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

source stringlengths 1 2.05k ⌀	target stringlengths 1 11.7k
Presuming	Presuming
amplitudes for cach pulsar. adding them to the observed residuals and refitting Each amplitude is due to an ensemble average of 1.000 incividual sources distributed isotropically on the sky.	amplitudes for each pulsar, adding them to the observed residuals and refitting Each amplitude is due to an ensemble average of 1,000 individual sources distributed isotropically on the sky.
οσο sources are drawn from a distribution that follows Equation l.	These sources are drawn from a distribution that follows Equation \ref{eq:strain}.
The end result of this process is a distribution of the fitted: parameters at 200 CWD amplitudes distributed logarithmically in the range 110.17 1510.4%.	The end result of this process is a distribution of the fitted parameters at 200 GWB amplitudes distributed logarithmically in the range $1\times 10^{-15}$ $1\times 10^{-13}$.
This range was chosen because it includes all previous upper limits and allows for lower backgrounds.	This range was chosen because it includes all previous upper limits and allows for lower backgrounds.
These distributions were then analvsed in several wavs to calculate the ellects of fitting for pulsar parameters when a CAV signal is present in the timing residuals and to determine upper limits on the GWD amplitude.	These distributions were then analysed in several ways to calculate the effects of fitting for pulsar parameters when a GW signal is present in the timing residuals and to determine upper limits on the GWB amplitude.
I is likely that there already is à CAV signal from the stochastic background present in the pulsar timing data.	It is likely that there already is a GW signal from the stochastic background present in the pulsar timing data.
Jecause we could be adding sipulated GWs to those already existing in the data. any upper limits that we set could be. at worst. underestimated by a factor of 4/2.	Because we could be adding simulated GWs to those already existing in the data, any upper limits that we set could be, at worst, underestimated by a factor of $\sqrt{2}$.
We used data for the pulsars PSR J04374715 and. PSR J1713\|0747.	We used data for the pulsars PSR J0437–4715 and PSR J1713+0747.
These data were collected with the Parkes 64-ni radio telescope at 20 em wavelength.	These data were collected with the Parkes 64-m radio telescope at 20 cm wavelength.
A full description of the data. sets and observing systems can be found. in 77. and references therein.	A full description of the data sets and observing systems can be found in \citet{vbs+08,vbc+09} and references therein.
“Phese pulsars were chosen for three reasons.	These pulsars were chosen for three reasons.
Firstly. the timing parallax measurements are consistent at the l-o level with those from VLBI. giving us the ability to place upper limits on the background. by comparing the timing and. VLBI measurements.	Firstly, the timing parallax measurements are consistent at the $\sigma$ level with those from VLBI, giving us the ability to place upper limits on the background by comparing the timing and VLBI measurements.
Secondly. roth pulsars have low rms timing residuals. which lead to the yest upper limits that can be obtained using the methods described above.	Secondly, both pulsars have low rms timing residuals, which lead to the best upper limits that can be obtained using the methods described above.
Finally. these data sets have a relatively ong time span. allowing us to see effects of Iow-frequenevy CGAVs more readily in the timing residuals.	Finally, these data sets have a relatively long time span, allowing us to see effects of low-frequency GWs more readily in the timing residuals.
A summary of the imine characteristics is given in Tables 1. and 2..	A summary of the timing characteristics is given in Tables \ref{tab:0437} and \ref{tab:1713}.
For the VLBI parallax measurements in this study we use an LBA xwallax for PSR. JO4374715 (2). and à VLBA parallax for "SI JITIS]0747 η.	For the VLBI parallax measurements in this study we use an LBA parallax for PSR J0437–4715 \citep{dvt+08} and a VLBA parallax for PSR J1713+0747 \citep{cbv+09}.
Figure 1 illustrates how a GWD can be absorbed into certain periodic timing parameters for PSR JOL374715.	Figure \ref{fig:fits} illustrates how a GWB can be absorbed into certain periodic timing parameters for PSR J0437–4715.
Figure fb) shows the timing residuals with a GWB with amplitude of 42510 added to the data.	Figure \ref{fig:gw} shows the timing residuals with a GWB with amplitude of $A=5\times 10^{-13}$ added to the data.
Figures He) and 1(d) show the timing residuals using the GW-induced (.4—9510 00) values of parallax ancl proper motion. and Dow. and d. respectively.	Figures \ref{fig:pmpx} and \ref{fig:pbom} show the timing residuals using the GW-induced $A=5\times10^{-13}$ ) values of parallax and proper motion, and $\dot{P}_{\rm b}$, $\omega$, and $\dot{\omega}$, respectively.
A very. large GAVB amplitude was used for illustration purposes. but this same ellect takes ace at smaller. amplitudes and is just not as visible bv eve.	A very large GWB amplitude was used for illustration purposes, but this same effect takes place at smaller amplitudes and is just not as visible by eye.
We can see from the figures that the GAVB can induce roth high and low-frequeney components in. residuals.	We can see from the figures that the GWB can induce both high and low-frequency components in residuals.
The oblem with fitting for these parameters is that. in elfect. one is fitting out a significant amount of the CN signal hat is contributing to the resicluals.	The problem with fitting for these parameters is that, in effect, one is fitting out a significant amount of the GW signal that is contributing to the residuals.
In this section. we will construct confidence intervals for the fitted parameters at. various CAB amplitudes and show that these confidence intervals become Larger as the GWD amplitude increases.	In this section we will construct confidence intervals for the fitted parameters at various GWB amplitudes and show that these confidence intervals become larger as the GWB amplitude increases.
The method for calculating these confidence intervals is quite straightforward.	The method for calculating these confidence intervals is quite straightforward.
The main simulation ciscussecl in Section 2.3) is used to obtain distributions of the given fitted. parameters at cach amplitude.	The main simulation discussed in Section \ref{sec:extended} is used to obtain distributions of the given fitted parameters at each amplitude.
As we have seen above. a CAVB will cause excess power to be absorbed. into timing xwameters.	As we have seen above, a GWB will cause excess power to be absorbed into timing parameters.
LExamples of the subsequent corruption of he parameters can be seen in the histograms of Figure 2..	Examples of the subsequent corruption of the parameters can be seen in the histograms of Figure \ref{fig:gauss}.
Since this simulation injects GAs with rancom sky »ositions ancl random. frequencies (within a certain range and with a given spectrum). the subsequent corruption of 1e fitted. parameters caused by absorbing parts of the CAV μα»ectrum. will result. in a Gaussian distribution. centered wound the unperturbecl parameter. values.	Since this simulation injects GWs with random sky positions and random frequencies (within a certain range and with a given spectrum), the subsequent corruption of the fitted parameters caused by absorbing parts of the GW spectrum will result in a Gaussian distribution centered around the unperturbed parameter values.
It can be seen rom Figure 2. that the FWHLIIAL of the distribution. and yerefore the confidence interval on the parameter increases with increasing GWD amplitude.	It can be seen from Figure \ref{fig:gauss} that the FWHM of the distribution and therefore the confidence interval on the parameter increases with increasing GWB amplitude.
This increased. spread. in »otential parameter estimates is the GW-ineluced corruption ju we aim to quantify in this paper.	This increased spread in potential parameter estimates is the GW-induced corruption that we aim to quantify in this paper.
Ht must be noted ju at sullictently high (ΝΟ amplitudes prominent low-pequency power will be visible in the timing residuals.	It must be noted that at sufficiently high GWB amplitudes prominent low-frequency power will be visible in the timing residuals.
‘To ensure phase-connection in our timing. we limited. our simulations to a maximum GWD amplitude of 1.10.οὐ.	To ensure phase-connection in our timing, we limited our simulations to a maximum GWB amplitude of $1\times 10^{-13}$.
We also note that towardsD. the higher end of the simulated CWD amplitude range. sullicient levels of low-frequeney noise will be present in the simulations to make the uncertainties returned [from the standard. least-squares fit unreliable (seee.g.2)..	We also note that towards the higher end of the simulated GWB amplitude range, sufficient levels of low-frequency noise will be present in the simulations to make the uncertainties returned from the standard least-squares fit unreliable \citep[see e.g.][]{vbs+08}.
Llowever. since our analysis only uses the best-fit and not its uncertainty. this has no ellect on our results.	However, since our analysis only uses the best-fit and not its uncertainty, this has no effect on our results.
‘These histograms can be used to directly study the elfects that the presence of GWs has on the parameter estimates resulting from the fit.	These histograms can be used to directly study the effects that the presence of GWs has on the parameter estimates resulting from the fit.
This is done hy plotting the ratio of the standard deviation of the fitted parameters and the MvO2--reportecl unperturbed error on the parameters against GAVB amplitude.	This is done by plotting the ratio of the standard deviation of the fitted parameters and the -reported unperturbed error on the parameters against GWB amplitude.
The original. ancl in some wavs still best. argument in favor of the white dwarf pulsation hypothesis is the observed simultaneous presence of (he inconmnenstrate P28 and P29 periodicities (Robinson et al.	The original, and in some ways still best, argument in favor of the white dwarf pulsation hypothesis is the observed simultaneous presence of the incommensurate P28 and P29 periodicities (Robinson et al.
1978).	1978).
Incommensurate periocliciGes are common Lor the ZZ Celi class of stars (isolated nonradial 4 mode pulsating white dwarls: see Kepler Dradley 1995 [or a good review of white dwarfs and pulsation).	Incommensurate periodicities are common for the ZZ Ceti class of stars (isolated non–radial $g$ –mode pulsating white dwarfs; see Kepler Bradley 1995 for a good review of white dwarfs and pulsation).
Also. the white cdwarl in GW Lib is known to exhibit ZZ Ceti(wpe pulsations (van Zvl et al.	Also, the white dwarf in GW Lib is known to exhibit ZZ Ceti–type pulsations (van Zyl et al.
2000: Szkocly οἱ al.	2000; Szkody et al.
2002).	2002).
Additional support. albeit weak. comes from the UV spectrum of the oscillations that are consistent with a white dwarf photospheric origi (Skidimore et al.	Additional support, albeit weak, comes from the UV spectrum of the oscillations that are consistent with a white dwarf photospheric origin (Skidmore et al.
1999. Welsh οἱ al.	1999, Welsh et al.
LOOT),	1997).
Yel the ZZ Celi stars (and GW Lib) have much longer periods (hundreds of seconds) than WZ See.	Yet the ZZ Ceti stars (and GW Lib) have much longer periods (hundreds of seconds) than WZ Sge.
Furthermore. (he quiescent temperature of (he white dwarl in WZ See. ~14.600 Ix (Cheng οἱ al.	Furthermore, the quiescent temperature of the white dwarf in WZ Sge, $\sim$ 14,600 K (Cheng et al.
1997. Godon et al.	1997, Godon et al.
2003). exceeds (the nominal upper temperature limit (the "blue edge) of 213.500 IX of the instability strip for ZZ Ceti stars.	2003), exceeds the nominal upper temperature limit (the “blue edge”) of $\sim$ 13,500 K of the instability strip for ZZ Ceti stars.
However. more massive white chwarls have a hotter "blue edge" (han the canonical 0.6 ΔΙ. white dwarf (Bradley Winget 1994: Dergeron οἱ al.	However, more massive white dwarfs have a hotter “blue edge” than the canonical 0.6 $\Msun$ white dwarf (Bradley Winget 1994; Bergeron et al.
1995: Giovannini οἱ al.	1995; Giovannini et al.
1998) and recent studies do in [act suggest WZ See has a massivewhite dwarf. exceeding 70.8 AL. ancl perhaps even as high as 1.2 M. (Sleeehs οἱ al.	1998) and recent studies do in fact suggest WZ Sge has a massivewhite dwarf, exceeding $\sim$ 0.8 $\Msun$ and perhaps even as high as 1.2 $\Msun$ (Steeghs et al.
2001: Skichmore et al.	2001; Skidmore et al.
2000: Ixnigge et al.	2000; Knigge et al.
2002: Long et al.	2002; Long et al.
2003: Godon et al.	2003; Godon et al.
2003).	2003).
By linearly extrapolating the blue edge temperature versus mass presented in Giovanninni οἱ al.	By linearly extrapolating the blue edge temperature versus mass presented in Giovanninni et al.
1998. a g mode pulsating white dwarl with a temperature of 14.600 IX would require a white dwarf mass 31.2\1.. barely within acceptable mass estimates.	1998, a $g$ –mode pulsating white dwarf with a temperature of 14,600 K would require a white dwarf mass $\gtsimeq1.2 \Msun$, barely within acceptable mass estimates.
However. (he extrapolation (ο values above 1M. is highly uncertain so this crude mass limit should be taken as nothing more than a statement that g mode pulsations cannot be ruled out by quiescent while dwarf temperature arguments.	However, the extrapolation to values above $1 \Msun$ is highly uncertain so this crude mass limit should be taken as nothing more than a statement that $g$ –mode pulsations cannot be ruled out by quiescent white dwarf temperature arguments.
Furthermore. as was suggested by Szkody et al. (	Furthermore, as was suggested by Szkody et al. (
2002) for GW Lib. it could be that the temperature determined for WZ See is a elobal average. ancl a cooler region could be responsible [ον the pulsations for GW Lib. a twotemperature white dwarl model fits substantially better (hen a one temperature model.	2002) for GW Lib, it could be that the temperature determined for WZ Sge is a global average, and a cooler region could be responsible for the pulsations — for GW Lib, a two–temperature white dwarf model fits substantially better then a one temperature model.
Note that the thickness of the surface convective zone responsible for ihe pulsations in WZ See should be very thin compared to other ZZ Celi stars since the timescale of the periodicity depends on the depth of the base of the convective zone (e.g. see Dergeron et al.	Note that the thickness of the surface convective zone responsible for the pulsations in WZ Sge should be very thin compared to other ZZ Ceti stars since the timescale of the periodicity depends on the depth of the base of the convective zone (e.g. see Bergeron et al.
1995) [ast periodicities require a shallow convective zone.	1995) — fast periodicities require a shallow convective zone.
Skidmore et al. (	Skidmore et al. (
1999) extrapolated the observed temperature.period relation of ZZ Celi stars using (he cata in Clemens (1993) and found the extrapolation falls tantalizinely close to the quiescent temperature and period of WZ See.	1999) extrapolated the observed temperature–period relation of ZZ Ceti stars using the data in Clemens (1993) and found the extrapolation falls tantalizingly close to the quiescent temperature and period of WZ Sge.
This bolstered (he viability of the white cdwarf pulsation hypothesis. and mitigated the objection that the 28 s and 29 s periods are too short to be related to the ZZ Ceti phenomenon.	This bolstered the viability of the white dwarf pulsation hypothesis, and mitigated the objection that the 28 s and 29 s periods are too short to be related to the ZZ Ceti phenomenon.
We re-examined this extrapolation of ligure 2 of Clemens (1993) and while the observed temperatureperiod relation lor ZZ Ceti	We re-examined this extrapolation of figure 2 of Clemens (1993) and while the temperature–period relation for ZZ Ceti
6 ea fundamental aud first harmonic.	of a fundamental and first harmonic.
In both of those stars. the harmonic minima coincide with the maxima and minima of the fundamental.	In both of those stars, the harmonic minima coincide with the maxima and minima of the fundamental.
This results iu a pulse shape with a deepened imininuun at the location of the fundamental minima: relatively large harmonic auplitucdes (as in 07113) produce secondary minia at the location of the fundamental maxima: aud sanaller harmonic amplitudes fatten the fundamental miaxina (as in 5752)).	This results in a pulse shape with a deepened minimum at the location of the fundamental minimum; relatively large harmonic amplitudes (as in ) produce secondary minima at the location of the fundamental maxima; and smaller harmonic amplitudes flatten the fundamental maxima (as in ).
We investigate the phase relationship between the two modes in uunder the asstuption that they are harmonically related Gf they are uot. the shape of the ight curve does not repeat at the fundamental frequency).	We investigate the phase relationship between the two modes in under the assumption that they are harmonically related (if they are not, the shape of the light curve does not repeat at the fundamental frequency).
To show that this assumption 1s consistent with the data. we compute a weielted average of the frequencies ou the four nights using the inverse variuices as weights (Tavlor1997).	To show that this assumption is consistent with the data, we compute a weighted average of the frequencies on the four nights using the inverse variances as weights \citep{tay97}.
. This gives f, = 2957 + 7 ullz aud f = 5906 + Gyllz. which is consistent with f) = 98.	This gives $_{1}$ = 2957 $\pm$ 7 $\mu$ Hz and $_{2}$ = 5906 $\pm$ $\mu$ Hz, which is consistent with $_{2}$ = $_{1}$.
We refit the data for cach wight applying this frequency constraint.	We refit the data for each night applying this frequency constraint.
A weighted average of these results eives fy = 2053.6 c 2.7 pile (338.57 + 0.30 s): the aliasing in the combined 2009 amplitude spectrum preveuts us from confidently determining amore accurate frequency.	A weighted average of these results gives $_{1}$ = 2953.6 $\pm$ 2.7 $\mu$ Hz (338.57 $\pm$ 0.30 s); the aliasing in the combined 2009 amplitude spectrum prevents us from confidently determining a more accurate frequency.
Consistent with the data. we assune the frequencies are the same on cach wight aud again refit the leht curves with the frequencies fixed to look for changes in auplitude aud relative phase.	Consistent with the data, we assume the frequencies are the same on each night and again refit the light curves with the frequencies fixed to look for changes in amplitude and relative phase.
We multiply the best-Bt amplitudes aud their errors by z T.,f/su(xT. f) o correct for the effect of a finite exposure time. T. (Baldry1999).	We multiply the best-fit amplitudes and their errors by $\pi$ $_{exp}$ $\pi$ $_{exp}$ f) to correct for the effect of a finite exposure time, $_{exp}$ \citep{bal99}.
. Table 3. lists these results.	Table \ref{table:fit2} lists these results.
We report phase difference as the number of secouds between the nimii of the harmonic aud the umm/10aximnmna of the fundamental aud use uegative values to indicate he harmonic minima is shifted left of the fundamental ΜΙΤπαπα.	We report phase difference as the number of seconds between the minimum of the harmonic and the minimum/maximum of the fundamental and use negative values to indicate the harmonic minimum is shifted left of the fundamental minimum/maximum.
The one-sigmia errors reported for he phase differences come frou bootstrap Monte Carlo siuulations. and in each case the value falls between he suni of the errors for the individual phases aud the quadrature stun of those errors.	The one-sigma errors reported for the phase differences come from bootstrap Monte Carlo simulations, and in each case the value falls between the sum of the errors for the individual phases and the quadrature sum of those errors.
By folding the leht curves at the period of the "udenaeutal we eet a picture of these quantitative results (Fie. 2)).	By folding the light curves at the period of the fundamental, we get a picture of these quantitative results (Fig. \ref{fig:flcs}) ).
The pulse shape is like those of aand0711.	The pulse shape is like those of and.
. There is some sugeestion that the phase relationship between the fundamental aud harmonic nuüeht not be exactly zero. but the errors iu phase are large making this hard to determine.	There is some suggestion that the phase relationship between the fundamental and harmonic might not be exactly zero, but the errors in phase are large making this hard to determine.
Similarly. there is no statistically significant chauee in amplitude or phase difference among the nights.	Similarly, there is no statistically significant change in amplitude or phase difference among the nights.
The discovery of a fourth variable among the hot DQ white dwarf stars means the variable fraction of the known hot DOs is at least	The discovery of a fourth variable among the hot DQ white dwarf stars means the variable fraction of the known hot DQs is at least.
This is a high percentage compared with the hwdrogen- aud heliumatmosphere white dwarf variables.	This is a high percentage compared with the hydrogen- and helium-atmosphere white dwarf variables.
Thus. as we get to know the hot DQ stars better. we find thon disiucliued to be photometrically constant.	Thus, as we get to know the hot DQ stars better, we find them disinclined to be photometrically constant.
Further. there is no obvious observational characteristic that serves as a predictor of whether a given hot DQ is variable.	Further, there is no obvious observational characteristic that serves as a predictor of whether a given hot DQ is variable.
Of the four reported variables. hhas a spectral featureidentified with helimuu etal. 2008b):: hhas a spectral feature identified with livdrogeu (Dufouretal. 20082): two aand 0711)) have broacened spectral lines (Dufouretal.2008a) possibly resulting from a maguectic Ποια (Dufouretal.2008b): the other two exhibit uo such spectral distortions.	Of the four reported variables, has a spectral featureidentified with helium \citep{duf08mag}; has a spectral feature identified with hydrogen \citep{duf08}; two and ) have broadened spectral lines \citep{duf08} possibly resulting from a magnetic field \citep{duf08mag}; the other two exhibit no such spectral distortions.
Thus. hvdroseu. helium. aud nagnetic fields do uot discourage variabilitv. and none of them appears necessary to encourage it.	Thus, hydrogen, helium, and magnetic fields do not discourage variability, and none of them appears necessary to encourage it.
Indeed. so fav. the best predictor of a hot DQ stars variability is hat it is a hot DO star.	Indeed, so far, the best predictor of a hot DQ star's variability is that it is a hot DQ star.
Not ouly do we not know the reason one hot DO varies aud another doesut. we do uot ‘mow why heir pulse shapes differ.	Not only do we not know the reason one hot DQ varies and another doesn't, we do not know why their pulse shapes differ.
Based ou suggestious of Greenetal. (2009).. Dufouretal(2009a)— predict a connection between magnetic field aud pulse shape.	Based on suggestions of \citet{gre09}, , \citet{duf09} predict a connection between magnetic field and pulse shape.
In this work we present a new phenomenology based technique to address the issue of non-thermal line width and the temperature of the diffuse neutral hydrogen of our Galaxy assuming a rough pressure equilibrium between different phases of the ISpa	In this work we present a new phenomenology based technique to address the issue of non-thermal line width and the temperature of the diffuse neutral hydrogen of our Galaxy assuming a rough pressure equilibrium between different phases of the ISM.
y A possible connection between the observed Kolmogorov-like scaling of the non-thermal velocity dispersion in the Galactic H and the turbulence of the interstellar medium is discussed.	A possible connection between the observed Kolmogorov-like scaling of the non-thermal velocity dispersion in the Galactic H and the turbulence of the interstellar medium is discussed.
This scaling relation is used to re-examine the issue of the temperature of the Galactic ISM with the help of the millennium Arecibo 21 em absorption-line survey measurements.	This scaling relation is used to re-examine the issue of the temperature of the Galactic ISM with the help of the millennium Arecibo 21 cm absorption-line survey measurements.
The distribution of the derived. temperature is found to be significantly different from the distribution of the upper limits of the kinetic temperature.	The distribution of the derived temperature is found to be significantly different from the distribution of the upper limits of the kinetic temperature.
A considerable fraction (— 29%) of the gas is found to be in the thermally unstable phase. qualitatively contirming earlier results.	A considerable fraction $\sim 29\%$ ) of the gas is found to be in the thermally unstable phase, qualitatively confirming earlier results.

Presuming

amplitudes for cach pulsar. adding them to the observed residuals and refitting Each amplitude is due to an ensemble average of 1.000 incividual sources distributed isotropically on the sky.

amplitudes for each pulsar, adding them to the observed residuals and refitting Each amplitude is due to an ensemble average of 1,000 individual sources distributed isotropically on the sky.

οσο sources are drawn from a distribution that follows Equation l.

These sources are drawn from a distribution that follows Equation \ref{eq:strain}.

The end result of this process is a distribution of the fitted: parameters at 200 CWD amplitudes distributed logarithmically in the range 110.17 1510.4%.

The end result of this process is a distribution of the fitted parameters at 200 GWB amplitudes distributed logarithmically in the range $1\times 10^{-15}$ $1\times 10^{-13}$.

This range was chosen because it includes all previous upper limits and allows for lower backgrounds.

These distributions were then analvsed in several wavs to calculate the ellects of fitting for pulsar parameters when a CAV signal is present in the timing residuals and to determine upper limits on the GWD amplitude.

These distributions were then analysed in several ways to calculate the effects of fitting for pulsar parameters when a GW signal is present in the timing residuals and to determine upper limits on the GWB amplitude.

I is likely that there already is à CAV signal from the stochastic background present in the pulsar timing data.

It is likely that there already is a GW signal from the stochastic background present in the pulsar timing data.

Jecause we could be adding sipulated GWs to those already existing in the data. any upper limits that we set could be. at worst. underestimated by a factor of 4/2.

Because we could be adding simulated GWs to those already existing in the data, any upper limits that we set could be, at worst, underestimated by a factor of $\sqrt{2}$.

We used data for the pulsars PSR J04374715 and. PSR J1713|0747.

We used data for the pulsars PSR J0437–4715 and PSR J1713+0747.

These data were collected with the Parkes 64-ni radio telescope at 20 em wavelength.

These data were collected with the Parkes 64-m radio telescope at 20 cm wavelength.

A full description of the data. sets and observing systems can be found. in 77. and references therein.

A full description of the data sets and observing systems can be found in \citet{vbs+08,vbc+09} and references therein.

“Phese pulsars were chosen for three reasons.

These pulsars were chosen for three reasons.

Firstly. the timing parallax measurements are consistent at the l-o level with those from VLBI. giving us the ability to place upper limits on the background. by comparing the timing and. VLBI measurements.

Firstly, the timing parallax measurements are consistent at the $\sigma$ level with those from VLBI, giving us the ability to place upper limits on the background by comparing the timing and VLBI measurements.

Secondly. roth pulsars have low rms timing residuals. which lead to the yest upper limits that can be obtained using the methods described above.

Secondly, both pulsars have low rms timing residuals, which lead to the best upper limits that can be obtained using the methods described above.

Finally. these data sets have a relatively ong time span. allowing us to see effects of Iow-frequenevy CGAVs more readily in the timing residuals.

Finally, these data sets have a relatively long time span, allowing us to see effects of low-frequency GWs more readily in the timing residuals.

A summary of the imine characteristics is given in Tables 1. and 2..

A summary of the timing characteristics is given in Tables \ref{tab:0437} and \ref{tab:1713}.

For the VLBI parallax measurements in this study we use an LBA xwallax for PSR. JO4374715 (2). and à VLBA parallax for "SI JITIS]0747 η.

For the VLBI parallax measurements in this study we use an LBA parallax for PSR J0437–4715 \citep{dvt+08} and a VLBA parallax for PSR J1713+0747 \citep{cbv+09}.

Figure 1 illustrates how a GWD can be absorbed into certain periodic timing parameters for PSR JOL374715.

Figure \ref{fig:fits} illustrates how a GWB can be absorbed into certain periodic timing parameters for PSR J0437–4715.

Figure fb) shows the timing residuals with a GWB with amplitude of 42510 added to the data.

Figure \ref{fig:gw} shows the timing residuals with a GWB with amplitude of $A=5\times 10^{-13}$ added to the data.

Figures He) and 1(d) show the timing residuals using the GW-induced (.4—9510 00) values of parallax ancl proper motion. and Dow. and d. respectively.

Figures \ref{fig:pmpx} and \ref{fig:pbom} show the timing residuals using the GW-induced $A=5\times10^{-13}$ ) values of parallax and proper motion, and $\dot{P}_{\rm b}$, $\omega$, and $\dot{\omega}$, respectively.

A very. large GAVB amplitude was used for illustration purposes. but this same ellect takes ace at smaller. amplitudes and is just not as visible bv eve.

A very large GWB amplitude was used for illustration purposes, but this same effect takes place at smaller amplitudes and is just not as visible by eye.

We can see from the figures that the GAVB can induce roth high and low-frequeney components in. residuals.

We can see from the figures that the GWB can induce both high and low-frequency components in residuals.

The oblem with fitting for these parameters is that. in elfect. one is fitting out a significant amount of the CN signal hat is contributing to the resicluals.

The problem with fitting for these parameters is that, in effect, one is fitting out a significant amount of the GW signal that is contributing to the residuals.

In this section. we will construct confidence intervals for the fitted parameters at. various CAB amplitudes and show that these confidence intervals become Larger as the GWD amplitude increases.

In this section we will construct confidence intervals for the fitted parameters at various GWB amplitudes and show that these confidence intervals become larger as the GWB amplitude increases.

The method for calculating these confidence intervals is quite straightforward.

The main simulation ciscussecl in Section 2.3) is used to obtain distributions of the given fitted. parameters at cach amplitude.

The main simulation discussed in Section \ref{sec:extended} is used to obtain distributions of the given fitted parameters at each amplitude.

As we have seen above. a CAVB will cause excess power to be absorbed. into timing xwameters.

As we have seen above, a GWB will cause excess power to be absorbed into timing parameters.

LExamples of the subsequent corruption of he parameters can be seen in the histograms of Figure 2..

Examples of the subsequent corruption of the parameters can be seen in the histograms of Figure \ref{fig:gauss}.

Since this simulation injects GAs with rancom sky »ositions ancl random. frequencies (within a certain range and with a given spectrum). the subsequent corruption of 1e fitted. parameters caused by absorbing parts of the CAV μα»ectrum. will result. in a Gaussian distribution. centered wound the unperturbecl parameter. values.

Since this simulation injects GWs with random sky positions and random frequencies (within a certain range and with a given spectrum), the subsequent corruption of the fitted parameters caused by absorbing parts of the GW spectrum will result in a Gaussian distribution centered around the unperturbed parameter values.

It can be seen rom Figure 2. that the FWHLIIAL of the distribution. and yerefore the confidence interval on the parameter increases with increasing GWD amplitude.

It can be seen from Figure \ref{fig:gauss} that the FWHM of the distribution and therefore the confidence interval on the parameter increases with increasing GWB amplitude.

This increased. spread. in »otential parameter estimates is the GW-ineluced corruption ju we aim to quantify in this paper.

This increased spread in potential parameter estimates is the GW-induced corruption that we aim to quantify in this paper.

Ht must be noted ju at sullictently high (ΝΟ amplitudes prominent low-pequency power will be visible in the timing residuals.

It must be noted that at sufficiently high GWB amplitudes prominent low-frequency power will be visible in the timing residuals.

‘To ensure phase-connection in our timing. we limited. our simulations to a maximum GWD amplitude of 1.10.οὐ.

To ensure phase-connection in our timing, we limited our simulations to a maximum GWB amplitude of $1\times 10^{-13}$.

We also note that towardsD. the higher end of the simulated CWD amplitude range. sullicient levels of low-frequeney noise will be present in the simulations to make the uncertainties returned [from the standard. least-squares fit unreliable (seee.g.2)..

We also note that towards the higher end of the simulated GWB amplitude range, sufficient levels of low-frequency noise will be present in the simulations to make the uncertainties returned from the standard least-squares fit unreliable \citep[see e.g.][]{vbs+08}.

Llowever. since our analysis only uses the best-fit and not its uncertainty. this has no ellect on our results.

However, since our analysis only uses the best-fit and not its uncertainty, this has no effect on our results.

‘These histograms can be used to directly study the elfects that the presence of GWs has on the parameter estimates resulting from the fit.

These histograms can be used to directly study the effects that the presence of GWs has on the parameter estimates resulting from the fit.

This is done hy plotting the ratio of the standard deviation of the fitted parameters and the MvO2--reportecl unperturbed error on the parameters against GAVB amplitude.

This is done by plotting the ratio of the standard deviation of the fitted parameters and the -reported unperturbed error on the parameters against GWB amplitude.

The original. ancl in some wavs still best. argument in favor of the white dwarf pulsation hypothesis is the observed simultaneous presence of (he inconmnenstrate P28 and P29 periodicities (Robinson et al.

The original, and in some ways still best, argument in favor of the white dwarf pulsation hypothesis is the observed simultaneous presence of the incommensurate P28 and P29 periodicities (Robinson et al.

1978).

Incommensurate periocliciGes are common Lor the ZZ Celi class of stars (isolated nonradial 4 mode pulsating white dwarls: see Kepler Dradley 1995 [or a good review of white dwarfs and pulsation).

Incommensurate periodicities are common for the ZZ Ceti class of stars (isolated non–radial $g$ –mode pulsating white dwarfs; see Kepler Bradley 1995 for a good review of white dwarfs and pulsation).

Also. the white cdwarl in GW Lib is known to exhibit ZZ Ceti(wpe pulsations (van Zvl et al.

Also, the white dwarf in GW Lib is known to exhibit ZZ Ceti–type pulsations (van Zyl et al.

2000: Szkocly οἱ al.

2000; Szkody et al.

2002).

Additional support. albeit weak. comes from the UV spectrum of the oscillations that are consistent with a white dwarf photospheric origi (Skidimore et al.

Additional support, albeit weak, comes from the UV spectrum of the oscillations that are consistent with a white dwarf photospheric origin (Skidmore et al.

1999. Welsh οἱ al.

1999, Welsh et al.

LOOT),

1997).

Yel the ZZ Celi stars (and GW Lib) have much longer periods (hundreds of seconds) than WZ See.

Yet the ZZ Ceti stars (and GW Lib) have much longer periods (hundreds of seconds) than WZ Sge.

Furthermore. (he quiescent temperature of (he white dwarl in WZ See. ~14.600 Ix (Cheng οἱ al.

Furthermore, the quiescent temperature of the white dwarf in WZ Sge, $\sim$ 14,600 K (Cheng et al.

1997. Godon et al.

1997, Godon et al.

2003). exceeds (the nominal upper temperature limit (the "blue edge) of 213.500 IX of the instability strip for ZZ Ceti stars.

2003), exceeds the nominal upper temperature limit (the “blue edge”) of $\sim$ 13,500 K of the instability strip for ZZ Ceti stars.

However. more massive white chwarls have a hotter "blue edge" (han the canonical 0.6 ΔΙ. white dwarf (Bradley Winget 1994: Dergeron οἱ al.

However, more massive white dwarfs have a hotter “blue edge” than the canonical 0.6 $\Msun$ white dwarf (Bradley Winget 1994; Bergeron et al.

1995: Giovannini οἱ al.

1995; Giovannini et al.

1998) and recent studies do in [act suggest WZ See has a massivewhite dwarf. exceeding 70.8 AL. ancl perhaps even as high as 1.2 M. (Sleeehs οἱ al.

1998) and recent studies do in fact suggest WZ Sge has a massivewhite dwarf, exceeding $\sim$ 0.8 $\Msun$ and perhaps even as high as 1.2 $\Msun$ (Steeghs et al.

2001: Skichmore et al.

2001; Skidmore et al.

2000: Ixnigge et al.

2000; Knigge et al.

2002: Long et al.

2002; Long et al.

2003: Godon et al.

2003; Godon et al.

2003).

By linearly extrapolating the blue edge temperature versus mass presented in Giovanninni οἱ al.

By linearly extrapolating the blue edge temperature versus mass presented in Giovanninni et al.

1998. a g mode pulsating white dwarl with a temperature of 14.600 IX would require a white dwarf mass 31.2\1.. barely within acceptable mass estimates.

1998, a $g$ –mode pulsating white dwarf with a temperature of 14,600 K would require a white dwarf mass $\gtsimeq1.2 \Msun$, barely within acceptable mass estimates.

However. (he extrapolation (ο values above 1M. is highly uncertain so this crude mass limit should be taken as nothing more than a statement that g mode pulsations cannot be ruled out by quiescent while dwarf temperature arguments.

However, the extrapolation to values above $1 \Msun$ is highly uncertain so this crude mass limit should be taken as nothing more than a statement that $g$ –mode pulsations cannot be ruled out by quiescent white dwarf temperature arguments.

Furthermore. as was suggested by Szkody et al. (

Furthermore, as was suggested by Szkody et al. (

2002) for GW Lib. it could be that the temperature determined for WZ See is a elobal average. ancl a cooler region could be responsible [ον the pulsations for GW Lib. a twotemperature white dwarl model fits substantially better (hen a one temperature model.

2002) for GW Lib, it could be that the temperature determined for WZ Sge is a global average, and a cooler region could be responsible for the pulsations — for GW Lib, a two–temperature white dwarf model fits substantially better then a one temperature model.

Note that the thickness of the surface convective zone responsible for ihe pulsations in WZ See should be very thin compared to other ZZ Celi stars since the timescale of the periodicity depends on the depth of the base of the convective zone (e.g. see Dergeron et al.

Note that the thickness of the surface convective zone responsible for the pulsations in WZ Sge should be very thin compared to other ZZ Ceti stars since the timescale of the periodicity depends on the depth of the base of the convective zone (e.g. see Bergeron et al.

1995) [ast periodicities require a shallow convective zone.

1995) — fast periodicities require a shallow convective zone.

Skidmore et al. (

1999) extrapolated the observed temperature.period relation of ZZ Celi stars using (he cata in Clemens (1993) and found the extrapolation falls tantalizinely close to the quiescent temperature and period of WZ See.

1999) extrapolated the observed temperature–period relation of ZZ Ceti stars using the data in Clemens (1993) and found the extrapolation falls tantalizingly close to the quiescent temperature and period of WZ Sge.

This bolstered (he viability of the white cdwarf pulsation hypothesis. and mitigated the objection that the 28 s and 29 s periods are too short to be related to the ZZ Ceti phenomenon.

This bolstered the viability of the white dwarf pulsation hypothesis, and mitigated the objection that the 28 s and 29 s periods are too short to be related to the ZZ Ceti phenomenon.

We re-examined this extrapolation of ligure 2 of Clemens (1993) and while the observed temperatureperiod relation lor ZZ Ceti

We re-examined this extrapolation of figure 2 of Clemens (1993) and while the temperature–period relation for ZZ Ceti

6 ea fundamental aud first harmonic.

of a fundamental and first harmonic.

In both of those stars. the harmonic minima coincide with the maxima and minima of the fundamental.

In both of those stars, the harmonic minima coincide with the maxima and minima of the fundamental.

This results iu a pulse shape with a deepened imininuun at the location of the fundamental minima: relatively large harmonic auplitucdes (as in 07113) produce secondary minia at the location of the fundamental maxima: aud sanaller harmonic amplitudes fatten the fundamental miaxina (as in 5752)).

This results in a pulse shape with a deepened minimum at the location of the fundamental minimum; relatively large harmonic amplitudes (as in ) produce secondary minima at the location of the fundamental maxima; and smaller harmonic amplitudes flatten the fundamental maxima (as in ).

We investigate the phase relationship between the two modes in uunder the asstuption that they are harmonically related Gf they are uot. the shape of the ight curve does not repeat at the fundamental frequency).

We investigate the phase relationship between the two modes in under the assumption that they are harmonically related (if they are not, the shape of the light curve does not repeat at the fundamental frequency).

To show that this assumption 1s consistent with the data. we compute a weielted average of the frequencies ou the four nights using the inverse variuices as weights (Tavlor1997).

To show that this assumption is consistent with the data, we compute a weighted average of the frequencies on the four nights using the inverse variances as weights \citep{tay97}.

. This gives f, = 2957 + 7 ullz aud f = 5906 + Gyllz. which is consistent with f) = 98.

This gives $_{1}$ = 2957 $\pm$ 7 $\mu$ Hz and $_{2}$ = 5906 $\pm$ $\mu$ Hz, which is consistent with $_{2}$ = $_{1}$.

We refit the data for cach wight applying this frequency constraint.

We refit the data for each night applying this frequency constraint.

A weighted average of these results eives fy = 2053.6 c 2.7 pile (338.57 + 0.30 s): the aliasing in the combined 2009 amplitude spectrum preveuts us from confidently determining amore accurate frequency.

A weighted average of these results gives $_{1}$ = 2953.6 $\pm$ 2.7 $\mu$ Hz (338.57 $\pm$ 0.30 s); the aliasing in the combined 2009 amplitude spectrum prevents us from confidently determining a more accurate frequency.

Consistent with the data. we assune the frequencies are the same on cach wight aud again refit the leht curves with the frequencies fixed to look for changes in auplitude aud relative phase.

Consistent with the data, we assume the frequencies are the same on each night and again refit the light curves with the frequencies fixed to look for changes in amplitude and relative phase.

We multiply the best-Bt amplitudes aud their errors by z T.,f/su(xT. f) o correct for the effect of a finite exposure time. T. (Baldry1999).

We multiply the best-fit amplitudes and their errors by $\pi$ $_{exp}$ $\pi$ $_{exp}$ f) to correct for the effect of a finite exposure time, $_{exp}$ \citep{bal99}.

. Table 3. lists these results.

Table \ref{table:fit2} lists these results.

We report phase difference as the number of secouds between the nimii of the harmonic aud the umm/10aximnmna of the fundamental aud use uegative values to indicate he harmonic minima is shifted left of the fundamental ΜΙΤπαπα.

We report phase difference as the number of seconds between the minimum of the harmonic and the minimum/maximum of the fundamental and use negative values to indicate the harmonic minimum is shifted left of the fundamental minimum/maximum.

The one-sigmia errors reported for he phase differences come frou bootstrap Monte Carlo siuulations. and in each case the value falls between he suni of the errors for the individual phases aud the quadrature stun of those errors.

The one-sigma errors reported for the phase differences come from bootstrap Monte Carlo simulations, and in each case the value falls between the sum of the errors for the individual phases and the quadrature sum of those errors.

By folding the leht curves at the period of the "udenaeutal we eet a picture of these quantitative results (Fie. 2)).

By folding the light curves at the period of the fundamental, we get a picture of these quantitative results (Fig. \ref{fig:flcs}) ).

The pulse shape is like those of aand0711.

The pulse shape is like those of and.

. There is some sugeestion that the phase relationship between the fundamental aud harmonic nuüeht not be exactly zero. but the errors iu phase are large making this hard to determine.

There is some suggestion that the phase relationship between the fundamental and harmonic might not be exactly zero, but the errors in phase are large making this hard to determine.

Similarly. there is no statistically significant chauee in amplitude or phase difference among the nights.

Similarly, there is no statistically significant change in amplitude or phase difference among the nights.

The discovery of a fourth variable among the hot DQ white dwarf stars means the variable fraction of the known hot DOs is at least

The discovery of a fourth variable among the hot DQ white dwarf stars means the variable fraction of the known hot DQs is at least.

This is a high percentage compared with the hwdrogen- aud heliumatmosphere white dwarf variables.

This is a high percentage compared with the hydrogen- and helium-atmosphere white dwarf variables.

Thus. as we get to know the hot DQ stars better. we find thon disiucliued to be photometrically constant.

Thus, as we get to know the hot DQ stars better, we find them disinclined to be photometrically constant.

Further. there is no obvious observational characteristic that serves as a predictor of whether a given hot DQ is variable.

Further, there is no obvious observational characteristic that serves as a predictor of whether a given hot DQ is variable.

Of the four reported variables. hhas a spectral featureidentified with helimuu etal. 2008b):: hhas a spectral feature identified with livdrogeu (Dufouretal. 20082): two aand 0711)) have broacened spectral lines (Dufouretal.2008a) possibly resulting from a maguectic Ποια (Dufouretal.2008b): the other two exhibit uo such spectral distortions.

Of the four reported variables, has a spectral featureidentified with helium \citep{duf08mag}; has a spectral feature identified with hydrogen \citep{duf08}; two and ) have broadened spectral lines \citep{duf08} possibly resulting from a magnetic field \citep{duf08mag}; the other two exhibit no such spectral distortions.

Thus. hvdroseu. helium. aud nagnetic fields do uot discourage variabilitv. and none of them appears necessary to encourage it.

Thus, hydrogen, helium, and magnetic fields do not discourage variability, and none of them appears necessary to encourage it.

Indeed. so fav. the best predictor of a hot DQ stars variability is hat it is a hot DO star.

Indeed, so far, the best predictor of a hot DQ star's variability is that it is a hot DQ star.

Not ouly do we not know the reason one hot DO varies aud another doesut. we do uot ‘mow why heir pulse shapes differ.

Not only do we not know the reason one hot DQ varies and another doesn't, we do not know why their pulse shapes differ.

Based ou suggestious of Greenetal. (2009).. Dufouretal(2009a)— predict a connection between magnetic field aud pulse shape.

Based on suggestions of \citet{gre09}, , \citet{duf09} predict a connection between magnetic field and pulse shape.

In this work we present a new phenomenology based technique to address the issue of non-thermal line width and the temperature of the diffuse neutral hydrogen of our Galaxy assuming a rough pressure equilibrium between different phases of the ISpa

In this work we present a new phenomenology based technique to address the issue of non-thermal line width and the temperature of the diffuse neutral hydrogen of our Galaxy assuming a rough pressure equilibrium between different phases of the ISM.

y A possible connection between the observed Kolmogorov-like scaling of the non-thermal velocity dispersion in the Galactic H and the turbulence of the interstellar medium is discussed.

A possible connection between the observed Kolmogorov-like scaling of the non-thermal velocity dispersion in the Galactic H and the turbulence of the interstellar medium is discussed.

This scaling relation is used to re-examine the issue of the temperature of the Galactic ISM with the help of the millennium Arecibo 21 em absorption-line survey measurements.

This scaling relation is used to re-examine the issue of the temperature of the Galactic ISM with the help of the millennium Arecibo 21 cm absorption-line survey measurements.

The distribution of the derived. temperature is found to be significantly different from the distribution of the upper limits of the kinetic temperature.

The distribution of the derived temperature is found to be significantly different from the distribution of the upper limits of the kinetic temperature.

A considerable fraction (— 29%) of the gas is found to be in the thermally unstable phase. qualitatively contirming earlier results.

A considerable fraction $\sim 29\%$ ) of the gas is found to be in the thermally unstable phase, qualitatively confirming earlier results.