centroids of the [OIII] lines are absolute spectral shifts which mostly reflect the kinematics $\le 150$ km $^{-1}$ ) of the narrow line clouds where the [OIII] originates.
The emission lines of OIII (4959 and 5008). and IL? (nairow. and broad. components) were simultaneously modeled by single Gaussian each.
The emission lines of OIII (4959 and 5008), and $\beta$ (narrow and broad components) were simultaneously modeled by single Gaussian each.
The wavelength position of each line of the [OTI] doublet was directly estimated as the central position of the corresponding Gaussian.
The wavelength position of each line of the [OIII] doublet was directly estimated as the central position of the corresponding Gaussian.
In principle this seems a very. simple description of the line profiles. and in many cases produces a poor fit to the data.
In principle this seems a very simple description of the line profiles, and in many cases produces a poor fit to the data.
However. in practice the method takes advantage of the expected similar shape for both lines of the doublet. aud removes most of the contribution of IL? in the spectral region of the [OL] doublet.
However, in practice the method takes advantage of the expected similar shape for both lines of the doublet, and removes most of the contribution of $\beta$ in the spectral region of the [OIII] doublet.
After removing the most extreme cases of poor fits. the results are quite consistent aud robust.
After removing the most extreme cases of poor fits, the results are quite consistent and robust.
Selecting those spectra in which each of the [OILI] lines are described by Gaussian with peak amplitudes >20 the level of the continuum noise. and o within the range 1.43.0 (vest frame of the [OIL] 5008 line) there were 1568 spectra (clean sample 2°) [rom which we obtained Aa/a=(42.442:2.5)x10.7.
Selecting those spectra in which each of the [OIII] lines are described by Gaussian with peak amplitudes $>20$ the level of the continuum noise, and $\sigma$ within the range 1.4-3.0 (rest frame of the [OIII] 5008 line) there were 1568 spectra ('clean sample 2') from which we obtained $\Delta \alpha/\alpha=(+2.4\pm 2.5)\times 10^{-5}$.
Figure 4. shows the wavelengths determined for the spectral position of both lines of [OIL] (io compute the rest frame wavelengths we have used the estimates of redshifts provided by the SDSS database).
Figure \ref{o3} shows the wavelengths determined for the spectral position of both lines of [OIII] (to compute the rest frame wavelengths we have used the estimates of redshifts provided by the SDSS database).
The wavelengths of both lines lie along a line crossing from the bottom left to the top right and dont show any svstematic effect.
The wavelengths of both lines lie along a line crossing from the bottom left to the top right and don't show any systematic effect.
The results obtained by both methods are compatible ancl quite similar.
The results obtained by both methods are compatible and quite similar.
Both estimations are also compatible with the local value.
Both estimations are also compatible with the local value.
Most of the spectra included in (he clean sample 2 (1223 out of 1568) ave also included in the clean sample 1.
Most of the spectra included in the clean sample 2 (1223 out of 1568) are also included in the clean sample 1.
Fie 5 shows a comparison between (he results of both methods.
Fig \ref{compara_metodos_o3} shows a comparison between the results of both methods.
There is a general good agreement between them. although the method of fitting Gaussian tends to be a bit more accurate (the rms of the distributions of Aa/a ave 9.8x10. and 8.0xLO1 [or the clean samples 1 and 2 respectively).
There is a general good agreement between them, although the method of fitting Gaussian tends to be a bit more accurate (the rms of the distributions of $\Delta \alpha /\alpha$ are $9.8\times 10^{-4}$ and $8.0\times 10^{-4}$ for the clean samples 1 and 2 respectively).
Then. here after along the paper. we will use the results obtained by the second method.
Then, here after along the paper, we will use the results obtained by the second method.
To analvze the value of Xa/o as a [unction of redshift (or look-back time) we compute
To analyze the value of $\Delta \alpha/\alpha $ as a function of redshift (or look-back time) we compute
Ciuiderdoni (1993) and Cole (1994). and explore the role of pre-galactic cooling Hows (Nulsen Fabian 1995).
Guiderdoni (1993) and Cole (1994), and explore the role of pre-galactic cooling flows (Nulsen Fabian 1995).
DDC would. like to acknowledge support from. ΑΝΤΕ (Portugal) through program PRAXIS XXI (erant. number DBD/2802/93-11M).
DDCR would like to acknowledge support from JNICT (Portugal) through program PRAXIS XXI (grant number BD/2802/93-RM).
Part of this paper was written while PAT was at the Institute for Pheoretical Physics at Santa Barbara and as such was supported in part by the National Science Foundation under Grant Number PIIY89-04035.
Part of this paper was written while PAT was at the Institute for Theoretical Physics at Santa Barbara and as such was supported in part by the National Science Foundation under Grant Number PHY89-04035.
The paper was completed while PAL was holding a Nullield Foundation Science Iesearch Lectureship.
The paper was completed while PAT was holding a Nuffield Foundation Science Research Lectureship.
We would like to thank Shaun Cole for. providing us with a copy of the Block Mocel program.
We would like to thank Shaun Cole for providing us with a copy of the Block Model program.
The production of this paper was aided. by use of the SPARLININ Minor Node at Sussex.
The production of this paper was aided by use of the STARLINK Minor Node at Sussex.
"difference" frame made by subtracting a scaled version of (he ΟΕ continuum image from the narrow-band [rame.
“difference” frame made by subtracting a scaled version of the $B$ $V$ continuum image from the narrow-band frame.
In this case. our detection algorithm was set to flag all objects brighter than four times the standard deviation of the local sky.
In this case, our detection algorithm was set to flag all objects brighter than four times the standard deviation of the local sky.
This difference technique produced a sample of several thousand additional candidates. most of which were below our equivalent width threshold.
This difference technique produced a sample of several thousand additional candidates, most of which were below our equivalent width threshold.
However. when (he weak emission-line sources were excluded. (he result. was a sample of objects that was ~15% larger than that produced by the two-color method alone.
However, when the weak emission-line sources were excluded, the result was a sample of objects that was $\sim 15\%$ larger than that produced by the two-color method alone.
For both detection algorithms. we intentionally biased our parameters to identify Lait sources αἱ the expense of false detections wwe introduced Type I errors into our dataset).
For both detection algorithms, we intentionally biased our parameters to identify faint sources at the expense of false detections we introduced Type I errors into our dataset).
To compensate for this. we visually inspected each candidate. both on the co-added: narrow-band and broadband: Lames. and on of the original images.
To compensate for this, we visually inspected each candidate, both on the co-added narrow-band and broadband frames, and on sub-samples of the original images.
This step excluded most of the false positives. which were tvpically at the [απο limit. and artifacts produced by cross-talk associated with the CCD electronics.
This step excluded most of the false positives, which were typically at the frame limit, and artifacts produced by cross-talk associated with the CCD electronics.
To derive the line {hixes and equivalent widths of our LAE candidates. we took advantage ol the fact that GrOT measured the 5000 AAD magnitudes of several ECDF-S field stars by comparing their large aperture instrumental magnitudes to those of spectrophotometric standard stars (Stone1977:Mannyοἱal.1992) taken throughout their survey.
To derive the line fluxes and equivalent widths of our LAE candidates, we took advantage of the fact that Gr07 measured the 5000 AB magnitudes of several ECDF-S field stars by comparing their large aperture instrumental magnitudes to those of spectrophotometric standard stars \citep{stone, hamuy92} taken throughout their survey.
To place our new 5010 nnarrow-band observations on (he same photometric svstem. we (herelore measured our LAE brightnesses with respect to these same stars.
To place our new 5010 narrow-band observations on the same photometric system, we therefore measured our LAE brightnesses with respect to these same stars.
We then converted our narrow-band 5010 AD magnitudes into monochromatie fluxes (P5010) bv comparing the filter's integral üransmission (which is the relevant quantity for field star photometry) to its monochromatic óransmission at the center of the bandpass (seeGr0TanclJacobyetal.
We then converted our narrow-band 5010 AB magnitudes into monochromatic fluxes $F_{5010}$ ) by comparing the filter's integral transmission (which is the relevant quantity for field star photometry) to its monochromatic transmission at the center of the bandpass \citep[see Gr07 and][]{jqa}.
1987)... Note that (his simple procedure is only exact for top-hat filters where the monochromatic transmission is insensitive to wavelength: as GrO7 showed. observations through filters with a transmission curve require a more sophisticated approach.
Note that this simple procedure is only exact for top-hat filters where the monochromatic transmission is insensitive to wavelength: as Gr07 showed, observations through filters with a Gaussian-shaped transmission curve require a more sophisticated approach.
Along with monochromatic flux. we also derived photometric equivalent widths for all our LAE candidates by comparing their narrow-band AB flix densities. fs. to their B+V. continuum [ιν densities. fj, via where AA=57 aapproximates (he contribution of the ealaxys underlying continuum within the narrow-bancl lilters bandpass.
Along with monochromatic flux, we also derived photometric equivalent widths for all our LAE candidates by comparing their narrow-band AB flux densities, $f_{5010}$, to their $B+V$ continuum flux densities, $f_{B+V}$ via where $\Delta\lambda = 57$ approximates the contribution of the galaxy's underlying continuum within the narrow-band filter's bandpass.
For consistency with Gr07. we (then excluded all sources with equivalent
For consistency with Gr07, we then excluded all sources with equivalent
their measurements.
their measurements.
We used the wavelength region 5210<Juosttrame<5390 A. which includes the many prominent Fe absorption features around 5325 A (see Fig. 2)).
We used the wavelength region $5210<\lambda_{\rm restframe}<5390$ $\AA$, which includes the many prominent Fe absorption features around 5325 $\AA$ (see Fig. \ref{spectra}) ).
Prior to. cross-correlation. we continuum subtracted the spectra.
Prior to cross-correlation, we continuum subtracted the spectra.
For this. we adjusted the continuum fitting order individually for each source such as to yield the lowest order that gives satisfactory results.
For this, we adjusted the continuum fitting order individually for each source such as to yield the lowest order that gives satisfactory results.
The peak position of the cross-correlation gives the relative radial velocity between object and template.
The peak position of the cross-correlation gives the relative radial velocity between object and template.
The width. c4. of the cross-correlation peak (Fig. 4))
The width, $\sigma_{\rm peak}$, of the cross-correlation peak (Fig. \ref{fxcor}) )
is the quadratic sum of the intrinsic object line width caused by random stellar motion plus twice the instrumental line width (equal to the template line width): r.e.. opeak=Oatoh472x
is the quadratic sum of the intrinsic object line width caused by random stellar motion plus twice the instrumental line width (equal to the template line width): i.e., $\sigma_{\rm peak}^2=\sigma_{\rm obj}^2+2\times \sigma_{\rm ins}^2$ .
By cross-correlating the un-broadened and continuum subtractedUT. templates against each other. we measured the template's intrinsic. line width oj, to be 9.7 km/s with a very small scatter of order 0.4 km/s. The intrinsic line width or, of the object spectrum is then calculated as: cjνι -2x«oc..
By cross-correlating the un-broadened and continuum subtracted templates against each other, we measured the template's intrinsic line width $\sigma_{\rm ins}$ to be 9.7 km/s with a very small scatter of order 0.4 km/s. The intrinsic line width $\sigma_{\rm obj}$ of the object spectrum is then calculated as: $\sigma_{\rm obj}=\sqrt{\sigma_{\rm peak}^2-2 \times \sigma_{\rm ins}^2}$ .
Note that the factor 2 in front of cL. Is necessary because both the object and template spectrum are broadened by the instrumental resolution (Dubath et al.
Note that the factor 2 in front of $\sigma_{\rm ins}^2$ is necessary because both the object and template spectrum are broadened by the instrumental resolution (Dubath et al.