Prospects for IXPE and eXTP polarimetric archaeology of the reflection nebulae in the Galactic center
L. Di Gesu, R. Ferrazzoli, I. Donnarumma, P. Soffitta, E. Costa, F. Muleri, M. Pesce-Rollins, F. Marin
AAstronomy & Astrophysics manuscript no. ms˙arxiv c (cid:13)
ESO 2020August 28, 2020
Prospects for IXPE and eXTP polarimetric archaeology of thereflection nebulae in the Galactic center
L. Di Gesu , R. Ferrazzoli , I. Donnarumma , P. So ffi tta , E. Costa , F. Muleri , M. Pesce-Rollins , and F. Marin Italian Space Agency (ASI), Via del Politecnico snc, 00133, Roma, Italy INAF / IAPS, via del Fosso del Cavaliere 100, 00133, Roma, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Pisa, I-56127 Pisa, Italy Universit´e de Strasbourg, CNRS, Observatoire astronomique de Strasbourg, UMR 7550, F-67000 Strasbourg, France
ABSTRACT
The X-ray polarization properties of the reflection nebulae in the Galactic center inform us about the direction of the illuminatingsource (through the polarization angle) and the cloud position along the line of sight (through the polarization degree). However, thedetected polarization degree is expected to be lowered because the polarized emission of the clouds is mixed with the unpolarizeddi ff use emission that permeates the Galactic center region. In a real observation, also the morphological smearing of the source dueto the point spread function and the unpolarized instrumental background contribute in diluting the polarization degree. So far, thesee ff ects have never been included in the estimation of the dilution.We evaluate the detectability of the X-ray polarization predicted for the MC2, Bridge-B2, G0.11-0.11, Sgr B2, Sgr C1, Sgr C2, andSgr C3 molecular clouds with modern X-ray imaging polarimeters such as the Imaging X-ray Polarimetry Explorer (IXPE), which isexpected to launch in 2021, and the Enhanced X-ray Timing and Polarimetry mission (eXTP), whose launch is scheduled for 2027. Weperform realistic simulations of X-ray polarimetric observations considering (with the aid of Chandra maps and spectra) the spatial,spectral, and polarization properties of all the di ff use emission and background components in each region of interest.We find that in the 4.0 − ∼
19% and ∼ − Key words.
Polarization Galaxy:nucleus X-rays:general
1. Introduction
The supermassive black hole (SMBH) Sgr A* that today liesin the center of our Galaxy, is a low-luminosity, X-ray dim( L X ∼ × erg s − , Bagano ff et al. 2001) galactic nucleus.Nonetheless, some observed phenomena in the Galactic center(GC) region are explained by past more luminous phases of SgrA* (see Ponti et al. 2013, for a review). For instance, the hugegamma-ray bubble that Fermi-LAT observed 10 kpc above andbelow the GC may be the remnant of an active phase of Sgr A*a few million years ago (Su et al. 2010; Zubovas et al. 2011).Determining the history of the activity of our Galactic nucleuswould allow us to assess the duty cycle of mass accretion of theSMBH (e.g., Park & Ricotti 2012) and thus provide unique in-sight into the coevolution of the SMBH and galaxies (Di Matteoet al. 2008).The quest of reconstructing the history of Sgr A* has motivatedthe interest in characterizing the central molecular zone (CMZ,Morris & Serabyn 1996), the ∼
100 pc extended region aroundSgr A*. The CMZ hosts several molecular cloud complexes(e.g., Sgr A, Sgr B, and Sgr C) that are visible, for instance, inthe thermal far-infrared images obtained with the Herschel satel-lite (Molinari et al. 2011). Interestingly, the physical conditionsin the CMZ inferred from infrared observations (i.e., the geomet-rical size, column density, and gas dynamics) are reminiscent ofan AGN torus (Ramos Almeida & Ricci 2017). The molecular gas in the CMZ is also traced by X-ray reflectionspectral features, such as a prominent Fe K α line and a reflectioncontinuum (Ponti et al. 2013). The lack of X-ray bright sourcesnearby led Sunyaev et al. (1993) to suggest that the observedemission is the echo of an outburst of Sgr A* that occurred afew hundred years ago and reached a peak luminosity of 10 − erg s − . According to this scenario, the reflected radiation is stillvisible because of the delay induced by the light travel time be-tween Sgr A* and the clouds in the CMZ.We sketch two possible scattering geometries of an individualcloud located in front or behind the Sgr A* plane in Fig. 1.Hereafter, we indicate with d proj the distance between the cloudand Sgr A* projected on the plane of the sky, with d los the line-of-sight displacement of the cloud with respect to the Sgr A*plane, and θ the scattering angle. In addition, c is the speed oflight and t light the light travel time between Sgr A* and the cloud.The two positions depicted in Fig. 1 result in the same e ff ectivescattering.The hypothesis of a previous Sgr A* outburst is appealing be-cause it implies that the X-ray variability of the CMZ is a fos-sil memory of how our Galactic nucleus acted a few hundredyears ago (Muno et al. 2007). Over the years, great e ff ort hasbeen devoted to reconstructing the past light curve of Sgr A*using X-ray spectral, timing, and imaging techniques (Koyamaet al. 1996; Murakami et al. 2001). A single-outburst scenario(Ponti et al. 2010), a two-burst scenario (Clavel et al. 2013), and a r X i v : . [ a s t r o - ph . H E ] A ug i Gesu L. et al: Prospects for polarimetric archaeology of the reflection nebulae in the Galactic center Fig. 1.
Scattering geometry for a molecular cloud located in front orbehind the Sgr A* plane. The two positions result in the same e ff ectivescattering and polarization degree. In this scheme, d proj is the cloud-SgrA* distance projected in the plane of the sky, d los is the line-of-sightdisplacement of the cloud with respect to the Sgr A* plane, c is thespeed of light, t light is the light travel time between Sgr A* and the cloud, θ and π − θ are the two possible scattering angles. a number of short-lived events (Terrier et al. 2018) have beensuggested to explain the data. These flares may be superposed toa long-term high state of Sgr A* (Ryu et al. 2013).The main source of uncertainty in these studies is that d los ispoorly constrained, which makes it di ffi cult to infer the timedelay t light and the number of illuminating events. So far, twomethods have been used to overcome this problem. Some workssearched for correlating variations in multiple regions through-out the CMZ, which provides indications on the number and na-ture of the illuminating events (Clavel et al. 2013; Churazov et al.2017; Terrier et al. 2018). Conversely, other authors have at-tempted to derive the line-of-sight positions of individual clumpsfrom a detailed modeling of the iron line and of the reflectioncontinuum (Capelli et al. 2012; Walls et al. 2016; Chuard et al.2018). These reflection models assume a geometry in which theilluminating source is in Sgr A*, which is still debated. Althoughdisfavored as an explanation for the steady part of the emission,alternative sources of illumination, such as cosmic rays from alocal source penetrating the clouds (Yusef-Zadeh et al. 2013;Dogiel et al. 2014), are not conclusively ruled out by currentdata (Mori et al. 2015; Zhang et al. 2015).An independent way to address these ambiguities is providedby X-ray polarimetry. The reflected emission from a compactilluminating, source is linearly polarized by scattering in the ab-sence of depolarizing agent. The expected polarization angle isnormal to the scattering plane and therefore carries clean in-formation of the direction of the illuminating source. The ex-pected polarization degree P depends on the scattering angle θ (McMaster 1961) by P = − cos θ + cos θ . (1)Thus, a measurement of the polarization degree of a molecularcloud allows us to determine d los because according to the ge-ometry of Fig. 1, d los = d proj cot θ. (2) The remaining ambiguity of whether d los is positive or negativecan be broken, for instance, using spectral information (i.e., thedependence of the equivalent width of the iron line on the scatter-ing angle and iron abundances, see Churazov et al. 2017). An X-ray polarization study of the molecular clouds in the GC has thepotential of addressing the critical uncertainties that still hampera full understanding of the origin of the reflection of the nebu-lae in the GC (Churazov et al. 2002; Marin et al. 2014, 2015;Churazov et al. 2017).A physical limit of this experiment is the fact that the molec-ular clouds are embedded in the di ff use unpolarized emissionof the GC region (Koyama et al. 1989; Sidoli et al. 1999). Inaddition to the X-ray reflection from the molecular clouds, the2 − ff use emission components (see Ponti et al. 2013, andreferences therein) that hereafter we call soft and hard plasma.The soft plasma is traced by the Si xii , Si xiii , S xv , and Ar xvii lines, for example. They are ascribed to a ∼ xxv -He α line emission at ∼ . ∼ ff use hot gas, possibly originating from supernovaremnants.Because of the complexity of the di ff use emission in the GC re-gion, the synergy between polarimetric and imaging capabilitiesis a crucial asset for this study because it allows us to resolve thefaint molecular clouds from the di ff use emission in the back-ground. The NASA / ASI Imaging X-ray Polarimetry Explorer(IXPE, Weisskopf et al. 2016) that will be launched in 2021 isthe first mission that is entirely dedicated to X-ray polarimetrythrough imaging-capable detectors (i.e., gas pixel detector, GPD,Costa et al. 2001) in the 2 − ff er thefirst opportunity to investigate the X-ray polarization of the GCregion. The Enhanced X-ray Timing and Polarimetry mission(eXTP, Zhang et al. 2019), which is planned to launch in 2027,will also carry a GPD polarimeter. The e ff ective area of eXTP isexpected to be larger by a factor ∼
2i Gesu L. et al: Prospects for polarimetric archaeology of the reflection nebulae in the Galactic center larization by computing the minimum detectable polarization(MDP). The MDP (Weisskopf et al. 2010) is the fundamentalquantity for the statistical significance of an X-ray polarizationmeasurement and is defined asMDP = . µ R (cid:114) R + BT , (3)where R is the detected source rate (in counts / s), B is the back-ground rate, T is the observation time (in seconds), and µ is theadimensional modulation factor of the detector. The MDP isnot the uncertainty of the polarization measurement, but ratherthe degree of polarization that can be determined with a 99%probability against the null hypothesis.The paper is organized as follows. In section 2 we describe theselection and preparation of the Chandra data, and in section 3we present our simulation procedure. Finally, in section 4 we dis-cuss the results, and in Sect. 5 we summarize our conclusions.
2. Chandra data preparation
We consider as candidate targets for an X-ray polarimetry ob-servation the molecular clouds for which Marin et al. (2015)computed the polarization properties expected in a theoreticalscenario where the source of illumination is a past unpolarizedoutburst of Sgr A ∗ . The molecular clouds MC1, MC2, Bridge-D,Bridge-E, Bridge-B2 and G0.11-0.11 belong to the Sgr A com-plex. The Sgr B complex comprises two substructures namedSgr B1 and Sgr B2. Conversely, the clouds Sgr C1, Sgr C2, andSgr C3 are substructures of the Sgr C complex.The morphology of the molecular clouds is known from exten-sive Chandra and XMM-Newton observational campaigns thatwere carried out in the past 20 years. The extension of the clouds(see, e.g., Terrier et al. 2018) is typically larger than the nomi-nal PSF of IXPE (which has a radius of ∼ (cid:48)(cid:48) ). Furthermore, thedi ff use plasma in which the clouds are embedded has an inho-mogeneous morphology. In some of the simulations that follow,we therefore use Chandra maps to define the extended spatialmorphology of the cloud and the soft and hard plasma compo-nent. Moreover, Chandra spectra are used to input the spectralshape of each emission component.As a first step in the preparation of the IXPE simulations, we re-trieved from the public archive the Chandra observations of theSgr A, Sgr B, and Sgr C complexes. We selected in the archiveall the Chandra ACIS-I observations that were taken since 1999without any gratings in place.For the Sgr A field, the total Chandra exposure time is ∼ ffi cient to produce sensible maps of the emissioncomponents separately. For these clouds we therefore use themost recent available Chandra observation for the spectral anal-ysis (Sect. 2.4). We list in Table A.1 all the Chandra observationsthat we used. We processed the Chandra data using the CIAO software(Fruscione et al. 2006), version 4.11, in combination withversion 4.8.2 of the Chandra calibration database (CALDB). Foreach observation, we ran the chandra repro routine to create theclean level 2 event file. Hence, for the Sgr A region, we createdbackground and continuum-subtracted counts maps of the softand hard plasma, and the clouds. For all the images, we kept thenative ACIS pixel size (i.e., ∼ (cid:48)(cid:48) ).We proceeded as follows. For each observation, we created thebackground event-file using the blank-sky event files that areprovided in the Chandra CALDB. For this, we used the blankskyCIAO routine, which customizes a blanksky background file forthe input event file, finding the instrument-specific backgroundfiles in the CALDB and combining and reprojecting them tomatch the input coordinates.For each observation we ran the blanksky-image script tocreate background-subtracted Chandra count maps of eachemission component. For the soft plasma, we created a mapin the 2.35 − xv and Ar xvii emission lines. For the hard plasma, we created amap centered on the Fe xxv -He α line (6.62 − α line (6.32 − − xv , Ar xvii ,Fe xxv -He α, and Fe-K α line. By averaging the results of thiscontinuum model for the four targets of interest, we derivedthe scaling factors (0.38, 0.10, and 0.09 for the soft and hardplasma, and the cloud band, respectively) that we used torescale the continuum images in the band of each emissioncomponent. Thus, these scaling factors were optimized for theregions we used the simulations that followed. The final imagesof each emission component were obtained by subtracting therescaled continuum count-maps from the signal count maps. Wenormalized all the maps by dividing by the maximum value. Wedisplay the final background- and continuum-subtracted mapsof the three emission components in Fig 2. We searched for the targets analyzed in Marin et al. (2015) inthe background- and continuum-subtracted Fe K α map of theSgr A field (Fig. 2, first panel). We excluded from our searchand thus from the IXPE simulations MC1 and the Bridge Dcloud because they are predicted to be basically unpolarized. Weidentified MC 2, Bridge B2, Bridge E, and G0.11-0.11, whichare displayed as circular regions in Fig. 2. In Table 1 we listthe central coordinates, the radius, and the projected distancefrom Sgr A* of each cloud. The cloud sizes are the same ofMarin et al. (2015). As a final step in the preparation of themaps for the simulations of the MC2, Bridge B2, Bridge E, andG0.11-0.11 clouds, we created for each emission component
3i Gesu L. et al: Prospects for polarimetric archaeology of the reflection nebulae in the Galactic center
Fig. 2.
From left to right: Background- and continuum-subtracted Chandra maps of the cloud, hard plasma, and soft plasma component in the SgrA region. Images are smoothed using a 3-pixel Gaussian kernel. The color bar displayed at the bottom has adimensional units because the imagesare normalized to the maximum value. The regions comprising the targets selected for IXPE simulations (i.e., MC2, Bridge-B2, Bridge-E, andG0.11-0.11) are shown. In the first panel, a circle with the size of the IXPE PSF is shown for comparison. The direction of Sgr A* is indicatedwith an arrow.
Table 1.
Input data for IXPE simulations of molecular clouds.Region a Identification b d los c Polarization properties d Center, radius, d proj P φ (hh:mm:ss.s, dd:mm:ss.s, (cid:48)(cid:48) pc) (pc) (%) ( ◦ )17:46:00.6,-28:56:49.2, 49 -14 MC2 -17 25 .
8% 73 . ◦ .
8% 77 . ◦ .
7% 67 . ◦ .
8% 61 . ◦ .
0% 88 . ◦ .
1% 94 . ◦ .
9% 99 . ◦ .
9% 106 . ◦ Notes. ( a ) Data of the regions for the spectral analysis and IXPE simulations. Positive and negative projected distances mean east and west of theGC. ( b ) Cross identification with the target names used in Marin et al. (2015). ( c ) Distance along the line of sight assumed in Marin et al. (2015).See references therein. Positive and negative means behind and in front of the Galactic plane. ( d ) Polarization properties from the model of Marinet al. (2015). smaller Chandra maps cut in the region of interest (i.e., theregion listed in Table 1). This is because we simulated IXPEobservations of each target individually and on axis. We note,however, that the IXPE field of view is 9 (cid:48) in radius, and thus asingle IXPE pointing of the Sgr A field will catch more thanone target. A simulation mapping the entire IXPE field of viewwill be presented in a future expansion of this work. Here, wesimulate each cloud individually, with the aim of collectinguseful information in order to decide the best target for apointing.We centered each map on the brightest Fe K α patch. Becausethe morphology of the clouds varies with time, these coordinatesare shifted with respect to those used in Marin et al. (2015).This does not a ff ect the expected polarization degree becauseit depends mainly on the galactic depth (Eq. 1). The expectedpolarization angle may be a ff ected, but changes are expected tobe less than one degree (F. Marin, private communication).In the case of Sgr B1, Sgr C1, Sgr C2, and Sgr C3, we wereunable to create the Fe-K α map to search for the cloud positions.For these clouds we therefore used the same regions as Marinet al. (2015) to extract the spectra from the most recent Chandra observations. The regions used for Sgr B2, Sgr C1, Sgr C2, andSgr C3 are also listed in Table 1.Finally, we list in Table 1 all the other cloud data that we inputin the IXPE simulations, that is, the polarization degrees andangle resulting from the model of Marin et al. (2015) that werecomputed assuming a position d los along the line of sight of theclouds. The assumed distance is the key parameter determiningthe polarization degree and hence the IXPE detectability. Weexplore the e ff ect of the assumed distances for our simulationsin Sect. 4. The last necessary ingredient for simulating IXPE observationsof the selected targets is the spectral shape of each emissioncomponent. For all the regions listed in Table 1, we extracted thespectrum from the most recent available Chandra observation.These are highlighted in bold in Table A.1. We confirmed thatthe extraction regions include no contamination of known brightX-ray sources (listed in, e.g., Terrier et al. 2018).
4i Gesu L. et al: Prospects for polarimetric archaeology of the reflection nebulae in the Galactic center
Fig. 3.
From top to bottom: Unfolded spectra and residuals to the best-fit model for MC2, Bridge B2, Bridge E, G0.11-0.11, Sgr B2, Sgr C1, SgrC2, and Sgr C3. The total best-fit model and the reflection component are displayed as a solid line. The spectrum of the hard plasma is displayedas a dashed line. The spectrum of the soft plasma is displayed as a dotted line. 5i Gesu L. et al: Prospects for polarimetric archaeology of the reflection nebulae in the Galactic center
Table 2.
Results of the spectral analysis of the molecular clouds described in Sect. 2.4.Target N H a Model component fluxes b Soft plasma: 2.0-4.0 keV 4.0-8.0 keVHard plasma: 2.0-4.0 keV 4.0-8.0 keVCloud: 2.0-4.0 keV 4.0-8.0 keV(10 cm − ) (10 − erg s − cm − )MC2 6 ± ± ± . ± . . ± . . ± .
06 1 . ± . ≤ . ± . . ± . . ± . . ± . . ± − . ± . ± . ± . . ± . . ± . . ± . . ± .
09 14 ± . ± . ± . ± . . ± . ± . ± .
08 11 ± ± . ± . . ± . . ± . . ± . . ± .
03 3 . ± . ± . ± . . ± . . ± . ± . ± .
03t 6 . ± . ± . ≤ . . ± . . ± . . ± . . ± .
05 3 . ± . ± . ± .
05 0 . ± . . ± . ± . ± .
07 8 ± Notes. ( a ) Galactic hydrogen column density. ( b ) Fluxes of each model component in the quoted bands.
To extract the spectra, we used the CIAO script specxtract,which creates the source and background spectra and thenecessary weighted response matrices. We used the customizedblank-sky event file to extract the background spectrum in thesame region. We binned the spectra requiring that a minimumof 30 counts is reached in each spectral bin.We fit all the spectra in the 2.0-8.0 keV band with Xspec version12.10.1. We used a model including the Galactic absorption, thesoft and hard plasma, and the cloud emission. For the Galacticabsorption we used the phabs model, with the hydrogen columndensity N H as a free parameter. For the plasma components, weused a collisionally ionized plasma model (APEC, Smith et al.2001) with a temperature set to 1.0 and 6.5 keV for the soft andhard plasma, respectively. We considered solar abundances andset the redshift to zero. For the molecular clouds, we used theneutral reflection PEXMON model (Nandra et al. 2007), wherewe set (as in, e.g., Ponti et al. 2010) the photon index Γ to 2, thedisk inclination to 60 ◦ , and the cuto ff energy to 150 keV. Thefree parameters of our fits are therefore the Galactic N H andthe normalization of each emission component. We show thespectra of all the clouds in Fig. 3. We list the parameters anderrors resulting from our spectral analysis in Table 2. All thespectral fits are statistically acceptable ( χ d . o . f ≤ .
3. Simulation of IXPE observations
We simulated IXPE observations of the targets listed in Table1 using the dedicated simulation framework ixpeobssim (Pesce-Rollins et al. 2019). This is a python-based tool that can be fed byan arbitrary source model, including morphological, temporal, spectral, and polarimetric information. Hence, the frameworkuses the IXPE instrument response functions (i.e., the PSF andthe detector e ff ective area) to produce the IXPE-simulated eventfiles. These can be used to create images, spectra, and modula-tion curves in di ff erent bands.For each target, we performed the simulation in the region listedin Table 1 and centered the field of view on the coordinates ofthe target. Within the regions of interest, we simulated all thecomponents that contribute to the di ff use X-ray emission. Inaddition to the polarized emission of the molecular clouds, wethus included the soft and hard plasma, the cosmic X-ray back-ground, and the instrumental background in our simulations. Foreach emission component, we input in the simulation the spec-trum, the polarization degree, the polarization position angle,and when possible, the spatial morphology. We took the polar-ization degree and polarization angle of each molecular cloudfrom the model of Marin et al. (2015), as listed in Table 1. Weconsidered a polarization degree that is constant with energy, butnull at the energy of the fluorescence Fe K α line (6 . − .
6i Gesu L. et al: Prospects for polarimetric archaeology of the reflection nebulae in the Galactic center
Fig. 4.
Histograms showing the distribution of the polarization degreein the 4.0-8.0 keV band obtained by simulating the cloud G0.11-0.11for di ff erent instrumental resolutions. The orange histogram shows thecase with infinite spatial resolution. The blue histogram represents thecase with IXPE resolution. below 1% and thus negligible. For the instrumental background,we took the spectrum from the measurement of the non-X-raybackground of the neon-filled detector that flew on board ofOSO-8 (Bunner 1978). The gas mixture and absorption coe ffi -cient of the OSO-8 detector were similar to the one of the IXPEGPD. For the instrumental background, we simulated a uniformmorphology on the detector. In the simulation, the instrumentalbackground is internal to the detector, thus it is not convolvedwith the instrumental response functions. Finally, for the skybackground, we used the parameters of the CXB spectrum ofMoretti et al. (2009), and we renormalized it to match the sim-ulated sky area. We simulated it as a sky source with a uniformmorphology.
4. Results and discussion
Using the input ingredients described in Sect. 2 and the pro-cedure described in Sect. 3, we simulated IXPE observationsof all the targets. We extracted two main quantities from thesimulations: the degree to which polarization is diluted by theambient and background radiation, and which MDP can bereached in a realistic exposure time. These pieces of informationserve to evaluate the detectability of the considered targets in anX-ray polarimetric study of the GC.In order to obtain a sensible measurement of the diluted po-larization degree, we proceeded as follows. For all the targets,we ran mock simulations of observations reaching an MDPof at least 1%. Thus, the mock exposure time (i.e., 100 Ms)was chosen to obtain that the absolute error on the polarizationdegree is 1% or lower. This mimics an ideal case where thestatistical uncertainty of the determined polarization degree isnegligible. Any observed di ff erence between the determinedpolarization degree and the theoretical one in these simulationsmust thus be caused by the mixing between polarized andunpolarized components. We note indeed that in simulationswithout unpolarized sources in the field of view, the theoreticalpolarization degree is always recovered within 3% or less whenthe MDP of the simulation is at least 1%.In Table 3 we list the diluted polarization degrees resulting fromthe simulations and compare them with the scaled polarization degrees that result from a simple rescaling using the ratiobetween the reflection flux and the total flux (e.g., Marin et al.2015). We consider that the scaled polarization degrees area ff ected by the uncertainty of the spectral decomposition. Theranges given in Table 3 are obtained as P × ( F cloud ± eF cloud ) / F tot , where F cloud and eF cloud are the flux and error, respectively,for the cloud component, F tot is the total flux and P is thetheoretical polarization degree. We observe that the dilutedpolarization degrees are in some cases lower than the scaledpolarization degrees. This additional dilution must be inducedby the morphological smearing of the source due to the finitePSF. We illustrate this point in Fig. 4. We ran 100 simulationsof G0.11-0.11 for an ideal case of an instrument with infinitespatial resolution and zero background and 100 normal sim-ulations, where the convolution with the instrumental PSF isconsidered. In this exercise, we considered a mock exposuretime of 100 Ms, so that the statistical fluctuations of thesimulated polarization degree were within 1%. In Fig. 4 wecompare the distribution of the polarization degree obtainedin the two cases. We found that an instrument with infinitespatial resolution would observe a polarization degree of ∼ ∼ ff erence is notexplained by the statistical fluctuations of the simulation resultbecause that is by design lower than 1% in our simulations. Inconclusion, our work shows that the finite spatial resolution ofthe polarimeter can add a sensible additional dilution dependingon the extension and on the morphological details of the source.The quality of the imaging output plays a significant role for anX-ray polarimetric study of the GC region, where the polarizedregions have to be resolved out of the surrounding unpolarizedemission.The diluted polarization degrees have to be compared with theMDP that can be achieved in a realistic exposure time. From ourIXPE simulations, we computed the MDP in the 2.0 − − − −
7i Gesu L. et al: Prospects for polarimetric archaeology of the reflection nebulae in the Galactic center
Table 3.
Simulations results for the reflection nebulae.Target Scaled P a Diluted P b MDP (2 Ms) c F min d − erg s − cm − )MC2 ∗ − − ≤
1% 5% 15% 19% 0.2Bridge B2 ∗ − −
12% 3% 8% 14% 20% 0.1Bridge E ∗ − − ∗ − −
29% 3% 16% 7% 9% 0.5Sgr B2 ∗∗ −
8% 23% −
29% 13% 26% 26% 21% 3.5Sgr C1 ∗∗ − −
23% 1% 10% 13% 14% 0.7Sgr C2 ∗∗ −
6% 12% −
27% 4% 10% 15% 15% 1.1Sgr C3 ∗∗ −
4% 10% −
14% 3% 8% 12% 11% 2.3
Notes. ( a ) Obtained from the fluxes and errors listed in Table 1. ( b ) Obtained from mock simulations reaching an MDP of 1%. By design, theabsolute error on the diluted polarization degree is of 1% or lower. ( c ) Obtained for 2 Ms exposure time. ( d ) Minimum flux detectable by IXPEin 2 Ms with a signal-to-noise ratio of at least 3. ( ∗ ) Simulation performed using Chandra maps to define the morphology of all the components. ( ∗∗ ) Simulation performed assuming a uniform morphology for all the components.
Fig. 5.
Simulated IXPE polarization maps of G0.11-0.11 (left panel) and Sgr B2 (right panel). The background is color-scaled according to thepolarization degree. The colored arrows represent the direction of the polarization angle and are color-scaled accordingly. The color scales for thepolarization degree and angle are shown at the right of each figure. The direction of Sgr A* is also indicated for comparison. background accounts for 2% of the total counts, while the CXBaccounts for 3% of the total counts. Nonetheless, by the time ofthe IXPE observation, the flux of the molecular clouds may behigher or lower than we considered here. In a recent study ofthe long-term flux variability of the molecular clouds, Terrieret al. (2018) found that MC2, G0.11-0.11, and Sgr B are fadingwhile the Bridge is brightening up. The trend for Sgr C is morestable, although within a larger uncertainty. It is therefore usefulto compute the minimum flux that would be detectable by IXPEin 2 Ms for each target with a signal-to-noise ratio of at least3. Exploiting our estimates of the background contribution,we determined these flux thresholds and list them in Table 3.We found that the targets in the Sgr A field remain detectableunless the total flux decreases by one (e.g., for MC 2 and BridgeB2) or even two orders of magnitude (e.g., for Bridge E andG0.11-0.11) with respect to the level we considered here. In thecase of Sgr B2, the total flux would need to be lower by a factor3 with respect to the level observed in 2010 (i.e., 1.1 × − erg s − cm − ) to fall below the detection threshold.In addition to the variability in flux, the molecular clouds inthe GC also exhibit variability in morphology. For instance,the brightest centroid in Sgr C2 underwent a displacementof 1.6 (cid:48) in 12 years (Terrier et al. 2018). We investigated thee ff ect of the morphology for the result of our simulations. At first, we assessed the e ff ect of positioning the simulated IXPEpointing well onto the brightest Fe K α patch. We tested thisissue using the 2 Ms long simulation of the Bridge-B2 cloud,which displays a well-defined bright knot. We find that shiftingthe IXPE pointing just ∼ (cid:48)(cid:48) away from the brightest patchcauses a loss of ∼
300 counts and decreases the MDP by 1%.This suggests that it is convenient to center the IXPE pointingon a bright knot in order to maximize the collected counts andthus the chance of detecting a significant polarization.We therefore evaluated the e ff ect of the morphology on deter-mining the diluted polarization in the region of interest. In figure5 we show as an example the simulated IXPE polarization mapsof the two best targets. These were produced from the mock sim-ulations. In these maps, the colored arrows indicate the directionof the polarization angle. In the case of a reflection nebula, thisis normal to the projected direction of the illuminating source.In the simulated map of Sgr B2, the nebula is uniform in colorand polarization degree because it was simulated assuming auniform morphology for all the components. In the simulatedmap of G0.11-0.11, this was obtained by starting from theChandra maps of the di ff erent components, and the irregulardistribution of polarization fraction and color within the nebulareflects the di ff erent level of mixing between polarized andunpolarized emission.
8i Gesu L. et al: Prospects for polarimetric archaeology of the reflection nebulae in the Galactic center
Nonetheless, the dilution of the polarization degree averagedover the regions of interest mildly depends on the internalmorphology, likely because the substructures are one scalesmaller than the IXPE PSF. We verified this point by runningsimulations of the G0.11-0.11 field assuming a uniform mor-phology for all the components and a mock exposure time of100 Ms. The results for the diluted polarization degree are thesame within the uncertainty as in the run using the Chandramaps. We are therefore a posteriori confident that our estimatesof the polarization dilution in Sgr B2, Sgr C1, Sgr C2, and SgrC3 are trustworthy.All in all, we remark that an X-ray observation of the GC wouldbe useful prior the IXPE pointing. With the Spectrum R¨ontgenGamma (SRG) on board of eROSITA, for example, it is possibleto measure the flux level of the candidate targets. With Chandraor XMM-Newton, it is possible to determine which patchesare currently illuminated. This would help in deciding the bestpointing.Finally, in Table 4 we investigate the most critical uncertaintythat a ff ects the evaluation of the detectability of the polarizationof the molecular cloud. The theoretical polarization degreerelies on the poorly constrained line-of-sight distance of thecloud and will be corrected when a more robust determinationof d los is found. We searched in the literature for determinationsof the line-of-sight distance of the clouds di ff erent from thoseassumed in Marin et al. (2015) (listed as d otherlos in Table 4). Thesewere obtained in works where the scattering angle is derivedfrom modeling of the reflection spectrum (Capelli et al. 2012;Walls et al. 2016; Chuard et al. 2018) and were often looselyconstrained. Starting from the range of d otherlos , we used equations1 and 2 to compute the correspondent range of polarizationdegree ( P other ), and we used the dilution factors in the 4.0-8.0keV band that can be inferred from Table 3 to determine thecorresponding range in diluted polarization degree ( P otherdil ).Thus, we were able to verify whether for a di ff erent assumptionon d los , the diluted polarization degree of our targets rises ordrops below the MDP that can be obtained by IXPE in the4.0-8.0 keV band in 2 Ms. The values listed in Table 4 confirmthe detectability of G011-0.11 and Sgr B2 also for other possibledistances reported in the literature. The molecular clouds BridgeB2, Bridge E, and Sgr C1 might be detectable if their realdistance along the line of sight lies within the upper bound ofthe range determined by Capelli et al. (2012) and Chuard et al.(2018).We also investigated how the enhanced sensitivity of eXTPallows enlarging the pool of suitable targets. The e ff ective areaof eXTP will be larger by a factor ∼
4, which implies (usingequation 3) that the MDP for the case of eXTP is lower thanthose of IXPE by a factor 0.51. When this factor is applied to theMDP values listed in Table 3, this implies that G0.11-0.11, SgrB2, Sgr C1, Sgr C2, and Sgr C3 are potential targets for eXTPin the 4.0-8.0 keV band. The ranges of diluted polarizationdegrees obtained in Table 4 by relaxing the constraints on d los o ff er a window of eXTP detectability for virtually all the targets.More sensitive telescopes, for instance, the X-ray PolarimetryProbe (XPP, Jahoda et al. 2019) or the New Generation X-rayPolarimeter (NGXRP, So ffi tta et al. 2019) mission conceptwould allow detecting the X-ray polarization of the molecularclouds with shorter exposure times.In conclusion, an X-ray polarimetric study of the CMZ is achallenging experiment because of the dynamic behavior ofthe reflection emission and because of the complex gaseousenvironment in which the nebulae are embedded. In this work,we set up a simulation method that allows realistically assessing Table 4.
Polarization obtained for alternative values of d los reported inthe literature.Target d otherlos a P other b P otherdil c Ref. d (pc) (%) (%)MC2 -29.7 − −
53 9 −
10 ABridge B2 -6.9 − ≤ ≤
42 ABridge E -13.7 − ≤ ≤
45 AG0.11-0.11 -3.1 − ≤ ≤
26 ASgr B2 -50 − -47 61 −
83 24 −
33 BSgr C1 -0.61 −
47 50 − −
32 CSgr C2 -38 − -25 50 −
54 14 −
16 C
Notes. ( a ) Range of d los from the quoted references. ( b ) Range of po-larization degree corresponding to d los , obtained from Eqs. 1 and 2. ( c ) Range of diluted polarization degree obtained from the values ofTable 3 ( d ) A: Capelli et al. (2012), B: Walls et al. (2016), and C: Chuardet al. (2018). how some critical factors (i.e., the variability in flux andmorphology of the clouds, and the dilution of the polarizationdegree in the unpolarized ambient and background radiation)a ff ect the detectability of a reflection nebula observed on axis.Nonetheless, other levels of complexity remain unexplored. Ina future expansion of this work, we will produce a simulatedIXPE map of the entire Sgr A field of view. This would allowus to investigate, for instance, how the detectability degradesfor a nebula o ff axis and what happens in regions where gasfilaments with a di ff erent level of polarization are mixed.Because the time required to make a significant measurementof the reflection nebulae in the GC is some milliseconds, theimpact on the planning of IXPE observations is significant.Our realistic predictions are therefore important to inform thedecision of including these observations in the planning.
5. Summary and conclusions
Measuring the X-ray polarization property of a reflection nebulain the GC allows us to confirm (or discard) that they are illu-minated by a past outburst of Sgr A* (through the polarizationangle) and to determine the position of the nebula along theline of sight (through the polarization degree). These are criticaluncertainties that hamper our ability of using the variability ofthe reflection emission to infer how our Galactic nucleus wasbehaving a few hundred years ago. Assessing the history of ourGalactic nucleus has implications for our understanding of theduty cycle of mass accretion onto SMBH that is believed todrive to the coevolution of SMBH and galaxies.We have evaluated the feasibility of this experiment with IXPE,which is expected to launch in 2021, and with eXTP, which isscheduled for launch in 2027. We simulated IXPE observationsof the molecular clouds MC2, Bridge-B2, Bridge E, G0.11-0.11,Sgr B2, Sgr C1, Sgr C2 and, Sgr C3 considering the polarizationproperties predicted by the model of Marin et al. (2015). Weused the Monte Carlo-based simulation tool ixpeobssim toindividually simulate IXPE images of these targets. In our sim-ulations, we considered the spectrum (using Chandra spectra),the polarization properties, and (when possible, using Chandraimages) the spatial morphology of the molecular clouds and ofthe di ff use emission that is comprised in the region of interest.We modeled the di ff use emission of the GC using two thermalplasma components ( T soft − plasma ∼ T hard − plasma ∼
9i Gesu L. et al: Prospects for polarimetric archaeology of the reflection nebulae in the Galactic center background and the cosmic X-ray background. Our strategy isdesigned to estimate the degree to which the polarization degreeof the clouds is diluted by the unpolarized ambient radiationand by the morphological smearing of the sources due to theinstrumental PSF.We determined for each cloud the minimum flux that wouldbe detectable by IXPE in 2 Ms. We find that the molecularclouds considered here become undetectable when the totalflux decreases by a factor 3 −
100 (depending on the cloud) withrespect to the level considered here. Moreover, we found thatthe dilution of the polarization degree ranges between 0.3% and23% in the 2.0 − − ff ective area is larger by a factor ∼ − References
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The Italian contribution to the IXPE mission is supportedby the Italian Space Agency through agreements ASI-INAF n.2017-12-H.0 andASI-INFN n.2017.13-H.0. FM acknowledges the support from the ProgrammeNational des Hautes Energies of CNRS / INSU with INP and IN2P3, co-fundedby CEA and CNES. We thank Gabriele Ponti and Alessandra De Rosa for usefulchats about the Chandra data analysis and the eXTP capability. We thank theanonymous referee for the helpful comments that improved this manuscript.
Appendix A: Chandra analysis log
10i Gesu L. et al: Prospects for polarimetric archaeology of the reflection nebulae in the Galactic center
Table A.1.
Log of the Chandra observations.Target Obs. ID Date Pointing Exposure timeName hh mm ss.s (ks)MC2, Bridge-B2, Bridge E, G0.11-0.11 2951 2002-02-19 Sgr A ∗
17 45 40.00 -29 00 28.10 12MC2, Bridge-B2, Bridge E, G0.11-0.11 2952 2002-03-23 Sgr A ∗
17 45 40.00 -29 00 28.10 12MC2, Bridge-B2, Bridge E, G0.11-0.11 2953 2002-04-19 Sgr A ∗
17 45 40.00 -29 00 28.10 12MC2, Bridge-B2, Bridge E, G0.11-0.11 2954 2002-05-07 Sgr A ∗
17 45 40.00 -29 00 28.10 12MC2, Bridge-B2, Bridge E, G0.11-0.11 2943 2002-05-22 Sgr A ∗
17 45 40.00 -29 00 28.10 38MC2, Bridge-B2, Bridge E, G0.11-0.11 3663 2002-05-24 Sgr A ∗
17 45 40.00 -29 00 28.10 38MC2, Bridge-B2, Bridge E, G0.11-0.11 3392 2002-05-25 Sgr A ∗
17 45 40.00 -29 00 28.10 170MC2, Bridge-B2, Bridge E, G0.11-0.11 3393 2002-05-28 Sgr A ∗
17 45 40.00 -29 00 28.10 158MC2, Bridge-B2, Bridge E, G0.11-0.11 3665 2002-06-03 Sgr A ∗
17 45 40.00 -29 00 28.10 90MC2, Bridge-B2, Bridge E, G0.11-0.11 3549 2003-06-19 Sgr A ∗
17 45 40.00 -29 00 28.00 25MC2, Bridge-B2, Bridge E, G0.11-0.11 4683 2004-07-05 Sgr A ∗
17 45 40.00 -29 00 28.00 50MC2, Bridge-B2, Bridge E, G0.11-0.11 4684 2004-07-06 Sgr A ∗
17 45 40.00 -29 00 28.00 50MC2, Bridge-B2, Bridge E, G0.11-0.11 6113 2005-02-27 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 5950 2005-07-24 Sgr A ∗
17 45 40.00 -29 00 28.00 48MC2, Bridge-B2, Bridge E, G0.11-0.11 5951 2005-07-27 Sgr A ∗
17 45 40.00 -29 00 28.00 49MC2, Bridge-B2, Bridge E, G0.11-0.11 5952 2005-07-29 Sgr A ∗
17 45 40.00 -29 00 28.00 45MC2, Bridge-B2, Bridge E, G0.11-0.11 5953 2005-07-30 Sgr A ∗
17 45 40.00 -29 00 28.00 49MC2, Bridge-B2, Bridge E, G0.11-0.11 5954 2005-08-01 Sgr A ∗
17 45 40.00 -29 00 28.00 18MC2, Bridge-B2, Bridge E, G0.11-0.11 6639 2006-04-11 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 6640 2006-05-03 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 6641 2006-06-01 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 6642 2006-07-04 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 6363 2006-07-17 Sgr A ∗
17 45 40.00 -29 00 28.00 30MC2, Bridge-B2, Bridge E, G0.11-0.11 6643 2006-07-30 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 6644 2006-08-22 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 6645 2006-09-25 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 6646 2006-10-29 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 7554 2007-02-11 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 7555 2007-03-25 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 7556 2007-05-17 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 7557 2007-07-20 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 7558 2007-09-02 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 7559 2007-10-26 Sgr A ∗
17 45 40.00 -29 00 28.00 5MC2, Bridge-B2, Bridge E, G0.11-0.11 9169 2008-05-05 Sgr A ∗
17 45 40.00 -29 00 28.10 28MC2, Bridge-B2, Bridge E, G0.11-0.11 9170 2008-05-06 Sgr A ∗
17 45 40.00 -29 00 28.10 27MC2, Bridge-B2, Bridge E, G0.11-0.11 9171 2008-05-10 Sgr A ∗
17 45 40.00 -29 00 28.10 28MC2, Bridge-B2, Bridge E, G0.11-0.11 9172 2008-05-11 Sgr A ∗
17 45 40.00 -29 00 28.10 27MC2, Bridge-B2, Bridge E, G0.11-0.11 9174 2008-07-25 Sgr A ∗
17 45 40.00 -29 00 28.10 29MC2, Bridge-B2, Bridge E, G0.11-0.11 9173 2008-07-26 Sgr A ∗
17 45 40.00 -29 00 28.10 28MC2, Bridge-B2, Bridge E, G0.11-0.11 10556 2009-05-18 Sgr A ∗
17 45 40.00 -29 00 28.10 113MC2, Bridge-B2, Bridge E, G0.11-0.11 11843 2010-05-13 Sgr A ∗
17 45 40.00 -29 00 28.00 79MC2, Bridge-B2, Bridge E, G0.11-0.11 13016 2011-03-29 Sgr A ∗
17 45 40.00 -29 00 28.10 18MC2, Bridge-B2, Bridge E, G0.11-0.11 13017 2011-03-31 Sgr A ∗
17 45 40.00 -29 00 28.10 18MC2, Bridge-B2, Bridge E, G0.11-0.11 13508 2011-07-19 Sgr A complex 17 45 59.70 -28 58 15.90 33MC2, Bridge-B2, Bridge E, G0.11-0.11 12949 2011-07-21 Sgr A complex 17 45 59.70 -28 58 15.90 58MC2, Bridge-B2, Bridge E, G0.11-0.11 13438 2011-07-29 Sgr A complex 17 45 59.70 -28 58 15.90 66MC2, Bridge-B2, Bridge E, G0.11-0.11 14941 2013-04-06 Sgr A ∗
17 45 40.00 -29 00 28.10 20MC2, Bridge-B2, Bridge E, G0.11-0.11 14942 2013-04-14 Sgr A ∗
17 45 40.00 -29 00 28.10 20MC2, Bridge-B2, Bridge E, G0.11-0.11 17236 2015-04-25 Sgr A complex 1 17 46 15.50 -28 55 00.70 79MC2, Bridge-B2, Bridge E, G0.11-0.11 17239 2015-08-19 Sgr A complex 2 17 46 07.00 -28 53 09.50 79MC2, Bridge-B2, Bridge E, G0.11-0.11 17237 2016-05-18 Sgr A complex 1 17 46 15.50 -28 55 00.70 21MC2, Bridge-B2, Bridge E, G0.11-0.11 18852 2016-05-18 Sgr A complex 1 17 46 14.10 -28 54 52.50 52MC2, Bridge-B2, Bridge E, G0.11-0.11 17240 2016-05-18 Sgr A complex 2 17 46 09.60 -28 53 43.80 75MC2, Bridge-B2, Bridge E, G0.11-0.11 17238 2017-07-17 Sgr A complex 1 17 46.14.10 -28 54 52.50 65MC2, Bridge-B2, Bridge E, G0.11-0.11 20118 2017-07-23 Sgr A complex 1 17 46 14.10 -28 54 52.50 14MC2, Bridge-B2, Bridge E, G0.11-0.11 17241 2017-10-02 Sgr A complex 2 17 46.07.00 -28 53 09.50 25MC2, Bridge-B2, Bridge E, G0.11-0.11 20807 2017-10-05 Sgr A complex 1 17 46.07.00 -28 53 09.50 28MC2, Bridge-B2, Bridge E, G0.11-0.11 ∗ ∗ ∗ ∗ Notes. ( ∗ ))