An X-ray measurement of Titan's atmospheric extent from its transit of the Crab Nebula

a r

X

i

v

:a

s t

r o

-

p

h

/

4

3

2

8

3v

1

1

1

M

a

r

2

4

Accepted for publication in the Astrophysical Journal An X-ray measurement of Titan’s atmospheric extent from its transit of the Crab Nebula Koji Mori Department of Astronomy and Astrophysics,Pennsylvania State University,525Davey Laboratory,University Park,PA.16802,USA mori@https://www.wendangku.net/doc/b55776999.html, Hiroshi Tsunemi and Haruyoshi Katayama 1Department of Earth and Space Science,Graduate School of Science,Osaka University,1-1Machikaneyama,Toyonaka,Osaka 560-0043Japan David N.Burrows and Gordon P.Garmire Department of Astronomy and Astrophysics,Pennsylvania State University,525Davey Laboratory,University Park,PA.16802,USA and Albert E.Metzger Jet Propulsion Laboratory,4800Oak Grove Drive,Pasadena,CA 91109,USA ABSTRACT Saturn’s largest satellite,Titan,transited the Crab Nebula on 5January 2003.We observed this astronomical event with the Chandra X-ray Observatory.

An “occultation shadow”has clearly been detected and is found to be larger than the diameter of Titan’s solid surface.The di?erence gives a thickness for Titan’s atmosphere of 880±60km.This is the ?rst measurement of Titan’s atmospheric extent at X-ray wavelengths.The value measured is consistent with or slightly larger than those estimated from earlier Voyager observations at other wavelengths.We discuss the possibility of temporal variations in the thickness of Titan’s atmosphere.

Subject headings:planets and satellites:individual (Titan)—X-rays:general

1.INTRODUCTION

Titan is the only satellite in the solar system with a thick atmosphere.Its atmosphere has a pressure near the surface is about1.5times greater than that of the Earth at sea level and extends much further than that of the Earth(Coustenis&Lorenz1999).Titan’s atmosphere is known to resemble the primitive environment of the Earth’s atmosphere in terms of chemistry,providing us with a laboratory to study the origin of life(Owen et al. 1997).The atmospheric structure of Titan has been investigated at radio(Lindal et al.1983), infrared(IR)(Lellouch et al.1989),optical(Sicardy et al.1990;Hubbard et al.1990),and ultraviolet(UV)wavelengths(Strobel,Summers,&Zhu1992;Smith et al.1982).These results came from the Voyager1spacecraft during its encounter with Titan and from a stellar occultation by Titan.Due to the wavelength dependence of transmissivity,the radio, IR,and optical observations measure the thermal structure of Titan’s atmosphere below an altitude of500km while the UV observation measures it above an altitude of1000km. No direct information has hitherto been obtained at intermediate altitudes where the X-ray observation is e?ective.

On5January2003,the Saturnian system passed across the2′wide X-ray bright region of the Crab Nebula.The Saturnian system has a conjunction with the Crab Nebula every 30years.However,because of an average o?set of a few degrees,it rarely transits the Crab Nebula.Although a similar conjunction occurred once in January of1296,the Crab Nebula, which is a remnant of SN1054,must have been too small to be occulted.Therefore,this may be the?rst transit since the birth of the Crab Nebula.The next similar conjunction will take place in August of2267,making its occurrence in2003a“once-in-a-lifetime”event.The Saturnian system is a million times brighter in visible light than the Crab Nebula whereas the Crab Nebula is a million times brighter in X-rays than the Saturnian system.This prevented us from observing the transit in the optical,but provided a unique opportunity for an X-ray observation which had never been performed.The Crab Nebula is one of the brightest synchrotron sources in the sky and,thus,makes an ideal di?use background light source to study X-ray shadows of interesting objects.

Here,we report results from an observation of this historical event with the Advanced CCD Imaging Spectrometer(ACIS)aboard the Chandra X-ray Observatory.Chandra has an angular resolution of0.′′5and can resolve Saturn,its rings,and the satellite Titan,whose angular size is about1′′.Unfortunately,it was not possible to observe the transit of Saturn due to Chandra’s concurrent passage through the Earth’s radiation zone.Only Titan was observable because Chandra had passed through the radiation zone by the time Titan tran-sited12hours later.We describe the observation in§2.The data analysis and results are presented in§https://www.wendangku.net/doc/b55776999.html,parison with previous observations and implications of this observation

will be discussed in§4.

2.OBSERVATION

The observation was performed from09:04to18:46(UT)on5January2003.Figure1 shows the Titan transit path on the Crab Nebula.In order to avoid event pile-up and telemetry saturation,which made di?culties for analysis of previous Chandra observations of the Crab Nebula(Weisskopf et al.2000;Hester et al.2002),we inserted a transmission grating,shortened the CCD frame time from the nominal value of3.2seconds to0.3seconds, and adopted a small subarray window(50′′×150′′).These observational modes did work e?ciently to result in no telemetry saturation and no apparent event pile-up.We will carefully investigate the possibility of the event pile-up e?ect on our result in§3.2.3.Since the restricted window could not cover the whole Titan transit path,we changed the pointing direction twice during the observation.In spite of the time loss due to the two maneuvers, we obtained an e?ective exposure time of32279seconds,which corresponds to92%of the total observing time duration.

3.ANALYSIS AND RESULTS

3.1.Reprojection To the Titan Fixed Frame

No hint of the Titan transit can be seen in the standard sky image in Figure1.Titan moved too fast to cast an observable shadow against the Crab Nebula in the sky image.In order to search for a shadow,we reprojected each photon’s position to a frame?xed with respect to Titan.We used CIAO1tool sso

freeze,we removed the pixel randomization,which was applied by default in the stan-dard data processing,and applied our subpixel resolution method(Tsunemi et al.2001;Mori et al.2001)2to obtain the best available spatial resolution.Figure2shows the Titan?xed frame image.A clear shadow can be seen,which was made by Titan’s occultation of the Crab Nebula.Measurement of the e?ective radius of the occultation shadow provides us with information on Titan’s atmospheric extent.

resolution.1.4.html

3.2.E?ective Radius of the Occultation Shadow

Figure3shows a radial pro?le of the photon number density from the center of the occultation shadow(black points).From this radial pro?le,we computed the e?ective radius of the occultation shadow,R shadow.

3.2.1.Method

We assumed that the distribution of photons in Figure2is symmetric with respect to the center of the occultation shadow.The observed photon number density as a function of the distance from the center of the occultation shadow,D obs(r),can be given by a convolution of the intrinsic photon number density,D int(r),and the point spread function(PSF),P SF(r):

D obs(r)= D int(r′)P SF(|r?r′|)d r′.(1)

The Chandra PSF has a very sharply peaked core with extended wings and is strongly energy dependent due to larger scattering of higher energy photon by the mirror surface (Chandra Proposers’Observatory Guide2002).In general,it is quite di?cult to obtain a precise analytical form of the PSF,which prevents us from solving equation1to obtain D int directly from D obs.Instead,its numerical form can be generated through a raytrace code which has been determined by the Chandra team on the basis of both ground-based and on-orbit calibrations.Therefore,we performed Monte Carlo simulations incorporating the numerical form of the PSF.We approximated D int by a step function with a threshold radius,R disk.We?tted the data points in Figure3with D obs(r),varying R disk to obtain the best?t.R shadow is de?ned by R disk which gives the minimumχ2.Justi?cation for the approximation using the step function will be discussed in§4.

The PSF was derived from raytrace tools ChaRT3and MARX4.ChaRT provides the best available mirror response at any o?-axis angle and for any spectrum.MARX reads the output of ChaRT and creates the PSF taking into account the detector responses and aspect reconstruction uncertainties.We obtained the PSF appropriate for the observation conditions:at o?-axis angle of about45′′and for the observed spectrum.The output PSF from MARX includes the pixel randomization.Since the pixel randomization broadens PSF,

we sharpened it by the appropriate amount.To account for our application of the subpixel method,we further sharpened the PSF by5%in terms of the Half Power Diameter(HPD), which is the expected improvement for this o?-axis angle on the ACIS-S CCD(Tsunemi et al.2002;Mori et al.2002).The HPD of the resultant PSF was0.′′844.We will discuss the validity of this PSF in§3.2.3.

In order to compare the results of the Monte Carlo simulation with the data,we must also account for gradients in the sky background level and for instrumental e?ects like trailing events.A big advantage of our observation was the ability to determine the background level across the shadow based on knowledge of the surface brightness of the Crab Nebula along the Titan transit path.We derived the background pro?le across the shadow by averaging two pro?les which were taken centered at3′′ahead of and3′′behind of the occultation shadow center.The background pro?les are presented as red points in Figure3.Then,the gradient of the background was determined by?tting the red points within the shadow(r<1.′′5)and the black points outside of it with a quadratic function,which is shown with a dotted line in Figure3.

The trailing events are de?ned as events detected during the CCD readout.Since the positions of the trailing events are recorded improperly along the readout direction,they cause an o?set in the image.The contribution of the trailing events to the total photon number density can be evaluated because its level is proportional to the fraction of the total e?ective exposure time spent in transferring the charge across the X-ray bright region, F trailing.In the case of ACIS,it takes40μsec to transfer the charge from one pixel to another. The width of the X-ray bright region along the readout direction is about210pixels(≈103′′; see Fig.1).Therefore,it takes0.0084seconds to transfer the charge across the X-ray bright region.Since CCD frame time is0.3seconds,F trailing becomes0.0084/(0.0084+0.3)≈2.7%. The resultant estimate for the background level due to the trailing events is shown as a dashed line in Figure3.

3.2.2.Result

The?rst30data points from the center(r<1.′′5)were used for theχ2test because data points further from the center hardly a?ected the result.Figure4showsχ2as a function of R disk.Theχ2values are well described with a quadratic function.The best?t value was obtained as R shadow=0.588±0.011arcseconds withχ2/d.o.f of30.36/29.The uncertainty is68.3%(1σ)con?dence level.The best?t curve is shown in Figure3(red line)along with a curve simulating R shadow=0.′′437(blue line)which corresponds to the radius of the Titan solid surface(2575km).The di?erence between those two curves is attributed to X-ray

absorption by Titan’s atmosphere.

3.2.3.Systematic checks

The validity of the PSF,the e?ect of event pile-up,and the contribution from the intrinsic background of ACIS were examined.The accuracy of the adopted PSF was checked using a point source in the Orion Nebula Cluster,CXOONC J053514.0-052338,located at a J2000position ofα=05h35m14.s06,δ=?05?23′38.′′4(Getman et al.in preparation).The point source has an o?-axis angle of45′′,comparable with that of Titan in our observation. We processed the data of the point source in the same manner described in§3.2.1;removing the pixel randomization and applying the subpixel resolution method.The PSF was obtained again through ChaRT/MARX,but appropriate for the spectrum of the point source,and was sharpened again in the same manner described in§3.2.1.We con?rmed that the PSF originally obtained from ChaRT/MARX had a HPD15%larger than that of the point source, but that the PSF sharpened for our data processing e?ects was consistent with the point source data to within a few percent.Next,we studied the dependency of R shadow on the PSF by performing simulations using PSFs with10%larger and smaller HPDs than that of adopted one.In an ideal case,even if a wrong PSF was used,R shadow would be always the same although theχ2value would increase and the?t would not be statistically acceptable. In reality,R shadow depended on the HPD;R shadow became larger and smaller by about0.018 arcseconds which is comparable to about a1.6σstatistical error.However,considering that the adopted PSF is accurate to a few percent,we can safely assume that this dependency is negligible compared with the statistical error.We note that those simulations using broader and narrower PSFs resulted in higherχ2value by about3than the simulation described in§3.2.1,also supporting the validity of the adopted PSF.Therefore,we conclude that the adopted PSF is reliable and its uncertainty hardly a?ected the result.

In order to examine the pile-up e?ect,the data were divided into two time intervals according to?ux level,“high?ux time interval”and“low?ux time interval”.The division is indicated in Figure1.The average background count rates in the high and low?ux time intervals are8.1and4.0×10?2counts sec?1arcsec?2,respectively.Separate calculations of R shadow for the two data sets were performed in the same way described above.Plots ofχ2as a function of R disk are shown in Figure4.The resultant values were R shadow=0.599±0.016 and0.581±0.016arcseconds for the high and low?ux time intervals,respectively.Since the values are statistically consistent with each other and with the result obtained using all the data,we conclude that event pile-up is unlikely to have a?ected the result.

The contribution of the intrinsic ACIS background cannot be a problem because it is

about1.5×10?6counts sec?1arcsec?2(Chandra Proposers’Observatory Guide2002).It is three order of magnitude lower than that of the trailing events.

4.DISCUSSION

Taken with the distance of1.214×109km to Titan at the time of this observation, R shadow=0.588±0.011arcseconds gives a thickness for Titan’s atmosphere of880±60km. This value can be compared with estimates from the models for Titan’s atmosphere which have been constructed based on Voyager1observations at radio,IR,and UV wavelengths. Figure5a shows pro?les of the tangential column density(cm?2)along the line-of-sight as a function of altitude(distance above Titan’s surface),which are compiled from density(cm?3) pro?les provided by Yelle et al.(1997)(red)and Vervack,Sandel,&Strobel(manuscript in preparation)(blue).Nitrogen dominates,making up more than95%of the atmospheric con-stituents,and methane is the second major component,although proportions slightly di?er in the two models.In those models,the pro?les in the altitude range of500–1000km,where no data were available,were interpolated between the data of higher and lower altitudes assuming hydrostatic equilibrium.The step function we used to determine the atmospheric thickness is a simpli?cation of the transmission curve of X-rays through the atmosphere.In reality,X-rays su?er photoelectric absorption as they pass through the atmosphere,with a transmissivity determined by the atmospheric composition,the tangential column density for a given altitude,and photon energy.We have calculated transmission curves by using the atmospheric compositions of the above two models,the tangential column densities in Figure5a,and integrating over the observed Crab spectrum.The curves are shown in Fig-ure5b.The step function with a threshold of R shadow is also shown.Figure5c shows a χ2curve which is identical with the black curve shown in Figure4,but the de?nitions of the x-axis are di?erent.We compared the simulation treating the atmosphere as a solid disk(disk model)with the simulations based on the transmission curves shown in Figure5b (atmosphere model)as follows.We calculatedχ2for the atmosphere model simulations and de?ned the“characteristic altitude”h for those models by

h= ∞0(1?T(h′))dh′,(2)

where T(h′)is transmissivity as a function of altitude,h′.We?nd that h=750and780km for the Yelle et al.and Vervack et al.models,respectively.The points(h,χ2)for those two atmosphere models fall very close to theχ2curve for the disk model,as shown in Figure5c. In other words,our step-function transmissivity is indistinguishable from a more realistic

transmissivity with h at the threshold of the step in the simulation.This fact strongly justi?es the approximation of transmission curve with a step function in our simulation and suggests that R shadow and h can be directly compared with each other.Then,our result for the thickness of Titan’s atmosphere is consistent with or slightly larger than those estimated from Voyager1observations(1.9and1.4σseparation).

Although the statistical signi?cance is not so large,it is still worth discussing a temporal variation of Titan’s upper atmosphere.Distances between the Sun and Saturn were1.42 and1.35×109km at the time of Voyager’s encounter(November1980)and our observation (January2003),respectively.The solar luminosity is known to be fairly stable with an uncertainty of0.3%regardless of its11years active cycle(Fr¨o ehlich&Lean1998;Quinn& Fr¨o ehlich1999).Accordingly,the closer distance to the Sun in our observation might have resulted in the higher temperature and the larger extent of the atmosphere.Although the size of this e?ect cannot be ascertained without detailed modeling,the increase in solar?ux incident on Titan may account for some part of the slightly larger value of Titan’s atmosphere measured here.More detailed information will be obtained by the Cassini/Huygens mission in2005.

Finally,we note that the spectrum taken from the shadow has no absorption nor emis-sion line feature and is statistically indistinguishable from the spectrum taken from the surrounding region.Those facts indicate that photons penetrating the atmosphere hardly contributed to the spectrum taken from the shadow;if they did,excess absorption due to Titan’s atmosphere would be seen in the shadow spectrum.The absence of excess absorption is reasonable considering that the PSF is much broader(the HPD corresponds to about5000 km)than the corresponding atmospheric thickness interval of about500km within which the tangential optical depth changes from unity to zero(see Fig.5b).

We thank H.Marshall and S.Wolk for supporting observation planning,R.Yelle and R. Vervack for providing their results,and K.Getman and E.Feigelson for providing their data. K.M.and D.N.B.thank J.Kasting for useful discussions.K.M.acknowledges the support of JSPS through the fellowship for research abroad.This work was supported in part by the NASA through Chandra Award GO3-4002A and was carried out as a part of“Ground-based Research Announcement for Space Utilization”promoted by the Japan Space Forum.

REFERENCES

Coustenis A.,&Lorenz,R.D.1999,in Encyclopedia of the Solar System,P.Weissman,L.

McFadden,T.Johnson,Eds.(London,Academic Press)pp.377-404

Chandra Proposers’Observatory Guide,Version 5.0,2002, https://www.wendangku.net/doc/b55776999.html,/proposer/POG/index.html

Fr¨o ehlich,C.,&Lean,J.1998,Geophys.Res.Let.25,4377

Hester,J.J.,Mori,K.,Burrows,D.N.et al.2002,ApJ,577,L49

Hubbard,W.B.,Hunten,D.M.,Reitsema,H.J.,Brosch,N.,Nevo,Y.,Carreira,E.,Rossi,

F.,&Wasserman,L.H.1990,Nature,343,353

Lellouch,E.,Coustenis,A.,Gautier,D.,Raulin,F.,Dubouloz,N.&Frere,C.1989,Icarus, 79,328

Lindal,G.F.,Wood,G.E.,Hotz,H.B.,Sweetnam,D.N.,Eshleman,V.R.,&Tyler,G.L.

1983,Icarus,53,348

Mori,K.,Tsunemi,H.,Miyata,E.,Baluta,C.,Burrows,D.N.,Garmire,G.P.,&Chartas,

G.2001,in ASP Conf.Ser.251,New Century of X-Ray Astronomy,ed.H.Inoue&

H.Kunieda(San Francisco:ASP),576

Owen,T.,Raulin,F.,McKay,C.P.,Lunine,J.I.,Lebreton,J.-P.,&Matson,D.L.1997, in Huygens,Payload and Mission,ESA SP-1177

Quinn,T.J.,&Fr¨o ehlich,C.1999,Nature401,841

Sicardy,B.et al.1990,Nature,343,350

Smith,G.R.,Strobel,D.F.,Broadfoot,A.L.,Sandel,B.R.,Shemansky,D.E.,&Holberg, J.B.1982,J.Goephys.Res.,87,1351

Strobel,D.F.,Summers,M.E.,&Zhu,X.1992,Icarus,100,512

Tsunemi,H.,Mori,K.,Miyata,E.,Baluta,C.,Burrows,D.N.,Garmire,G.P.,&Chartas,

G.2001,ApJ,554,496

Weisskopf,M.C.,Hester,J.J.,Tennant,A.F.,et al.2000,ApJ,536,L81

Yelle,R.V.,Strobel,D.F.,Lellouch,E.,&Gautier,D.1997,Eur.Space Agency Sci.Tech.

Rep.,ESA SP-1177,243

09:04 (UT)

1 arcmin

Fig.1.—Chandra image in equatorial coordinates with intensity displayed on a logarithmic scale.The solid curve running from east to west represents the Titan transit path seen from Chandra.Red and white colors show the assigned“high?ux time interval”and“low?ux time interval”,respectively(see text).The observation started at09:04and ended at18:46 (UT)on5January2003.The right bottom arrow de?nes one arc-minute of scale.A hole at the pulsar and a narrow line through the pulsar are instrumental e?ects.

Fig.3.—The radial pro?le of the photon number density from the center of the occultation shadow(black points).The red curve shows the best?t of the disk model simulation to the radial pro?le data,while the blue curve shows the simulated shadow pro?le of Titan’s solid surface.The red points represent the background across the shadow.The dotted and dashed lines indicate the slope of the background and the contribution of the trailing events, respectively.The dotted line was determined based on the red points within the shadow and black points outside of it.

Fig.4.—χ2s as a function of R disk(points).Solid curves show the?ts of these points with a quadratic function.Black,red,and blue colors represent the results for data sets of the entire time interval,the high?ux time interval,and the low?ux time interval,respectively.

Fig.5.—(a)Tangential column density along the line-of-sight as a function of altitude.Red and blue curves were compiled from density pro?les provided by Yelle et al.and Vervack et al.(b)X-ray transmissivities for the observed spectrum as a function of altitude.The curves are calculated from the tangential column densities shown in Figure5a with the same color coding.The black line represents the transmissivity assumed in our best?t disk model.(c)χ2curve as a function of altitude obtained for disk model simulations.Red and blue stars are plotted at(h,χ2)for simulations with the red and blue transmissivity curves shown in Figure5b,respectively.h represents the characteristic altitude(see text).The horizontal dashed lines indicate1and2σcon?dence levels for the disk model.