TW Hydrae is Forming a SubSaturn Gas Giant

Deep imaging search for planets forming in the TW Hya protoplanetary disk with the Keck/NIRC2 vortex coronagraph


Authors:

Ruane et al

Abstract:
Distinct gap features in the nearest protoplanetary disk, TW Hya (distance of 59.5±0.9 pc), may be signposts of ongoing planet formation. We performed long-exposure thermal infrared coronagraphic imaging observations to search for accreting planets especially within dust gaps previously detected in scattered light and submm-wave thermal emission. Three nights of observations with the Keck/NIRC2 vortex coronagraph in L′ (3.4-4.1μm) did not reveal any statistically significant point sources. We thereby set strict upper limits on the masses of non-accreting planets. In the four most prominent disk gaps at 24, 41, 47, and 88 au, we obtain upper mass limits of 1.6-2.3, 1.1-1.6, 1.1-1.5, and 1.0-1.2 Jupiter masses (MJ) assuming an age range of 7-10 Myr for TW Hya. These limits correspond to the contrast at 95\% completeness (true positive fraction of 0.95) with a 1\% chance of a false positive within 1′′ of the star. We also approximate an upper limit on the product of planet mass and planetary accretion rate of MpM˙≲10−8M2J/yr implying that any putative ∼0.1MJ planet, which could be responsible for opening the 24 au gap, is presently accreting at rates insufficient to build up a Jupiter mass within TW Hya's pre-main sequence lifetime.

On the formation of multiple concentric rings and gaps in protoplanetary disks

On the formation of multiple concentric rings and gaps in protoplanetary disks

Authors:

Bae et al

Abstract:

As spiral waves driven by a planet in a gaseous disk steepen into a shock, they deposit angular momentum, opening a gap in the disk. This has been well studied using both linear theory and numerical simulations, but so far, only for the primary spiral arm -- the one directly attached to the planet. Using two-dimensional hydrodynamic simulations, we show that the secondary and tertiary arms driven by a planet can also open gaps as they steepen into shocks. The depths of the secondary/tertiary gaps in surface density grow with time in a low viscosity disk (α=5×10−5), so even low-mass planets (e.g., super-Earth or mini-Neptune) embedded in the disk can open multiple observable gaps, provided that sufficient time has passed. Applying our results to the HL Tau disk, we show that a single 30 Earth-mass planet embedded in the ring at 68.8 au (B5) can reasonably well reproduce the positions of the two major gaps at 13.2 and 32.3 au (D1 and D2), and roughly reproduce two other major gaps at 64.2 and 74.7 au (D5 and D6) seen in the mm continuum. The positions of secondary/tertiary gaps are found to be sensitive to the planetary mass and the disk temperature profile, so with accurate observational measurements on the temperature structure we can use the positions of multiple gaps to constrain the mass of the planet. We also comment on the gaps seen in the TW Hya and HD 163296 disk.

Mass inventory of the giant-planet formation zone in a solar nebula analog

Mass inventory of the giant-planet formation zone in a solar nebula analog
Authors:

Zhang et al

Abstract:
The initial mass distribution in the solar nebula is a critical input to planet formation models that seek to reproduce today's Solar System. Traditionally, constraints on the gas mass distribution are derived from observations of the dust emission from disks, but this approach suffers from large uncertainties in grain growth and gas-to-dust ratio. On the other hand, previous observations of gas tracers only probe surface layers above the bulk mass reservoir. Here we present the first partially spatially resolved observations of the 13C18O J=3-2 line emission in the closest protoplanetary disk, TW Hya, a gas tracer that probes the bulk mass distribution. Combining it with the C18O J=3-2 emission and the previously detected HD J=1-0 flux, we directly constrain the mid-plane temperature and optical depths of gas and dust emission. We report a gas mass distribution of 13+8−5×(R/20.5AU)−0.9+0.4−0.3 g cm−2 in the expected formation zone of gas and ice giants (5-21AU). We find the total gas/millimeter-sized dust mass ratio is 140 in this region, suggesting that at least 2.4M_earth of dust aggregates have grown to >centimeter sizes (and perhaps much larger). The radial distribution of gas mass is consistent with a self-similar viscous disk profile but much flatter than the posterior extrapolation of mass distribution in our own and extrasolar planetary systems.

Multiple Disk Gaps and Rings Generated by a Single Super-Earth

Multiple Disk Gaps and Rings Generated by a Single Super-Earth
Authors:

Dong et al

Abstract:
We investigate the observational signatures of super-Earths (i.e., Earth-to-Neptune mass planets) in their natal disks of gas and dust. Combining two-fluid global hydrodynamics simulations with a radiative transfer code, we calculate the distributions of gas and of sub-mm-sized dust in a disk perturbed by a super-Earth, synthesizing images in near-infrared scattered light and the mm-wave thermal continuum for direct comparison with observations. In low viscosity gas (α≲10−4), a super-Earth opens two annular gaps to either side of its orbit by the action of Lindblad torques. This double gap and its associated gas pressure gradients cause dust particles to be dragged by gas into three rings: one ring sandwiched between the two gaps, and two rings located at the gap edges farthest from the planet. Depending on system parameters, additional rings may manifest for a single planet. A double gap located at tens of AUs from a host star in Taurus can be detected in the dust continuum by the Atacama Large Millimeter Array (ALMA) at an angular resolution of ~0".03 after two hours of integration. Ring and gap features persist in a variety of background disk profiles, last for thousands of orbits, and change their relative positions and dimensions depending on the speed and direction of planet migration. Candidate double gaps have been observed by ALMA in systems like HL Tau (D5 and D6) and TW Hya (at 37 and 43 AU); we submit that each double gap is carved by one super-Earth in nearly inviscid gas.

Radial Drift of Dust in Protoplanetary Disks: The Evolution of Ice lines and Dead zones

Radial Drift of Dust in Protoplanetary Disks: The Evolution of Ice lines and Dead zones

Authors:

Cridland et al

Abstract:

We have developed a new model for the astrochemical structure of a viscously evolving protoplanetary disk that couples an analytic description of the disk's temperature and density profile, chemical evolution, and an evolving dust distribution. We compute evolving radial distributions for a range of dust grain sizes, which depend on coagulation, fragmentation and radial drift processes. In particular we find that the water ice line plays an important role in shaping the radial distribution of the maximum grain size because ice coated grains are significantly less susceptible to fragmentation than their dry counterparts. This in turn has important effects on disk ionization and therefore on the location of dead zones. In comparison to a simple constant gas-to-dust ratio model for the dust as an example, we find that the new model predicts an outer dead zone edge that moves in by a factor of about 3 at 1 Myr (to 5 AU) and by a factor of about 14 by 3 Myr (to 0.5 AU). We show that the changing position of the dead zone and heat transition traps have important implications for the formation and trapping of planets in protoplanetary disks. Finally, we consider our results in light of recent ALMA observations of HL Tau and TW Hya.

A Photo-evaporative gap Observed in the TW Hydrae

A photo-evaporative gap in the closest planet forming disc

Authors:

Ercolano et al

Abstract:

The dispersal of the circumstellar discs of dust and gas surrounding young low- mass stars has important implications for the formation of planetary systems. Photo- evaporation from energetic radiation from the central object is thought to drive the dispersal in the majority of discs, by creating a gap which disconnects the outer from the inner regions of the disc and then disperses the outer disc from the inside-out, while the inner disc keeps draining viscously onto the star. In this Letter we show that the disc around TW Hya, the closest protoplanetary disc to Earth, may be the first object where a photoevaporative gap has been imaged around the time at which it is being created. Indeed the detected gap in the ALMA images is consistent with the expectations of X-ray photoevaporation models, thus not requiring the presence of a planet. The photoevaporation model is also consistent with a broad range of properties of the TW Hya system, e.g. accretion rate and the location of the gap at the onset of dispersal. We show that the central, unresolved 870 {\mu}m continuum source might be produced by free free emission from the gas and/or residual dust inside the gap.

First detection of gas-phase methanol in a protoplanetary disk

First detection of gas-phase methanol in a protoplanetary disk

Authors:

Walsh et al

Abstract:

The first detection of gas-phase methanol in a protoplanetary disk (TW Hya) is presented. In addition to being one of the largest molecules detected in disks to date, methanol is also the first disk organic molecule with an unambiguous ice chemistry origin. The stacked methanol emission, as observed with ALMA, is spectrally resolved and detected across six velocity channels (>3σ), reaching a peak signal-to-noise of 5.5σ, with the kinematic pattern expected for TW~Hya. Using an appropriate disk model, a fractional abundance of 3×10−12−4×10−11 (with respect to H2) reproduces the stacked line profile and channel maps, with the favoured abundance dependent upon the assumed vertical location (midplane versus molecular layer). The peak emission is offset from the source position suggesting that the methanol emission has a ring-like morphology: the analysis here suggests it peaks at ≈30~AU reaching a column density ≈3−6×1012~cm−2. In the case of TW Hya, the larger (up to mm-sized) grains, residing in the inner 50~AU, may thus host the bulk of the disk ice reservoir. The successful detection of cold gas-phase methanol in a protoplanetary disk implies that the products of ice chemistry can be explored in disks, opening a window to studying complex organic chemistry during planetary system formation.

Is TW Hydrae About to Lose its Disk?

The dusty disk surrounding the star TW Hydrae exhibits circular features that may signal the formation of protoplanets. LMU astrophysicist Barbara Ercolano argues, however, that the innermost actually points to the impending dispersal of the disk.

When the maps appeared at the end of March, experts were electrified. The images revealed an orange-red disk pitted with circular gaps that looked like the grooves in an old-fashioned long-playing record. But this was no throwback to the psychedelic Sixties. It was a detailed portrait of a so-called protoplanetary disk, made up of gas and dust grains, associated with a young star - the kind of structure out of which planets could be expected to form. Not only that, the maps showed that the disk around the star known as TW Hydrae exhibits several clearly defined gaps. Astronomers speculated that these gaps might indicate the presence of protoplanets, which had pushed away the material along their orbital paths. And to make the story even more seductive, one prominent gap is located at approximately the same distance from TW Hydrae as Earth is from the Sun - raising the possibility that this putative exoplanet could be an Earth-like one.

Now an international team led by Professor Barbara Ercolano at LMU's Astronomical Observatory has compared the new observations with theoretical models of planet formation. The study indicates that the prominent gap in the TW Hydrae system is unlikely to be due to the action of an actively accreting protoplanet. Instead, the team attributes the feature to a process known as photoevaporation. Photoevaporation occurs when the intense radiation emitted by the parent star heats the gas, allowing it to fly away from the disk. But although hopes of a new exo-Earth orbiting in the inner gap of TW Hydrae may themselves have evaporated, the system nevertheless provides the opportunity to observe the dissipation of a circumstellar disk in unprecedented detail. The new findings appear in the journal Monthly Notices of the Royal Astronomical Society (MNRAS).

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Measuring Turbulence in TW Hya with ALMA

Measuring Turbulence in TW Hya with ALMA: Methods and Limitations

Authors:

Teague et al

Abstract:

We obtain high spatial and spectral resolution images of the CO J=2-1, CN N=2-1 and CS J=5-4 emission with ALMA in Cycle~2. The radial distribution of the turbulent broadening is derived with three approaches: two `direct' and one modelling. The first requires a single transition and derives \Tex{} directly from the line profile, yielding a \vturb{}. The second assumes two different molecules are co-spatial thus their relative linewidths allow for a calculation of \Tkin{} and \vturb{}. Finally we fit a parametric disk model where physical properties of the disk are described by power laws, to compare our `direct' methods with previous values. The two direct methods were limited to the outer r>40~au disk due to beam smear. The direct method found \vturb{} ranging from ≈~\vel{130} at 40~au, dropping to ≈~\vel{50} in the outer disk, qualitatively recovered with the parametric model fitting. This corresponds to roughly 0.2−0.4 cs. CN was found to exhibit strong non-LTE effects outside r≈140~au, so \vturb{} was limited to within this radius. The assumption that CN and CS are co-spatial is consistent with observed linewidths only within r≲100~au, within which \vturb{} was found to drop from \vel{100} (≈ 0.4 cs) to nothing at 100~au. The parametric model yielded a near constant \vel{50} for CS (0.2−0.4 cs). We demonstrate that absolute flux calibration is and will be the limiting factor in all studies of turbulence using a single molecule. The magnitude of the dispersion is comparable with or below that predicted by the magneto-rotational instability theory. A more precise comparison would require to reach an absolute calibration precision of order 3\%, or to find a suitable combination of light and heavy molecules which are co-located in the disk.

Volatile carbon locking and release in protoplanetary disks

Volatile carbon locking and release in protoplanetary disks. A study of TW Hya and HD 100546

Authors:

Kama et al

Abstract:

The composition of planetary solids and gases is largely rooted in the processing of volatile elements in protoplanetary disks. To shed light on the key processes, we carry out a comparative analysis of the gas-phase carbon abundance in two systems with a similar age and disk mass, but different central stars: HD 100546 and TW Hya. We combine our recent detections of C0 in these disks with observations of other carbon reservoirs (CO, C+, C2H) and gas mass and warm gas tracers (HD, O0), as well as spatially resolved ALMA observations and the spectral energy distribution. The disks are modelled with the DALI 2D physical-chemical code. Stellar abundances for HD 100546 are derived from archival spectra. Upper limits on HD emission from HD 100546 place an upper limit on the total disk mass of ≤0.1M⊙. The gas-phase carbon abundance in the atmosphere of this warm Herbig disk is at most moderately depleted compared to the interstellar medium, with [C]/[H]gas=(0.1−1.5)×10−4. HD 100546 itself is a λBo\"{o}tis star, with solar abundances of C and O but a strong depletion of rock-forming elements. In the gas of the T Tauri disk TW Hya, both C and O are strongly underabundant, with [C]/[H]gas=(0.2−5.0)×10−6 and C/O greater than 1. We discuss evidence that the gas-phase C and O abundances are high in the warm inner regions of both disks. Our analytical model, including vertical mixing and a grain size distribution, reproduces the observed [C]/[H]gas in the outer disk of TW Hya and allows to make predictions for other systems.

Multiple gaps with large grain deficit in the protoplanetary disk around TW Hya

Multiple gaps with large grain deficit in the protoplanetary disk around TW Hya

Authors:

Tsukagoshi et al

Abstract:

We report ∼3 au resolution imaging observations of the protoplanetary disk around TW Hya at 138 and 230 GHz with the Atacama Large Millimeter/Submillimeter Array. Our observations revealed two deep gaps (∼25--50 %) at 22 and 37 au and shallower gaps (a few %) at 6, 28, and 44 au, as recently reported by Andrews et al. (2016). The central hole with a radius of ∼3 au was also marginally resolved. The most remarkable finding is that the power-law index of the dust opacity β, derived from the spectral index α between bands 4 and 6, peaks at the 22 au gap with β∼1.7 and decreases toward the disk center to β∼0. Our model fitting suggests that the overall disk structure can be reproduced with the inner hole and the gaps at 22 and 37 au. The most prominent gap at 22~au could be caused by the gravitational interaction between the disk and an unseen planet with a mass of ≲1.5 MNeptune although other origins may be possible. The planet-induced gap is supported by the fact that β is enhanced at the 22 au gap, indicating a deficit of ∼mm-sized grains within the gap due to dust filtration by a planet. Alternatively, the destruction of large dust aggregates due to the sintering of major volatiles might cause the multiple ring structure. We also find weak sinusoidal patterns with wavelengths of 5--10 au, which may be related to dynamical instabilities within the disk.

The Carbon monoxide Snowline is at 17-23 AU for TW Hydrae's Protoplanetary Disk

The Radial Distribution of H2 and CO in TW Hya as Revealed by Resolved ALMA Observations of CO Isotopologues

Authors:

Schwartz et al

Abstract:

CO is widely used as a tracer of molecular gas. However, there is now mounting evidence that gas phase carbon is depleted in the disk around TW Hya. Previous efforts to quantify this depletion have been hampered by uncertainties regarding the radial thermal structure in the disk. Here we present resolved ALMA observations of 13CO 3-2, C18O 3-2, 13CO 6-5, and C18O 6-5 emission in TW Hya, which allow us to derive radial gas temperature and gas surface density profiles, as well as map the CO abundance as a function of radius. These observations provide a measurement of the surface CO snowline at ~30 AU and show evidence for an outer ring of CO emission centered at 53 AU, a feature previously seen only in less abundant species. Further, the derived CO gas temperature profile constrains the freeze-out temperature of CO in the warm molecular layer to < 21 K. Combined with the previous detection of HD 1-0, these data constrain the surface density of the warm H2 gas in the inner ~30 AU. We find that CO is depleted by two orders of magnitude from R=10-60 AU, with the small amount of CO returning to the gas phase inside the surface CO snowline insufficient to explain the overall depletion. Finally, this new data is used in conjunction with previous modeling of the TW Hya disk to constrain the midplane CO snowline to 17-23 AU.

The inner structure of the TW Hya Disk as revealed in scattered light

The inner structure of the TW Hya Disk as revealed in scattered light

Authors:

Debes et al

Abstract:

We observe a significant change in the TW Hya disk interior to 40~AU via archival unpolarized multi-wavelength Hubble Space Telescope/STIS and NICMOS images with an inner working angle (IWA) of 0\farcs4 (22~AU). Our images show the outer edge of a clearing at every wavelength with similar behavior, demonstrating that the feature is structural, rather than due to some property of polarized light in the disk. We compare our observations to those taken by Akiyama et al. (2015) and Rapson et al. (2015), and discuss the spectral evolution of the disk interior to 80~AU. We construct a model with two gaps: one at 30~AU and one at 80~AU that fit the observed surface brightness profile but overpredicts the absolute brightness of the disk. Our models require an additional dimming to be consistent with observations, which we tentatively ascribe to shadowing. The gap structures seen in scattered light are spatially coincident with sub-mm detections of CO and N2H+, and are near expected condensation fronts of these molecular species, providing tentative evidence that the structures seen in scattered light may be correlated with chemical changes in the disk.

A Gap and Ring in TW Hydrae's Protoplanetary Disk

ALMA Observations of a Gap and a Ring in the Protoplanetary Disk around TW Hya

Authors:

Nomura et al

Abstract:

We report the first detection of a gap and a ring in dust continuum emission from the protoplanetary disk around TW Hya, using the Atacama Large Millimeter/Submillimeter Array. The gap and ring are located at 25 and 41 AU from the central star, respectively, and are associated with the CO snowline at ~ 30AU. The gap width and depth are 15AU at the maximum and 23% at the minimum, respectively, regarding that the observations are limited to an angular resolution of ~ 15AU. In addition, we detect a decrement in CO line emission down to ~ 10AU, indicating freeze-out of gas-phase CO onto grain surfaces and possible subsequent surface reactions to form larger molecules. According to theoretical studies, the gap could be caused by gravitational interaction between the disk gas and a planet with a mass less than super-Neptune (2 Neptune mass), or result from destruction of large dust aggregates due to the sintering of CO ice.

TW Hydrae Disk Definitely has at Least One .2 Jupiter Mass Gas Giant at ~23 AU

Peering into the Giant Planet Forming Region of the TW Hydrae Disk with the Gemini Planet Imager

Authors:

Rapson et al

Abstract:

We present Gemini Planet Imager (GPI) adaptive optics near-infrared images of the giant planet-forming regions of the protoplanetary disk orbiting the nearby (D = 54 pc), pre-main sequence (classical T Tauri) star TW Hydrae. The GPI images, which were obtained in coronagraphic/polarimetric mode, exploit starlight scattered off small dust grains to elucidate the surface density structure of the TW Hya disk from 80 AU to within 10 AU of the star at 1.5 AU resolution. The GPI polarized intensity images unambiguously con?rm the presence of a gap in the radial surface brightness distribution of the inner disk. The gap is centered near 23 AU, with a width of 5 AU and a depth of 50%. In the context of recent simulations of giant planet formation in gaseous, dusty disks orbiting pre-main sequence stars, these results indicate that at least one young planet with a mass 0.2 M_J could be present in the TW Hya disk at an orbital semi-major axis similar to that of Uranus. If this (proto)planet is actively accreting gas from the disk, it may be readily detectable by GPI or a similarly sensitive, high-resolution infrared imaging system.

TW Hydrae's Protoplanetary Disk has a "Puffed up" Inner Rim

The Effects of Self-Shadowing by a Puffed up Inner Rim in Scattered Light Images of Protoplanetary Disks

Author:

Dong

Abstract:

We explore whether protoplanetary disks with self-shadowing from puffed up inner rims exhibit observable features in scattered light images. We use both self-consistent hydrostatic equilibrium calculations and parameterized models to produce the vertically puffed up inner rims. We find that, in general, the transition between the shadowed and flared regions occurs in a smooth manner over a broad radius range, and no sudden jump exists at the outer edge of the shadow in either the disk temperature or density structures. As a result, a puffed up rim cannot create sharp ring/arc/spiral-arm-like features in the outer disk as have been detected in recent direct NIR imaging of disks. On the other hand, if the puffed up rim has a sharp edge in the vertical direction, the shadowing effect can produce a distinct 3-stage broken power law in the radial intensity profile of the scattered light, with 2 steep surface brightness radial profiles in the inner and outer disk joined by a shallow transition region around the shadow edge. These types of scattered light profiles may have already been observed, such as in the recent Subaru direct imaging of the TW Hydrae system.

How Dust Collects into Rings in Protoplanetary Disks

Toroidal vortices and the conglomeration of dust into rings in protoplanetary discs

Authors:

Loren-Aguilar et al

Abstract:

We identify a new hydrodynamical instability in protoplanetary discs that may arise due to variations in the dust-to-gas ratio and may lead to concentration of dust grains within a disc. The instability can arise due to dust settling, which produces a vertical compositional entropy gradient. The entropy gradient drives a baroclinic instability that is capable of creating toroidal gas vortices that gather dust into rings. Such dust rings are potentially observable via continuum emission of the dust or scattered light. Indeed, this instability may offer an explanation for the rings recently observed in the discs around the young stars HL Tau and TW Hya that does not rely on clearing by protoplanets. The instability may also have wider ramifications, potentially aiding dust agglomeration, altering the radial migration of larger planetesimals, and modifying angular momentum transport within a disc.

HNC in Protoplanetary Disks

HNC in Protoplanetary Disks

Authors:

Graninger et al

Abstract:

The distributions and abundances of small organics in protoplanetary disks are potentially powerful probes of disk physics and chemistry. HNC is a common probe of dense interstellar regions and the target of this study. We use the Submillimeter Array (SMA) to observe HNC 3--2 towards the protoplanetary disks around the T Tauri star TW Hya and the Herbig Ae star HD 163296. HNC is detected toward both disks, constituting the first spatially resolved observations of HNC in disks. We also present SMA observations of HCN 3--2, and IRAM 30m observations of HCN and HNC 1--0 toward HD 163296. The disk-averaged HNC/HCN emission ratio is 0.1--0.2 toward both disks. Toward TW Hya, the HNC emission is confined to a ring. The varying HNC abundance in the TW Hya disk demonstrates that HNC chemistry is strongly linked to the disk physical structure. In particular, the inner rim of the HNC ring can be explained by efficient destruction of HNC at elevated temperatures, similar to what is observed in the ISM. To realize the full potential of HNC as a disk tracer requires, however, a combination of high SNR spatially resolved observations of HNC and HCN, and disk specific HNC chemical modeling.

Volatile Depletion in the TW Hydrae Disk

Volatile depletion in the TW Hydrae disk atmosphere

Authors:

Du et al

Abstract:

An abundance decrease in carbon- and oxygen-bearing species relative to dust has been frequently found in planet-forming disks, which can be attributed to an overall reduction of gas mass. However, in the case of TW Hya, the only disk with gas mass measured directly with HD rotational lines, the inferred gas mass (≲0.005 solar mass) is significantly below the directly measured value (≳0.05 solar mass). We show that this apparent conflict can be resolved if the elemental abundances of carbon and oxygen are reduced in the upper layers of the outer disk but are normal elsewhere (except for a possible enhancement of their abundances in the inner disk). The implication is that in the outer disk, the main reservoir of the volatiles (CO, water, ...) resides close to the midplane, locked up inside solid bodies that are too heavy to be transported back to the atmosphere by turbulence. An enhancement in the carbon and oxygen abundances in the inner disk can be caused by inward migration of these solid bodies. This is consistent with estimates based on previous models of dust grain dynamics. Indirect measurements of the disk gas mass and disk structure from species such as CO will thus be intertwined with the evolution of dust grains, and possibly also with the formation of planetesimals.

Detection of N2H+ Ring Around TW Hyadrae

Analytical Formulas of Molecular Ion Abundances and N2H+ Ring in Protoplanetary Disks

Authors:

Aikawa et al

Abstract:

We investigate the chemistry of ion molecules in protoplanetary disks, motivated by the detection of N2H+ ring around TW Hya. While the ring inner radius coincides with the CO snow line, it is not apparent why N2H+ is abundant outside the CO snow line in spite of the similar sublimation temperatures of CO and N2. Using the full gas-grain network model, we reproduced the N2H+ ring in a disk model with millimeter grains. The chemical conversion of CO and N2 to less volatile species (sink effect hereinafter) is found to affect the N2H+ distribution. Since the efficiency of the sink depends on various parameters such as activation barriers of grain surface reactions, which are not well constrained, we also constructed the no-sink model; the total (gas and ice) CO and N2 abundances are set constant, and their gaseous abundances are given by the balance between adsorption and desorption. Abundances of molecular ions in the no-sink model are calculated by analytical formulas, which are derived by analyzing the full-network model. The N2H+ ring is reproduced by the no-sink model, as well. The 2D (R-Z) distribution of N2H+, however, is different among the full-network model and no-sink model. The column density of N2H+ in the no-sink model depends sensitively on the desorption rate of CO and N2, and the flux of cosmic ray. We also found that N2H+ abundance can peak at the temperature slightly below the CO sublimation, even if the desorption energies of CO and N2 are the same.